Upload
lynhu
View
224
Download
2
Embed Size (px)
Citation preview
Physiological Responses to Shifting
Bargaining Power: Micro-Foundations of
Commitment Problems1
Dustin Tingley2 Jooa Julia Lee3 Jonathan Renshon4
This draft: September 28, 2014
1We are especially grateful to Ariya Hagh, and the team at the Harvard Decision Science Lab-
oratory for facilitating this research, including Judith Ezike, Dan Zangri, Nicole Ludmir, Gabe
Mansur, Roseanne McManus, Jeanie Nguyen, Jakob Schneider, Phil Esterman, Claire Tan, Will
Boning, Carolyn Killea, Amee Xu, Jack Schultz, Sarah Sussman and Mark Edington. Tingley
thanks Harvard’s Weatherhead Center for International Affairs and Institute for Quantitative
Social Science for financial support. We thank Josh Kertzer, Rose McDermott, Paul Poast,
Alex Peysakhovich, Yunkyu Sohn, Jessica Weeks, and the UCSD Behavioral International Rela-
tions workshop organizers, especially David Victor, for their thoughtful comments on previous
versions of this paper.2Government Department, Harvard University, Cambridge, MA 02138. Email: dting-
[email protected], URL: scholar.harvard.edu/dtingley3PhD Candidate, Harvard Kennedy School. Email: [email protected], URL:
http://scholar.harvard.edu/jooajulialee4Assistant Professor, Department of Political Science, University of Wisconsin-Madison.
Email: [email protected], URL: http://jonathanrenshon.net
Abstract
Commitment problems are often regarded as one of the most important, and common,
causes of international conflict. IR work on the subject suggests that, at the micro-
level, shifting bargaining power can generate an incentive to reject offers, and thus lead
to a costly conflict that destroys resources. Despite this, there is a noticeable gap in
our understanding of how commitment problems change individual behavior in actual
bargaining. We use a novel experimental protocol to study how individuals react to
changes in bargaining power in a game where bargaining power is operationalized as
the probability of winning all the resources. We use a psycho-physiological measure–
skin conductance–in order to assess individuals’ reactions to bargaining. We find that i)
people are more likely to reject offers when they expect the opponent’s bargaining power
to increase (and hence support for a key pillar in IR theory). We also find, only in the
presence of a large shift in power: ii) higher (i.e., better) offers lead to less arousal, and
iii) higher physiological arousal decreases rejection decisions, perhaps due to an increase
in ‘aversive’ physiological arousal and the resultant difficulties in making “strategically
optimal” decisions. Our novel findings suggest that when individuals face large power
shifts, arousal may allow more intuitive decision-making and less backward induction.
This suggests that under certain circumstances, emotionally-aroused individuals are less
prone to commitment problems.
Given that conflict is costly and destroys resources, why does it occur? More than
any other, it is this foundational question that lies at the heart of the scientific study
of international relations. Given its prominence, scores of explanations have been posed
over the years. One of the most promising class of theories are rationalist accounts of
wars, which frequently turn on the presence of a commitment problem or incomplete
information. One mechanism in particular–commitment problems–has had an enormous
influence on the study of international conflict and is often argued to be fundamental to
understanding the breakdown of peace.
Commitment problems arise because shifts in bargaining strength generate incentives
in the future to renege on current commitments. For example, if country i is increasing
in strength relative to country j, country i will find it difficult to “credibly commit” to
not taking advantage of j in the future. With this in mind, the actor whose power is
declining prefers conflict while they have a bargaining advantage rather than a peace-
ful resolution that may leave them open to predation in the future. Due to liquidity
constraints, bargainers cannot prevent their opponents from being concerned about such
adverse shifts. This can lead to conflict despite the fact that it is costly (Fearon, 1995,
2004; Powell, 2006).1 Thus, future changes in bargaining power have been used to explain
preventive war, whereby a declining state chooses to wage a war against the opponent to
take advantage of its bargaining advantages (Fearon, 1995). In this paper we develop and
test for the role of emotions in a stylized decision-making context where there are shifts
in bargaining power over time. In doing so we try to push for a greater integration of
cognitive and affective forces in decision-making.
In recent years the international relations literature has seen a proliferation of work
studying the behavioral foundations of bargaining, drawing heavily on experimental meth-
ods that have human subjects bargaining over resources or responding to hypothetical
1Incomplete information explanations shift the focus to how the anarchic international environment
prevents bargainers from revealing their true valuation for a war outcome (Fearon, 1995). This type of
explanation for conflict has been studied using experimental methods elsewhere (Tingley and Wang, 2010).
The role of commitment problems in other settings is also well developed theoretically and empirically
with observational data (Greif et al., 1994; Simmons, 1994; Simmons and Danner, 2010).
1
crisis simulations (e.g., Tingley, 2011; Butler et al., 2007; Tingley and Walter, 2011b,a;
Tingley and Wang, 2010; Tomz, 2007). For example, Tingley (2011) and McBride and
Skaperdas (2012) examine how changes in the likelihood of future bargaining–the “shadow
of the future”–influence the extent to which commitment problems create conflict. Quek
(2012) presents a design where offers are either allowed to change or not in the future
following shifts in power. There has also been some recent work by international rela-
tions scholars that focus at an even greater depth by examining biological variables in
experimental bargaining environments (McDermott et al., 2007, 2009; Rosen, 2005).
We innovate by tying biological and physiological factors in to a behavioral game
which IR scholars will recognize as approximating the conditions that we typically as-
sociate with commitment problems. And while emotions have become a more common
object of study in IR (see, e.g., Crawford, 2000; Bleiker and Hutchison, 2008; Mercer,
2006, 2010), we present the first work of which we are aware to use emotional arousal (as
measured by physiological arousal) as a window into System I and II (automatic versus
reflective, intuitive versus thoughtful) decision-making.
This is important because intuitive, reflexive reactions play a greater role in IR than
it is perhaps comfortable to acknowledge. While firsthand accounts of crisis situations
often emphasize the emotions of leaders and their impact on the decision process, they
are often overlooked as a factor in IR theory. For every instance in which a leader (such
as JFK on October 16, 1962) “masters his emotions” (or at least is perceived as doing
so, see White, 1992) and makes the transition from the initial emotional reaction to a
more carefully considered strategic plan, there are others in which the initial reaction
dominates, such as in Roosevelt’s “emotional reaction” to the Munich Crisis (Farnham,
1992, 229). We refrain from value judgments concerning automatic versus deliberative
processing, as both can be useful given the proper context (Gigerenzer, 2007; Gigerenzer
and Gaissmaier, 2011), but simply note that understanding how they interact with one
another in the context of bargaining over resources is likely to be helpful in broadening
our understanding of international relations and conflict decision-making.
Drawing on a body of research that has identified a critical link between emotionally-
2
activated processes and intuitive decision-making (Epstein et al., 1996; Dane and Pratt,
2007), we investigate both affective and cognitive mechanisms that drive individual be-
havior in bargaining. Put more succinctly: while Welch (2003) argues that emotion can
be a “barrier to good judgment” in foreign policy, we provide evidence on the specific
mechanism by which emotions and physiological arousal tamper with our ability to make
strategically optimal decisions. By closely tracking the level of emotional arousal, we also
indirectly measure the extent to which subjects engage in intuitive (versus deliberative)
decision-making. This is accomplished via the measurement of electrodermal activities, a
physiological measure of arousal in the autonomic nervous system, which we describe in
more detail below. This allows us to measure participants’ sympathetic nervous system
activation free from any potentially disruptive social-masking or impression-management
effects and in a more direct manner than survey-based measures of emotion.
Using this novel method, we ask two broad questions in this paper. First, how does
the size of the power shift (large or small) affect how individual decision makers respond?
Second, what is the physiological mechanism that governs the reaction of individuals to
offers when a power shift is imminent? More specifically, when do offers trigger a certain
type of processing style, one that is intuitive and affect-laden, and what impact does this
have on bargaining outcomes? In order to examine these questions, we extend a recently-
developed experimental protocol (Tingley, 2011), that allows us to measure the impact of
shifting power – large and small power shifts, operationalized by the extent to which the
power each player holds differs –in a two-stage bargaining game. Our interest here is in
players’ decisions when confronted with conditions of shifting power; do they choose war
in the first round, or accept their opponents’ offers and play the second round under less
favorable conditions? Importantly, while war is typically seen as irrational because, ex
post, it makes both parties worse off, with shifting power, our model demonstrates that
rejecting offers (choosing war) is strategically optimal when the balance of power is about
to shift in your opponent’s favor.
We find that larger power shifts do in fact lead to higher probabilities of choosing
war (rejecting offers) in the first round; individuals are “taking their chances” before the
3
power balance turns against them. This fits very well with the standard explanations of
preventive military action in which declining powers prefer to take a gamble now rather
than face a steep decline relative to their adversaries. However, controlling for offer size,
we find that increased emotional arousal (higher skin conductance) led to a lower level of
offer rejection in the large power shift condition, but not the small power shift condition.
We interpret this finding in light of the dual-process model of cognition, which suggests
that what we call “aversive arousal” is tampering with the ability of those bargaining
to act in a strategically-optimal manner. This particular finding suggests that emotional
arousal does not necessarily lead to less optimal, inefficient outcomes, but may actually
run counter to decisions to engage in costly conflict. We also run a follow up experiment
where we allow for large shifts in power, but no changes in offer from the first period to
the next, such as what an institutional solution to commitment problems might do. Here,
as we predict, the role of arousal is also eliminated just as in the condition with small
shifts in power.
The paper is organized as follows. We provide a model of commitment problems in
Section 1.1 and then follow that in Section 2 with an explanation of how emotions are
likely to enter into the decision process, both in IR as well as in the context of bargaining
models and games. Section 3 outlines the design of the experiment, while Section 4
outlines our main findings related to physiological arousal and bargaining, as well as a
follow-up experiment in Section 5 that used an alternative experimental manipulation.
Section 6 concludes.
1 Bargaining, Shifting Power and Physiological Arousal
Commitment problems have gained traction as one of the more powerful explanations
of conflict in the study of international relations. They are part of a body of literature
that identify “mechanisms” that lead to conflict. In the sense the term is most often
employed, “mechanisms” denote a set of utility maximization assumptions and a partic-
ular bargaining environment that result in particular predictions about when conflict will
occur. However, they do not offer any guidance on how individual decision-makers might
4
be affected by these dynamics, nor how they are likely to respond. This is a critical next
step in understanding the dynamics of international conflict, just as study of micro-level
behaviors has furthered the study of strategic choice in other domains (Ostrom, 1998;
Camerer, 2011). In this section, we first present the basic intuitions of a model of com-
mitment problem dynamics, and then highlight how these dynamics might operate at the
individual level.
1.1 A Model of Commitment Problems
The intuition behind this type of bargaining model of conflict is as follows2: There are
two decision makers from competing countries (Antigua and Brazil, or more generally,
A and B) and two periods (present and future). In each period, Antigua makes Brazil
an offer to divide resource that has a value of 1. In the first period, Antigua makes a
demand to Brazil. If that demand is accepted, then the game continues in the second
period (the future) and Antigua again makes a demand. As before, if Brazil accepts the
demand, the resource is divided in the specified manner and the game ends. If in the
first period, Brazil rejects the demand, then both players/countries play a war lottery, in
which one player wins the resource (with probability p) but both players pay some costs
(since war destroys some of the value of the stake). If a “war” is fought in the first period,
then the winner automatically gets the whole resource in Period 2 as well (the future). If
Antigua’s offer is rejected in the second round, then (as before) both states play a war
lottery to determine who wins the resource (less the costs of the war).
The key question in this model is: what will make Brazil reject the offer (i.e., choose
war) in the first period? As noted by many IR scholars (rationalist and non-rationalist
alike), shifting balances of power (and in particular, the expectation of shifting power)
are likely to change both states’ calculations. If Antigua’s power is increasing relative to
Brazil’s, then a commitment problem dynamic exists, since there is no way for Antigua
to credibly commit to not taking advantage of Brazil in Period 2 (by demanding most
or all of the resource). We can operationalize this shifting power dynamic by increasing
the probability of Antigua’s victory in Period 2. If this dynamic holds, one would expect
2We provide a more detailed exposition of this model in Appendix A.
5
Brazil to make the strategical optimal decision to choose war (i.e., reject Antigua’s offer)
in the first period, since doing so allows it to take its chances with a war lottery before
the power dynamic has shifted in favor of its adversary. This is the logic of preventive
war.
If, on the other hand, both states expect the power balance to remain stable across
periods, we wouldn’t expect the dilemma posed by commitment problems to be as severe,
and hence expect to see fewer instances of preventive war. In the studies described in
this paper, we “switch on” the commitment problem dynamic by allowing A’s probability
of winning to increase over the two periods of the game. We also present a follow up
experiment inspired by Quek (2012) which allows for a large shift in power, but no ability
to change offers in the second period; that is, A actually can credibly commit to not
taking advantage of its adversary in the future.
Notice that this model does not offer mechanisms particular to the human decision-
makers that are ultimately of interest. To see this clearly, consider the contrast between
the pioneering work in behavioral economics that seeks to understand the physiological
bases of strategic choice versus simply relying on the abstract choice models themselves
(for brief review see Camerer 2003a, chapter 2). What physiological mechanisms operate
when people face situations with commitment problems? Do individuals calmly calculate
the prospects for conflict and respond accordingly, or do automatic, emotional processes
become involved?
In the following section, we attempt to complement the model describe above and
remedy some of the issues common to the study of these processes in IR. While emotions,
stress and physiological arousal have long been implicated in narratives of foreign policy
decision-making, we provide causal evidence on their role through the use of experimen-
tal methods. And while many schools of IR ignore the individual entirely, we bring the
individual back into rationalist theories of war. Parallel with other literatures in political
science using a novel method in psychophysiology (e.g., Oxley et al., 2008), we study the
physiological bases of bargaining in situations where commitment problems are present.
To that end, we set up our experiments to test not only key propositions well-known in
6
the commitment problem literature (e.g., the impact of power shifts on commitment prob-
lems), but additional individual-level theories that describe the physiological mechanisms
through which those power shifts exert their influence.
2 Emotions in Conflict Decision-Making
Our research design, described in the next section, allows us to examine the effects of
physiological arousal within the specific context of bargaining under the shadow of shift-
ing power. But the inspiration for the study is far broader. In fact, the question of
whether and how emotions and intuition affect political decision-making is a long-standing
puzzle in IR. Because of the obvious and inherent difficulties in “proving” that physio-
logical arousal, emotions or intuition can explain behavior in any given circumstance,
what we are left with is mostly speculation. Nevertheless, the speculation is intriguing,
as emotions are implicated strongly in a wide variety of contexts, from shifting leaders’
reference points (Farnham, 1994) and helping them interpret what would otherwise be
overwhelming amounts of information (Mercer, 2013) to general theories of international
war (Thayer, 2004; Cashman, 2013) and crises (Gordon and Arian, 2001; Winter, 2007).
Our goal in this paper is to provide micro-foundations that shed light on this elusive
phenomenon, but before we do so, we present several illustrative examples of what ways
in which emotions and intuition are commonly implicated in international politics.
One class of decisions in which emotions, intuition and arousal are commonly impli-
cated are those in which leaders react to new and surprising information. For example,
upon learning that the Soviets had installed missiles in Cuba, President Kennedy (quoted
in Allison, 1969, 713) famously exclaimed, “He can’t do that to me!” Less better known
is the quote of his brother Robert, “Oh shit! Shit! Shit! Those sons of bitches Russians”
(quoted in Stern, 2005, 22). More recently, virtually all members of the Bush administra-
tion had what were described as emotional reactions upon hearing of the terrorist attacks
on 9/11. President Bush’s was perhaps the most obvious, as he cried on television in
the Oval Office and “choked up” in Cabinet meetings in the days following the attack
(Woodward, 2002).
7
But surprise is not a necessary precondition for emotions to play a role in international
conflict. In other cases, the stress of a long, drawn-out conflict can wear leaders down.
During the Iranian Hostage crisis, President Carter went through several emotional stages,
from “elation” upon learning that Iranian President Banisdar had offered a deal to return
the hostages, to bitterness and anger when the deal failed to materialize (Harris, 2004). In
one of the interesting aspects of the historiography of the crisis, the dispute between Carter
and Cyrus Vance (who resigned following Carter’s decision) devolved for many years into
a war where each side attempted to pin the other as “emotionally overwrought” (see
discussion in Glad, 1989). Emotions have also been frequently invoked in explaining Israeli
decision-making during the Yom Kippur War. During those few days in 1973, Moshe
Dayan appeared to have an emotional breakdown, “frequently” repeating the phrase “the
‘Third Temple’ is under threat” (implying that the existence of Israel was threatened) and
crying while exclaiming that “everything was lost” (Bar-Joseph and McDermott, 2008).
Even wars and crises are not necessary for emotions to be implicated in critical ways
in explaining international politics. The feeling of injustice, for example, can trigger
powerful emotions, as traced by Welch (1995) through many long-standing rivalries in
world politics. And to return to the Cuban Missile Crisis, but approach it from a different
perspective, emotions have been strongly implicated on the Soviet side. In fact, all the
recent evidence we have points to a strong role of emotion and intuition in Khrushchev’s
decision to send missiles to Cuba in the first place. Taubman (2003) paints him as
a resentful figure, convinced that U.S. nuclear policy was “particularly arrogant” and
quoted as saying that “It’s high time their long arms were cut shorter.” Lebow (1990,
490), too, describes Khrushchev as “acting out of anger” in his decision to install missiles
in Cuba.
The above paragraphs provide a brief illustration of the ways in which emotions are
implicated in international relations, but three key issues are readily apparent. First,
in the literature in which emotions are explicitly called upon to help explain outcomes,
little evidence is provided for any causal role. Leaders may indeed have appeared to
have emotional breakdowns (as was the case for Moshe Dayan in 1973), but even if we
8
grant that basic fact (which also requires a leap of faith given the difficulty in imputing
emotions to others, incentives to misrepresent, etc.), it is far more difficult to argue
that this caused any particular even to occur. While statesmen typically overestimate
the influence of individuals, political scientists are justifiably skeptical that individual
reactions are anything more than noise distracting us from the larger, structural forces at
work. For example, even if Khrushchev had an emotional reaction to the strategic balance
in 1962 and shortly thereafter ordered the missiles delivered to Cuba, it is difficult to argue
that taking the emotion out of the situation would have changed anything; after all, the
balance of capabilities would still have been in the U.S.’s favor and Khrushchev had long
seen ICBMs as a shortcut to strategic parity.
But while the literature that draws upon emotions and intuition in decision-making
often relies upon speculation in making causal arguments, entire other schools of work
have left the individual–including their physiological reactions, emotions and intuition–out
of the picture entirely. Rationalist work is a primary example of this pattern. Ultimately,
rationalist explanations for international conflict must stand up to empirical testing, and
experimental methods provide one promising avenue for testing out the mechanisms drawn
from formal models (McDermott, 2002). In doing so, however, it would be a mistake to
waste the opportunity to derive additional implications at the individual level to test in
combination with the insights derived from models. These additional insights can help
provide additional information about the mechanisms through which larger, impersonal
forces work.
Finally, there is little general understanding of effects of emotions. The conventional
wisdom for many years was a version of emotion that was opposed to reason. Thankfully,
this straw-man has largely been put to rest (e.g., in McDermott, 2004). However, the
realization that emotions are neither inherently beneficial nor detrimental in their impli-
cations for decision-making has exposed a large gap in our collective knowledge. We lack
well-established theories and empirical foundations for understanding how emotions affect
outcomes of interest to international relations scholars (see Renshon and Lerner 2012).
This has left us largely in the dark on crucial questions such as whether and how emotions
9
might be incorporated into traditional theories of international relations, as well as under
what circumstances this is likely to have positive or negative consequences. In the next
section, we show how dual-process theory provides us leverage in examine the effects of
emotions in our bargaining experiment.
2.1 Dual Process Theory: A Window into Emotions in IR
To help address some of these shortcomings with respect to the study of emotions in
IR, we turn to dual-process theory. The idea that individuals’ cognitive processing can
be described as two parallel systems can be traced back at least as far as James (1890)
and Freud (1900), who described a dual system of “rational” and “irrational’ thinking.3
We follow Evans and Over (1996) in conceptualizing two parallel cognitive processes,
System I and System II (see also Kahneman 2011). The former is based upon previous
experiences and beliefs. It is characterized as “implicit, associative, fast and highly robust
(Gilinsky and Judd, 1994).” Perhaps most importantly, it is automatic: it occurs all the
time without our awareness. In contrast, System II is slow, controllable and explicit (in
the sense that one is consciously engaging in the act of analytical reasoning).
Emotions tend to be more closely associated with System I processing. That is, indi-
viduals seem to feel an emotion, and then construct a rational edifice around that feeling
in order to explain why they are angry/sad/happy/etc. (Haidt, 2001). In some cases,
emotions are explicitly linked to System I processing (Epstein, 1994; Hassin et al., 2004;
Evans, 2008), while in others, evidence is provided based on the parts of the brain involved
in both emotion-processing and System I processes (Lieberman, 2003). That emotions
are so strongly associated with System I processing is of immense help empirically, as we
are on firmer ground in measuring the generalized physiological arousal associated with
System I than we are in targeting specific emotions (Myers and Tingley, 2012).
The question we pose in this paper is: how do these different processing styles affect
bargaining? In non-political contexts, there is a substantial amount of research on the
benefits of System I processing (Plessner et al., 2007; Gigerenzer, 2007; Gigerenzer and
3For more detailed history of dual-process frameworks, see Osman (2004). For an overview of some of
the controversy associated with the framework, see Gigerenzer and Regier (1996).
10
Gaissmaier, 2011). In IR contexts, however, it is far more rare for scholars to make
the argument that the affect-laden System I processing is beneficial in terms of avoiding
conflict. One notable exception is Blight (1992), who argued that the fear experienced by
U.S. leaders at the height of the Cuban Missile Crisis was adaptive in aiding their careful
navigation of the crisis. A more theoretical treatment offered by McDermott (2004) makes
the important point that emotional processing is not definitionally opposed to rationality,
and in fact can be a key component of making strategically optimal decisions. However, an
underlying assumption of much of IR (and social science more generally) is that “logical,
rational calculation forms the basis of sound decisions” (McDermott, 2004, 691). Because
there is so little empirical research on this question, however, below we explain the ways
in which processing styles may affect political decision-making, and then draw hypotheses
from related behavioral work on bargaining.
The first, and most obvious way that processing style might have an affect on decision-
making is that political leaders might act on their initial, emotional reaction to a situation.
In high-pressure, time sensitive crises, there may simply not be very much time for re-
flection or deliberation. Emblematic of this is the “explosive reaction” of Kissinger and
Nixon to Syrian intervention in Jordan in 1970 (Dowty, 1984, 153).4 And in general, the
time pressure associated with intense crises seems to exacerbate the influence of emotions
(Crawford, 2000).
However, even if there is abundant time to reassess the situation and deliberate
over options, the initial automatic response may quite important. What Holsti (1970)
termed the “definition of the situation” and what psychologists refer to as “framing”
may exert tremendous influence over how the situation is handled even after reflection
(Levy, 1996; Mintz and Redd, 2003). The reason for this is two-fold, as even in longer
time frames, it is often the case that some options are discarded immediately (DeRouen
and Sprecher, 2004; Mintz, 2004), so that initial reactions may have far-reaching effects
even if the remaining options are considered carefully. Further, ways of understanding
4Nixon later recalled “they’re testing us...The testing was continuing, moving a few notches higher
each time. We would have to decide what to do very soon, or it might be too late to do anything (Dowty,
1984, 153).”
11
what is happening are often framed around analogies and metaphors that are chosen
instinctively (Khong, 1992; Shimko, 1994). If we return to the well-trod territory of the
Cuban Missile Crisis, one notices that even though Kennedy is often congratulated by
scholars for engaging in a thorough, deliberative decision-making process (following his
initial, emotional reaction), the basic premises of the crisis –particularly, that it was a
crisis– were settled on instinctively and never once challenged.5
As is evident, there is substantial anecdotal evidence to suggest that processing style
and emotions may impact conflict decision-making, but very little in the way of system-
atic evidence. Below, we turn to the behavioral literature on experimental bargaining to
provide some insight into how the dual-process model model may shed light on bargaining
decisions.
2.1.1 Micro-Level Studies of Bargain, Arousal and Intuitive Judgments
Behavioral investigations of bargaining have typically focused on the “ultimatum game
(UG).” In the UG, one person proposes a division of a resource to a second person. If
the second person accepts, then the resources is divided in the agreed upon manner; if
the responder rejects the offer then neither person gets anything. Thus, the responder
is always better off accepting as long as the offer > 0. Or, in other words, the standard
equilibrium analysis of the UG is that there should never be rejected offers, even when
they are arbitrarily low.
Initial evidence from the UG suggests that emotions play a powerful role, despite
assumptions that strategic thinking –“cold calculation” –should dominate. Blount (1995)
used a variant of the UG to show that unfair offers by the proposers can evoke anger in
responders when the allocation was intentional, but not when it was randomly generated.
Pillutla and Murnighan (1996) also found that responders who have full information about
the total endowment available to the proposer rejected more than those who did not have
any information. In other words, emotions like anger can be triggered under certain
5And, of course, the question of whether Kennedy actually “kept his emotions in check” is not yet
settled. See Lebow (1990).
12
circumstances, but there is a logic to how this process occurs; a “bad” offer by itself is
not enough to trigger anger. There must be some knowledge of the motivation behind
the allocation (to know whether there was an intent to be provocative or threatening) or
a larger understanding of the amount available to the proposer (to know if the allocation
was fair).
Advances in neurophysiology have supported these findings. Sanfey et al. (2003) used
functional neuroimaging to record the brain activity of responders who were faced with
different distribution of allocations. They observed that low offers resulted in a higher
level of activation in bilateral anterior insula, an area of the brain associated with negative
emotional arousal. The intensity of activation in this region was significantly correlated
with the extent to which the offers were low, and thus led to a higher probability of re-
jection (which is the non-equilibrium response). Van’t Wout et al. (2006) and Civai et al.
(2010) similarly observed increased electrodermal activity (skin conductance), which is
associated with insula activity, when responders received unfair offers. The relationship
between offer size, physiological arousal, and probability of rejection was consistent across
these studies. Drawing from this research, we hypothesize that lower offers in our bar-
gaining game (despite its difference set-up from the traditional UG) should trigger greater
physiological arousal than high offers. p However, the impact of physiological arousal on
the act of rejection is less clear in the current study, which differs from the traditional
UG in significant ways. In previous UG studies higher offers led to less arousal, and lower
arousal levels led to less rejections. Hence lower arousal is associated with equilibrium
predictions.
In contrast, our game involves two stages, in contrast to the traditional ultimatum
game set-up in which actors face a “one-shot” choice. Simply put, the game we investigate
is dramatically more familiar to international relations scholars than the ultimatum game.
Unlike the standard ultimatum game (in which rejection leads to both players receiving
0), the responder’s rejection leads to a gamble where one of the players receives all of
the resources. This mimics the observation that war (rejected offers) does not destroy all
resources (as in the ultimatum game) and that one country can often prevail. Furthermore,
13
as we describe next, the game has a repeated component that captures shifts in power,
which is absent from the ultimatum game. In the declining power condition, the responder
wins all of the resources with a probability of .7 in Round 1 and .3 in Round 2 (the
probabilities are reversed for the proposer, who wins with a probability of .3 in Round 1
and .7 in Round 2). In the control condition, the probability of winning stays at roughly
.5 for both rounds (responder wins with probability .55 in Round 1 and .45 in Round 2).
In other words, in the declining power condition, both parties know that the proposer will
be gaining power in the second round, and the responder will be losing power. Given this
knowledge, the rational course of action for the responder is to reject any initial offer and
take their chances in a costly lottery in Round 1, when they still enjoy a power advantage.
Responders in the declining power condition should, if motivated by self-interest and using
rational tools of backwards induction, reject all offers, even high ones.
Given these differences to the UG, what role should we expect arousal to play? Phys-
iological arousal may tamper with a more deliberate, cognitive processes of strategic
thinking. According to the dual-process framework (Kahneman, 2003; Sloman, 1996),
decisions are made by the interaction of intuitive and reflective processes. Physiological
arousal may give rise to more intuitive decision-making, which is associated with fast,
automatic, and effortless processing (Lambourne and Tomporowski, 2010). On the other
hand, the absence of physiological arousal would allow more reflective decision-making,
which is associated with slow, effortful, and deliberate processing.6 Deliberative process-
ing has been associated with greater equilibrium play, which in the shifting power condi-
tion would mean higher rejection rates. Hence physiological arousal may not necessarily
lead to high rejection rates in all circumstances.
To see this explicitly, in our bargaining game, the presence of large power shifts implies
that the responder’s dominant strategy is reject any offers in Round 1. Put simply, the
responder’s chances in Round 1 will always be better than in Round 2 under conditions
of declining power. Choosing this strategy requires the ability to look ahead and induct
6A good example of both intuitive and reflective processes in the ultimatum game can be found in
the work of Grimm and Mengel (2011), who found that time delays allowed more deliberation, and thus
decreased rejection rates.
14
backwards, but as Camerer (2003b) argues, people’s ability to engage in such strategic,
iterated thinking is limited. We thus predicted that responders with lower physiological
arousal should be more likely to reject Round 1 offers since their ability to engage in
reflective processing would not be impaired (compared to those with higher physiological
arousal). On the other hand, we predict that high physiological arousal should interfere
with this process of strategic thinking, which requires sufficient cognitive resources to
think about the implications of the shifting power dynamics that they will face in Round
2.
An alternative view could be that, again controlling for offer size, the effect of phys-
iological arousal on rejection decisions is positive. This would imply that individuals
with high arousal will be more likely to reject offers. This might occur because they are
tempted to reject based on spite, or some other fairness based consideration. There is
some preliminary evidence that physiological arousal is associated with the destruction
of shared resources in bargaining games (Ben-Shakhar et al., 2007), though the setup of
these games is noticeably different than the current paper (in the current work, rejection is
actually the strategically optimal choice, so to the extent that emotionally-aroused players
reject in our game, they would be doing the “right thing for the wrong reasons”). In this
story, the cognitive side (low arousal) of the dual systems approach might suggest lower
rejection rates because higher offers might be considered signals of intents to reciprocate.
We feel this story has less of a theoretical foundation, but our experiment can nonetheless
provide a test.
Taken together, we hypothesize that the size of offers will predict rejection rates,
and this relationship will be explained by the responder’s physiological arousal, measured
by skin conductance. More specifically, we expect that skin conductance reactivity will
mediate the relationship between high offers and higher rejection rates.
2.2 Hypotheses
Based on the previous discussion we have several hypotheses. First is the basic hypothesis
from the game theoretic model that when there is a larger power shift then we should see
more rejected offers. We operationalize this by investigating whether for any given offer
15
there will be a higher probability it is rejected when there is a large power shift (Tingley,
2011).
Hypothesis 1: When there is a large power shift, for any proposed division (offer size),
the probability of rejection will be higher.
The second hypothesis concerns the effect of offers on skin conductance. Following
previous work, we expect that low offers will lead to higher levels of physiological arousal,
but only in the presence of a large power shift. This follows from the logic that the
presence of a shifting power dynamic is likely to make lower offers more psychologically
salient, and aversive, than in conditions where conditions remain stable across periods. In
other words, the proposer’s lower offer in Round 1 would be interpreted as more threat-
ening and challenging to the responder, knowing that the proposer will be able to take
advantage of increased bargaining power in the next round. On the other hand, small
shifts may not activate the same aversive physiological responses against the low offer, as
the responder is not as likely to be concerned with future bargaining, but may be more
concerned with the cost of rejection.
Hypothesis 2: When there is a large power shift, low offers should be associated with
higher skin conductance. This relationship is likely to be attenuated or muted under
conditions in which power conditions remain stable across periods.
Our final hypothesis concerns the influence of arousal on rejection decisions, con-
trolling for offer size. In other words, what is the effect of offers on rejection rates that
are transmitted though changes in arousal, when the players are expecting a large power
shift? Following the dual process framework, we predict that the effect of low offers on
rejection rates that is transmitted through though greater physiological arousal will be
positive; that is, it will lower rejection rates. The effect of high offers will lead to higher
rejection rates, mediated by lower levels of physiological arousal.
16
Hypothesis 3: When there is a large power shift, the effect of offers on rejection rates
that is mediated by heightened physiological arousal will be positive. This mediation
effect will be absent in the low power shift condition.
3 Experimental Design
3.1 Lab Procedure
We conducted this study at the Harvard Decision Science Laboratory using 121 male
undergraduate students (agemean = 22) who signed up. Each session began with subjects
being hooked up to the physiological sensors described below. Then subjects read a set of
instructions that explained the basic rules of the bargaining game using neutral language.
A condition- and hypothesis-blind experimenter also gave the instructions verbally and
then answered any questions. After obtaining a baseline recording of the skin conductance,
the bargaining games began, described in Section 3.2.7 Each subject was randomly paired
with another subject and randomly assigned a position as described below in more detail.
Subjects then played the bargaining game sequentially. At each stage of the game a
unique signal was sent to the physiological recording device to indicate different outcomes
in the game, such as an offer being received, through parallel port communication. This
enables us to precisely match a given subject’s physiological response at a given time
to specific actions in the bargaining game. After playing 10 matches, subjects took a
short post-experiment questionnaire that included several policy questions and personality
inventories. Subjects were paid privately based on one randomly selected match. On
average, subjects earned $20 for approximately 50 minutes of time.
Before proceeding, we offer a disclaimer for those readers uncomfortable with the use
7Subjects watched a video (2m49s) featuring relaxing images of beaches and palm trees with calm
music in the background to measure the physiological responses at the baseline. This particular stimulus
and protocol has been used in previous research, and by the authors in Renshon et al. (2014).
17
of either lab experiments more generally or the specific use of samples of undergraduates.8
On the latter question, we note that while elite experiments are becoming somewhat
more common (Hafner-Burton et al., 2012, 2013; Renshon, 2015), they are logistically
implausible in many circumstances. Moreover, such experiments are only necessary and
desirable under a very specific set of circumstances. The primary rationale for such
experiments must be that leaders/elites are hypothesized to differ systematically from
convenience samples on dimensions that are theoretically relevant to the study at hand.
In the context of the current study, one would have to argue that, for example, elites would
be less likely to have emotional responses, which given some of our earlier discussion seems
unlikely. Even then, it may be unwise to use elite samples until convenience samples have
established the plausibility of a particular effect to begin with.
On the former question, concerns tend to cluster around the notion that–even if we
had access to subjects of theoretical interest–there is something artificial about the lab-
oratory which prevents us from generalizing to situations outside the lab. Here, we note
only that there is a long history of laboratory studies being replicated in diverse environ-
ments, using different samples, measures and contexts. This has occurred with aggression
(Anderson and Bushman, 1997), prospect theory (Camerer, 2004), donation experiments
(Benz and Meier, 2008), and more recently in political science as well (Ansolabehere et al.,
1999; Barabas and Jerit, 2010).9
Moreover, the common criticism of IR experiments that the stakes in the real world are
so high that experiments cannot mimic them rests on shaky foundations. In fact, empirical
work on this subject is relatively clear: stakes do not change the dynamic dramatically in
most instances, and to the extent they do, it is the inclusion of moderate stakes (compared
to no financial incentives) that make a difference, not marginally increasing stakes that are
already present in the experiment (see Camerer and Hogarth, 1999; Holt and Laury, 2001;
Hertwig and Ortmann, 2003).10 This is why our study was designed such that subjects’
8For a longer discussion of these issues, see Renshon (2015).9For an excellent discussion, see Levitt and List (2007).
10In fact, the relationship between incentives and performance does not appear to be entirely monotonic
when incentives are the extremely high, suggesting that ratcheting up the stakes is not necessarily an
18
decisions do have real (if small) economic consequences; subjects lose actual money if
they perform poorly, so there are strong incentives to pay attention and try to “win.”11
3.2 Experimental Game and Treatments
In our experiment subjects were anonymously paired with each other and randomly as-
signed to be in position A or B. After the second period each subject was randomly
matched with another subject and played the same 2 period game. Each period of the
game had the same basic structure. In period 1, player A proposes a division of a re-
source of size R = 10, (x1A, x1B = 10 − x1A). Here the subscripts represents the period
and position, so x1B is what player B would get from player A’s first period offer. Player
B decides whether or not to accept the offer. If they reject (i.e., choose a war lottery), the
entire resource is assigned by the computer to player A or B with probability p1 that A
wins the resource and 1− p1 B wins, where the subscript again represents period 1. Both
players also pay a cost cA, cB = 2. Following rejection in the first period, in the second
period the winner of the resource receives R = 10 points automatically. If the first period
offer is accepted, in the second period the same game is played with R = 10 points being
divided and both players stay in the same position (A or B).
The experiment had two treatment conditions that determined how the probability of
gaining the resources shifted from one period to the next. In BigShift p1 = .3 and p2 = .7.
In other words, player A starts out “weaker” in Period 1, but gains a significant amount
of power (i.e., higher probability of winning the costly lottery) such that in Period 2 the
power dynamics have reversed. In this situation, our game-theoretic model predicts that
player B is likely to reject offers in Period 1, since “taking their chances” in a Period 1
gamble is preferable to doing so in Period 2 once a major power shift has occurred. This
is illustrative of the commitment problem dynamics described earlier: player A has no
appreciate fix. See Ariely et al. (2009).11On the other hand, Kahneman and Tversky (1979) recommend large hypothetical gambles over
“contrived gambles for small stakes.” Notice that this solution would be even more unacceptable to those
political scientists worried about external validity than the inclusion of “only” small stakes. This may say
more about our almost religious beliefs concerns the appropriateness of various methods than anything
else.
19
way to credibly commit to not taking advantage of their increased power in the future
and player B thus has strong incentives to fight for the resource while their position is
advantageous.
In our second experimental condition, SmallShift, p1 = .49 and p2 = .51. In both
conditions, the power shifts in the same direction (player A becomes more powerful in the
second period), but in SmallShift the magnitude of the change is negligible and thus un-
likely to be associated with commitment problem dynamics. In this condition, our model
predicts fewer rejected offers and a higher likelihood of a “peaceful” bargaining resolution
as a result of the lack of a commitment problem. In particular, the model predicts that
any offer over 5.3 should always be accepted, whereas in the BigShift condition all offers
should be rejected (see appendix for additional details).
All aspects of the game are common knowledge. Subjects were paid based on one
randomly selected repetition of the experiment and received $1 for every 10 points earned.
3.3 Physiological Data Acquisition
Participants’ skin conductance levels (SCLs) were measured continuously throughout the
experiment. SCL is a reliable indicator of increased attention and arousal, and is asso-
ciated with greater insula activities (for reviews, see Christie, 1981; Sequeira and Roy,
1997). Skin conductance has also been used in similar contexts in past research to in-
vestigate the relationship between actors’ emotions (measured by physiological arousal)
and their decisions (Van’t Wout et al., 2006; Civai et al., 2010). Despite its important
advantages, one potential shortcoming of this measure of physiological arousal is that it
does not allow us to distinguish the valence of general feelings (i.e., positive or negative
feelings). However, given that one’s autonomic nervous system responses precede con-
scious awareness, and are difficult to control consciously (Gardner et al., 2000; Bechara
et al., 1997), we believe that the fluctuation (i.e., reactivity) in skin conductance should
provide valuable information about the extent to which intuitive vs. deliberate processes
are being utilized.
Skin conductance data for all participants was collected through the use of two dis-
posable Biopac (Santa Barbara, CA) electrodes (Model: EL507), which are filled with
20
Biopac Skin Conductance Electrode Isotonic Paste (specially formulated with 0.5% saline
in a neutral base). These electrodes were placed on the palms of the participant’s non-
dominant hand (the thenar and hypothenar eminences). A constant voltage of 0.5 V was
applied between the electrodes. SCL was then checked by research assistants to ensure
proper recordings, and following that participants watched a short video (2m49s) featur-
ing images of beaches and palm tress with calm music. SCL measurements of this time
period were used as “baseline” physiological arousal.
We followed the standard procedure of scoring the skin conductance data; raw mea-
sures were sampled at 1000 Hz, and amplified using a gain of 25µΩ and a low-pass filter
of 5Hz, using a BioNex mainframe and amplifier system, and BioLab 2.4 software (Mind-
ware Technologies, Gahanna, OH). Using Mindware’s software EDA module 3.0, research
assistants who were blind to both the study hypothesis and conditions calculated SCL (in
microsiemens). We then output the scored data into a time series. Finally, in order to
address potential individual differences in variability in skin conductance, our data were
transformed to deviations from the baseline condition (using the average SCLs while the
video was played) and standardized within each participant (see Ben-Shakhar, 1985; Bush
et al., 1993).
Our measure of SCL uses this standardized deviation from baseline score. To do this
our experimental design requires that we extract these standardized scores during the
period where decisions were made. We were able to do this because of the our procedure
of placing tags in the time series via parallel port communication (as discussed above).
Then, we took the average SCL deviation from the time after the offer was made, and
before responders make the decision to accept or reject the offer in the first round. This
average deviation from baseline during this particular phase of the experiment is our key
physiological variable.12
12Our physiological results are robust to using medians instead of means. Any deviations above 3 are
capped at 3 and below -3 is capped at -3, though our results hold not making this common restriction
which was rare in the data.
21
4 Results
We begin with simple descriptive statistics of the average first round offer in both condi-
tions. Figure 1 presents histograms of the amount offered to player B with vertical lines
indicating the average offers in the experimental conditions. Average offers in the BigShift
condition were slightly higher. Furthermore, the variation in offers was also much higher
in the BigShift condition. While the modal offer in both conditions was a 50/50 split,
there were many more offers above and below this point in the SmallShift condition. Next
we move to a discussion of our key hypotheses.13
SmallShift
Offer
Den
sity
0 2 4 6 8 10
0.0
0.1
0.2
0.3
0.4
0.5
0.6
BigShift
Offer
Den
sity
0 2 4 6 8 10
0.00
0.10
0.20
0.30
Figure 1: Histogram of first round offers by power shift condition.
4.1 Do Power Shifts Spur Commitment Problems?
Our results were consistent with Hypothesis 1, that offers are more likely to be rejected
in the BigShift condition. We estimated a probit regression model where the dependent
13Future versions of the paper could also investigate learning effects.
22
variable is whether or not the offer was rejected. The independent variables were the
size of the offer, an indicator for whether the experimental session used the BigShift or
SmallShift condition, and an interaction between the experimental condition and offer
size. Standard errors clustered at the individual level. Using the results of this model, we
then plot the predicted probability of an offer being rejected in Figure 2 using the Zelig
package in R.
Offers below 5 are almost always rejected in both the BigShift and SmallShift condi-
tions. Above an offer size of about 5, offers are more likely to be rejected when there is
a large power shift. That is, for more generous offers, individuals in both conditions are
more likely to accept the offers than less generous offers. However, for any of these more
generous offers they are more likely to be rejected in the BigShift condition.
0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
1.0
Offer
Pro
babi
lity
of R
ejec
tion
median
ci95
ci95
ci95
Big ShiftSmall Shift
Figure 2: Probability offer rejected as a function of offer size and whether power shiftlarge or small.
23
4.2 Do offers affect physiological arousal?
Next we investigate whether offer size affects arousal in the two experimental conditions.
To do this we estimated a simple linear regression model with our measure of arousal as the
dependent variable and offers as the independent variable.14 We found that higher offers
on average lead to lower levels of skin conductance but only in the BigShift condition,
t=-2.19, p<.05). In the SmallShift condition there was no significant relationship between
offers and arousal, t=-.3, n.s. To display the results, Figure 3 plots predicted arousal as
a function of offer size.
This finding suggests that responders in the BigShift condition were more physiolog-
ically reactive to low offers than to high offers, as we predicted. Lower offers made by
the rising power in the first round are perceived as more provocative, and may thus be
interpreted as a challenge, which might have activated more physiological arousal among
the responders. It should also be noted that the relationship between offer size and skin
conductance reactivity was more pronounced in the BigShift condition, as compared to
the SmallShift condition. This finding indicates that the typical outcomes of low offers –
aversive arousal – in the ultimatum game setting may not uniformly apply to our bargain-
ing setting. Due to the repeated nature of the bargaining, the anticipation of the power
shifts significantly moderates the effect of low offers on physiological arousal.
4.3 Do offers affect decisions through psychophysiological arousal?
Finally we turn to the role of physiological arousal in mediating the relationship between
offers and rejection decisions. The mediation effect is the change in the outcome while
holding the treatment condition constant but varying the values of the mediating variable.
Formally, the mediation effect under treatment condition t, δi(t) can be defined at the
individual level as:
δi(t) ≡ Yi(t,Mi(t))− Yi(t,Mi(t′)), (1)
14We also estimated generalized additive models that does not impose a linearity assumption. Results
were nearly identical to the linear model.
24
0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
1.0
Offer
Ave
rage
Ski
n C
ondu
ctan
ce S
core
median
ci90
ci90
ci90
Small Shift
Big Shift
Figure 3: Effect of offer sizes on skin conductance. 90% confidence intervals used forpresentational purposes and robust standard errors.
where Yi(t,Mi(t)) represents the value of the outcome variable under the treatment t. As
discussed elsewhere (Imai et al., 2011) inference about this requires the assumption of
sequential ignorability, where 1) there is no omitted variable that affects the treatment
and outcome and 2) there is no omitted variable that causes both the mediating variable
and outcome variable. In the current design, the offer is not randomized. But it is
implausible that rejection decisions by a different person (player B) could be influenced
by the same confounding variable that influences offer decisions (by Player A).15 The
second assumption is more difficult to deal with and can be approached either through
inclusion of pre-treatment controls, sensitivity analysis, or alternative designs (Imai et al.,
2013). We discuss each below.
We estimate a mediation model based on two parametric models. The first is the
model used in Section 4.2, which regresses arousal on offers. The second model uses
15All interactions were completely anonymous.
25
a probit regression where binary variable indicates whether the offer is rejected (1) or
rejected (0). We also permit an interaction between the treatment and mediator in the
outcome model, allowing for δi(t) 6= δi(t′). This could occur if the postulated arousal
process only occurs when offers are larger, rather than small. We estimate these models
separately for the two experimental conditions (BigShift and SmallShift).
Using the results from these models we estimate the mediation effects using the
methods described in Imai et al. (2010).16 With this method we must first define the
treatment contrast. In our setting this amounts to setting two treatment conditions,
t′, t, that correspond to two different offer levels. We focus on the contrast between
t′ = 5, t = 10. Thus, for example, in the second contrast δi(10) represents the change in
probability of rejection that occurs with an offer of the entire resource that is due to the
difference in physiological arousal (Yi(10,Mi(10)) − Yi(10,Mi(5))). A positive change in
probability is consistent with hypothesis 3.
Figures ?? and 4 plot the result for the BigShift (top) and SmallShift (bottom)
conditions. In each plot, the average causal mediation effect (ACME) for both treatment
conditions (dark line for t and dashed line for t′), direct effect, and total effect point
estimates and confidence intervals are reported. In both plots the mediation effect under
t is positive and statistically significant for the BigShift condition. The mediation effect
for an offer of 0 is not different for the BigShift condition, nor is either mediation effect
statistically different from 0 for the SmallShift condition. Consistent with hypothesis 1
and the previous results, the total effect of offers on rejection decisions is negative, large,
and statistically significant.
Controlling for offer size, higher levels of skin conductance lead to a lower probability
that the player chooses “war” (i.e., rejects offer). In the first stage model (regression of
offer on physiological arousal) the effect of the treatment is negative AND in the second
stage of the mediation model (rejection decision on offer and physiological arousal) the
effect of physiological arousal is negative. Thus the average causal mediation effect is
16Because a probit model is used, common approaches such as the product of coefficient method/Sobel
test are not applicable. We obtain substantively identical results if we use a linear model for the rejection
choice.
26
−0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 0.1
BigShift
TotalEffect
DirectEffect
ACME
−0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 0.1
SmallShift
TotalEffect
DirectEffect
ACME
Causal Effects
Figure 4: Mediation Effects for treatment change of 5 to 10. Top row BigShift treat-ment and bottom row SmallShift treatment, with 95% confidence intervals allowing forclustering at the individual level.
positive (the product of two negative effects is positive).17 The effect of increasing an
offer that is transmitted through changes in skin conductance increases the probability
of a rejected offer.
Two statistical considerations should be mentioned before proceeding. First, there
could be confounding pre-treatment variables that impact both our emotional measures
and outcome decision. Controlling for additional pre-treatment covariates of player B did
not change our results.18 Depending how an additional confounder impacts our emotional
measure and outcome, our results could be biased down or up. Unfortunately, the for-
mal sensitivity analysis proposed by Imai et al. (2010) that deals with omitted variables
17Again, to note the contrast with the UG, the first stage regressions would show a negative relationship
between offer size and arousal, whereas the second stage would show positive relationship between arousal
and rejection decisions.18We included a measure of right wing authoritarianism, generalized trust, and ideology.
27
effecting both the mediator and outcome is not possible here because our treatment vari-
able is continuous rather than binary.19 Second, we note that our measures of emotional
arousal will come with some degree of measurement error. What is the implication of
this for the current study? Given that the direct and indirect effects go in opposite direc-
tions, if anything we are likely to be under estimating the role of the emotional pathway
(VanderWeele et al., 2012).
Here, we found that higher levels of skin conductance do not necessarily predict more
rejection (war). Rather, higher levels of skin conductance actually predicted less rejection.
It should also be noted that this finding is robust even when offer size is controlled for.
On the face of it, this may perhaps seem puzzling; our intuitions typically lead us
to associate “emotional arousal” with aggression and conflict, but here the relationship
is reversed. Here, physiologically aroused subjects were less likely to choose war, and
more likely to accept player’s B’s first round offer. How do we reconcile this seeming
contradiction? The key is in the realization that if player B chooses war, they choose the
strategically optimal path. That higher levels of arousal are associated with the opposite
–accepting their adversary’s offer and taking their chances in a second round in which
their own power will be greatly diminished– suggests that the arousal is preventing sound
decision-making.
In sum, as we hypothesized, our data suggest that lower levels of physiological arousal
allowed participants to engage in more strategic thinking, while higher levels of arousal
inhibited this deliberate process. Despite the similarities of the ultimatum game and our
bargaining game, we argue that the two games are sufficiently different by design that
low offers did not necessarily led to homogeneous outcomes. In particular, the negative
effect of physiological arousal on rejection rates is indicative of the possibility that aversive
arousal impairs one’s ability to engage in strategic thinking, thus making it difficult for
the responders to choose the optimal strategy of rejection.
19Further, we note that while offers are not randomized within a condition, they are not a choice
variable of the person who is responding to the offer.
28
5 Follow-up Experiment: Shifting Power but No Shift-
ing Offers
In the previous section, we examined the effects of commitment problems by contrasting
two experimental conditions; one with a large shift, and one with a shift so small as to be
negligible. We found that the latter condition did not generate a commitment problem
by virtue of the fact that the shift in power was too small. This is one way to examine
the effects of a commitment problem, but it is by no means perfect. For example, the
BigShift condition might have primed fairness reference points (Kahneman, 1992). An
alternative manipulation of the commitment problem is to allow a large shift in power,
but prevent offers from changing in the first to second period (Quek, 2012). If a reduction
in concerns about shifting power occurs, then we should expect that the mediating role
of skin-conductance should also decrease.20
Figure 5 presents the results from a followup study that had the same large shift
in power, but did not permit offers to change from round 1 to round 2, using 36 new
subjects from the same subject pool. The results show that while increases in offers lead
to decreases in the probability an offer was rejected, the mediating role of our physiological
measure is now no longer statistically different from zero, with the point estimate quite
close to zero.
In other words, once we eliminated the commitment problem through the imposition
of institutional changes–here changing the rules of the game to prevent shifts in offers–the
affective mechanism linking offers to rejections disappears. Thus we have tried to “shut-
off” the commitment problem in two ways, with both having the same consequences for
our physiological measures. In Figure 6 we present the simulated impact of offers on our
skin conductance measure, and we see the same pattern as with the Small Shift condition
in Figure 3. By including this additional design we can be more confident that our results
20An alternative design would be to introduce communication where players could try to make verbal
commitments. This may or may not have the desired effect depending on whether cheap talk can be
persuasive (Tingley and Walter, 2011a).
29
relate to concerns about changes in offers that would occur in the future due to shifting
power.
−0.6 −0.4 −0.2 0.0
Big Shift no Offer Shift
TotalEffect
DirectEffect
ACME
Causal Effects
Figure 5: Mediation Effects for offer change of 5 to 10 using experimental condition thatallows for large shift in power, but no ability for offers to change from round 1 to round2, with 95% confidence intervals allowing for clustering at the individual level.
6 Discussion & Conclusion
Explanations for the failure of bargaining and the resulting conflict have centered heavily
in recent years on so-called “commitment problems” that arise from shifting bargaining
power. Because of the inherent difficulty in credibly committing oneself not to take
advantage of a rival in the future, bargaining under conditions of shifting power are likely
to result in violent conflict. This explanation is compelling, but makes no attempt to
connect to what individual, human, decision-makers might experience.
We posit a theory of “aversive arousal” that is activated under conditions of large
power shifts (but not, it should be noted, under stable conditions). While actors who
30
0 2 4 6 8 10
0.4
0.6
0.8
1.0
Offer
Ave
rage
Ski
n C
ondu
ctan
ce S
core
median
ci95
ci95
ci95
No Offer Change Allowed
Figure 6: Effect of offer sizes on skin conductance when large power shift and no oppor-tunity for changes in offer. 95% confidence intervals with robust standard errors.
face the prospect of substantially losing power should reject all offers, we show that offers
can trigger physiological reactions which may impair strategic reasoning that is part of
the deliberative, “System II,” process identified by psychologists. Nevertheless, we also
provide indirect evidence of System II thinking, in that for many offers rejection decisions
were more likely in the BigShift condition. This behavior is consistent with the predictions
of the rational choice model.
We have brought together a somewhat unusual combination of formal modeling to
derive hypotheses, psychological theories to suggest additional hypotheses, and experi-
mental methods and psychophysiological data to test those hypotheses. While this par-
ticular combination is not necessary in all cases, we hope that it serves as an example
of one promising way to test the micro-foundations of theories of conflict in a laboratory
setting. We also demonstrate how the role of physiological responses may differ depend-
ing on the type of game (e.g., previous studies look almost exclusively at the Ultimatum
31
game). A richer understanding of the relationship between emotion and decision-making
in different incentive environments would certainly be valuable (see Myers and Tingley,
tted; Lee et al., aper). Finally, unlike previous studies, we carefully design our experiment
in a way that lets us analyze the mediating role of physiological responses in a bargaining
setting using new statistical tools.
Of course, any successful experiment inevitably generates more questions than it
answers. In this case, we focus on deliberative versus intuitive thinking. However, a
large literature on emotions and bargaining suggests that specific emotions (e.g., anxiety,
anger) may be an important component of the process we describe in our study. Just as
importantly, one might start to add layers of complexity to the bargaining game we used
in order to more closely mimic important aspects of the international system, such as the
presence of international institutions that may under some conditions alleviate conflict
(e.g., by preventing shifts in offers from one period to the next). Finally, while we have
measured the effect of arousal generated in the game, future work could try and directly
manipulate this arousal. For example, if in the “Big Shift” condition we introduced a
greater time delay to making a decision, would we observe any differences as reflective
considerations kick in more?
Furthermore, there remain important questions about the applicability of such ex-
periments to the study of international relations. Our study uses a convenience sample.
We think the best way analytically to evaluate the impact of this is to “sign the bias.”
Recent work makes a good point that student subject pools and elite samples may differ
(Hafner-Burton et al., 2013; Renshon, 2015). Crucially, though, it is important to think
about whether any of the effects identified in the current paper would be magnified or
decreased were we to use an alternative sample. Such considerations are beyond the scope
of this paper, but our paper, we feel, provides an innovative platform for such a discus-
sion. Additionally, future studies might investigate important questions about selection
into crises. Perhaps those people that are more easily aroused also enter into zero sum
situations more readily because they are less able to recognize potential for joint gains?
Future experiments, and papers, designed with this in mind would speak to key themes
32
References
Allison, G. T. (1969). Conceptual models and the cuban missile crisis. The American
Political Science Review, 63(3):689–718.
Anderson, C. A. and Bushman, B. J. (1997). External validity of trivial experiments.
Review of General Psychology, 1(1):19–41.
Ansolabehere, S. D., Iyengar, S., and Simon, A. (1999). Replicating experiments using
aggregate and survey data. American Political Science Review, 93(4):901–909.
Ariely, D., Gneezy, U., Loewenstein, G., and Mazar, N. (2009). Large stakes and big
mistakes. The Review of Economic Studies, 76(2):451–469.
Bar-Joseph, U. and McDermott, R. (2008). Personal functioning under stress: Account-
ability and social support of israeli leaders in the yom kippur war. Journal of Conflict
Resolution, 52(1):144–70.
Barabas, J. and Jerit, J. (2010). Are survey experiments externally valid? American
Political Science Review, 104(2):226–242.
Bechara, A., Damasio, H., Tranel, D., and Damasio, A. (1997). Deciding advantageously
before knowing the advantageous strategy. Science, 275(5304):1293–1295.
Ben-Shakhar, G. (1985). Standardization within individuals: A simple method to neu-
tralize individual differences in skin conductance. Psychophysiology, 22(3):292–299.
Ben-Shakhar, G., Bornstein, G., Hopfensitz, A., and van Winden, F. (2007). Reciprocity
and emotions in bargaining using physiological and self-report measures. Journal of
Economic Psychology, 28(3):314–323.
Benz, M. and Meier, S. (2008). Do people behave in experiments as in the field?—evidence
from donations. Experimental Economics, 11(3):268–281.
Bleiker, R. and Hutchison, E. (2008). Fear no more: emotions and world politics. Review
of international studies, 34(I):115.
34
Blight, J. G. (1992). The shattered crystal ball: Fear and learning in the Cuban Missile
Crisis. Rowman & Littlefield Publishers.
Blount, S. (1995). When social outcomes aren? t fair: The effect of causal attributions
on preferences. Organizational behavior and human decision processes, 63(2):131–144.
Bush, L., Hess, U., and Wolford, G. (1993). Transformations for within-subject designs:
A monte carlo investigation. Psychological Bulletin, 113(3):566–579.
Butler, C. K., Bellman, M. J., and Kichiyev, O. A. (2007). Assessing power in spatial
bargaining: When is there advantage to being status-quo advantaged? International
Studies Quarterly, 51(3):607–623.
Camerer, C. (2003a). Behavioral Game Theory. Princeton University Press, Princeton.
Camerer, C. (2003b). Behavioural studies of strategic thinking in games. Trends in
Cognitive Sciences, 7(5):225–231.
Camerer, C. and Hogarth, R. (1999). The effects of financial incentives in experiments:
A review and capital-labor-production framework. Journal of Risk and Uncertainty,
19(1):7–42.
Camerer, C. F. (2004). Prospect theory in the wild. In Colin F. Camerer, G. L. and
Rabin, M., editors, Advances in Behavioral Economics, pages 148–161.
Camerer, C. F. (2011). Behavioral game theory: Experiments in strategic interaction.
Princeton University Press, Princeton, NJ.
Cashman, G. (2013). What causes war?: an introduction to theories of international
conflict. Rowman & Littlefield Publishers, New York, NY.
Christie, M. (1981). Electrodermal activity in the 1980s: a review. Journal of the Royal
Society of Medicine, 74(8):616–622.
35
Civai, C., Corradi-Dell Acqua, C., Gamer, M., and Rumiati, R. (2010). Are irrational
reactions to unfairness truly emotionally-driven? dissociated behavioural and emotional
responses in the ultimatum game task. Cognition, 114(1):89–95.
Crawford, N. C. (2000). The passion of world politics: Propositions on emotion and
emotional relationships. International Security, 24(4):116–156.
Dane, E. and Pratt, M. (2007). Exploring intuition and its role in managerial decision
making. Academy of Management Review, 32(1):33–54.
DeRouen, K. and Sprecher, C. (2004). Initial crisis reaction and poliheuristic theory.
Journal of Conflict Resolution, 48(1):56–68.
Dowty, A. (1984). Middle East crisis: US decision-making in 1958, 1970, and 1973.
University of California Press.
Epstein, S. (1994). Integration of the cognitive and the psychodynamic unconscious.
American psychologist, 49(8):709.
Epstein, S., Pacini, R., Denes-Raj, V., and Heier, H. (1996). Individual differences in
intuitive–experiential and analytical–rational thinking styles. Journal of personality
and social psychology, 71(2):390.
Evans, J. and Over, D. (1996). Rationality and Reasoning. Psychology Press, United
Kingdom.
Evans, J. S. B. (2008). Dual-processing accounts of reasoning, judgment, and social
cognition. Annu. Rev. Psychol., 59:255–278.
Farnham, B. (1992). Roosevelt and the munich crisis: Insights from prospect theory.
Political Psychology, 13(2):205–235.
Farnham, B. (1994). Roosevelt and the munich crisis: Insights from prospect theory. In
Avoiding losses/taking risks: Prospect theory and international conflict, pages 41–72.
University of Michigan Press.
36
Fearon, J. (1995). Rationalist explanations for war. International Organization, 49(3):379–
414.
Fearon, J. (2004). Why Do Some Civil Wars Last So Much Longer than Others? Journal
of Peace Research, 41:275–301.
Freud, S. (1900). The interpretation of dreams (Standard Edition, Vol. 4), volume 1900.
Gardner, W., Gabriel, S., and Diekman, A. B. (2000). In Cacioppo, J., Tassinary, L., and
Berntson, G., editors, Handbook of psychophysiology (2nd ed.), pages 643–664. New
York, NY, US: Cambridge University Press.
Gigerenzer, G. (2007). Gut feelings: The intelligence of the unconscious. Penguin.
Gigerenzer, G. and Gaissmaier, W. (2011). Heuristic decision making. Annual review of
psychology, 62:451–482.
Gigerenzer, G. and Regier, T. (1996). How do we tell an association from a rule? comment
on sloman (1996). Psychological Bulletin, 119(1):23–26.
Gilinsky, A. and Judd, B. (1994). Working memory and bias in reasoning across the life
span. Psychology and Aging, 9(3):356–371.
Glad, B. (1989). Personality, political and group process variables in foreign policy
decision-making: Jimmy carter’s handling of the iranian hostage crisis. International
Political Science Review, 10(1):35–61.
Gordon, C. and Arian, A. (2001). Threat and decision making. Journal of Conflict
Resolution, 45(2):196–215.
Greif, A., Milgrom, P., and Weingast, B. R. (1994). Coordination, commitment, and
enforcement: The case of the merchant guild. The Journal of Political Economy,
102(4):pp. 745–776.
Grimm, V. and Mengel, F. (2011). Let me sleep on it: Delay reduces rejection rates in
ultimatum games. Economics Letters.
37
Hafner-Burton, E., Leveck, B., Victor, D., and Fowler, J. (2012). A behavioral approach
to international legal cooperation. Working Paper.
Hafner-Burton, E. M., Hughes, D. A., and Victor, D. G. (2013). The cognitive revo-
lution and the political psychology of elite decision making. Perspectives on Politics,
11(02):368–386.
Haidt, J. (2001). The emotional dog and its rational tail: a social intuitionist approach
to moral judgment. Psychological Review, 108(4):814–834.
Harris, D. (2004). The Crisis: The President, the Prophet, and the Shah - 1979 and the
Coming of Militant Islam. New York: Little, Brown, and Company.
Hassin, R. R., Uleman, J. S., and Bargh, J. A. (2004). The new unconscious. Oxford
University Press, USA.
Hertwig, R. and Ortmann, O. (2003). Economists’ and psychologists’ experimental prac-
tices: How they differ, why they differ and how they could converge. In Brocas, I. and
Carrillo, J., editors, The Psychology of Economic Decisions, pages 253–272. Oxford
University Press.
Holsti, O. R. (1970). Individual differences in” definition of the situation.”. Journal of
Conflict Resolution, 14(3):303–310.
Holt, C. and Laury, S. (2001). Varying the scale of financial incentives under real and
hypothetical conditions. Behavioral and Brain Sciences, 24(3):417–417.
Imai, K., Keele, L., and Tingley, D. (2010). A general approach to causal mediation
analysis. Psychological Methods, 15(4):309–334.
Imai, K., Keele, L., Tingley, D., and Yamamoto, T. (2011). Unpacking the black box
of causality: Learning about causal mechanisms from experimental and observational
studies. American Political Science Review, 105(4):765–789.
38
Imai, K., Tingley, D., and Yamamoto, T. (2013). Experimental designs for identifying
causal mechanisms (with discussions). Journal of the Royal Statistical Society-Series
A, 176:5–51.
James, W. (1890). The principles of psychology. Henry Holt and Co.
Kahneman, D. (1992). Reference points, anchors, norms, and mixed feelings. Organiza-
tional behavior and human decision processes, 51(2):296–312.
Kahneman, D. (2003). A perspective on judgment and choice: mapping bounded ratio-
nality. American psychologist, 58(9):697.
Kahneman, D. (2011). Thinking, fast and slow. Macmillan.
Kahneman, D. and Tversky, A. (1979). Prospect theory: An analysis of decision under
risk. Econometrica, 47(2):263–291.
Khong, Y. F. (1992). Analogies at War: Korea, Munich, Dien Bien Phu, and the Vietnam
Decisions of 1965. Princeton University Press.
Lambourne, K. and Tomporowski, P. (2010). The effect of exercise-induced arousal on
cognitive task performance: A meta-regression analysis. Brain research, 1341:12–24.
Lebow, R. N. (1990). Domestic politics and the cuban missile crisis: The traditional and
revisionist interpretations reevaluated. Diplomatic History, 14(4):471–492.
Lee, J. J., Bhanot, S., and Bruder, M. (Working Paper). How does emotion shape social
preferences: Emotion as antecedents and consequences of experimental games.
Levitt, S. and List, J. (2007). What do laboratory experiments measuring social prefer-
ences reveal about the real world? The Journal of Economic Perspectives, 21(2):153–
174.
Levy, J. S. (1996). Loss aversion, framing, and bargaining: The implications of prospect
theory for international conflict. International Political Science Review, 17(2):179–195.
39
Lieberman, M. D. (2003). A social cognitive neuroscience approach. Social judgments:
Implicit and explicit processes, 5:44.
McBride, M. and Skaperdas, S. (2012). Conflict, settlement, and the shadow of the future.
working paper.
McDermott, R. (2002). Experimental methods in political science. Annual Review of
Political Science, 5(1):31–61.
McDermott, R. (2004). The feeling of rationality: The meaning of neuroscientific advances
for political science. Perspectives on Politics, 2(4):691–706.
McDermott, R., Johnson, D., Cowden, J., and S., R. (2007). Testosterone and aggression
in a simulated crisis game. The ANNALS of the American Academy of Political and
Social Science, 614:15–33.
McDermott, R., Tingley, D., Cowden, J., Frazzetto, G., and Johnson, D. (2009).
Monoamine oxidase a gene (MAOA) predicts behavioral aggression following provo-
cation. Proceedings of the National Academy of Sciences, 106(7):980–994.
Mercer, J. (2006). Human nature and the first image: emotion in international politics.
Journal of International Relations and Development, 9(3):288–303.
Mercer, J. (2010). Emotional beliefs. International Organization, 64(01):1–31.
Mercer, J. (2013). Emotion and strategy in the korean war. International Organization,
67(2):221–252.
Mintz, A. (2004). How do leaders make decisions? a poliheuristic perspective. Journal of
conflict resolution, 48(1):3–13.
Mintz, A. and Redd, S. B. (2003). Framing effects in international relations. Synthese,
135(2):193–213.
Myers, D. and Tingley, D. (2012). Influence of emotions on trust. Working Paper.
40
Myers, D. and Tingley, D. (Submitted). The influence of emotion on trust.
Odell, J. and Tingley, D. (2013). Negotiating agreements in intenational relations. Inter-
national Relations Working Group of the American Political Science Association 2013
Taskforce on Negotiating Agreements in Politics.
Osman, M. (2004). An evaluation of dual-process theories of reasoning. Psychonomic
Bulletin & Review, 11(6):988–1010.
Ostrom, E. (1998). A behavioral approach to the rational choice theory of collective
action: Presidential address, american political science association, 1997. American
Political Science Review, 92(1):1–22.
Oxley, D. R., Smith, K. B., Alford, J. R., Hibbing, M. V., Miller, J. L., Scalora, M.,
Hatemi, P. K., and Hibbing, J. R. (2008). Political Attitudes Vary with Physiological
Traits. Science, 321(5896):1667–1670.
Pillutla, M. and Murnighan, J. (1996). Unfairness, anger, and spite: Emotional rejec-
tions of ultimatum offers. Organizational Behavior and Human Decision Processes,
68(3):208–224.
Plessner, H., Betsch, C., and Betsch, T. (2007). Intuition in judgment and decision
making. CRC Press.
Powell, R. (2006). War as a commitment problem. International Organization, 60.
Quek, K. (2012). Rationalist experiments on war. working paper.
Renshon, J. (2015). Losing face and sinking costs: Experimental evidence on the judgment
of political and military leaders. International Organization.
Renshon, J., Lee, J. J., and Tingley, D. (2014). Physiological arousal and political beliefs.
Political Psychology, (forthcoming).
41
Renshon, J. and Lerner, J. (2012). The role of emotions in foreign policy decision making.
In Christie, D. J. and Montiel, C., editors, Encyclopedia of Peace Psychology, pages
313–317. Wiley-Blackwell Press.
Rosen, S. (2005). War and Human Nature. Princeton University Press, Princeton.
Sanfey, A., Rilling, J., Aronson, J., Nystrom, L., and Cohen, J. (2003). The neural basis
of economic decision-making in the ultimatum game. Science, 300(5626):1755.
Sequeira, H. and Roy, J. (1997). Neural control of electrodermal activity. In Jordan,
D., editor, Central Nervous Control of Autonomic Function, Vol. 11, pages 259–293.
Harwood Academic Publishers.
Shimko, K. L. (1994). Metaphors and foreign policy decision making. Political Psychology,
15(4):655–671.
Simmons, B. (1994). Who Adjusts? Domestic Sources of Foreign Economic Policy During
the Interwar Years. Princeton University Press, Princeton.
Simmons, B. A. and Danner, A. M. (2010). Credible commitments and the international
criminal court. International Organization, 64(2).
Sloman, S. (1996). The empirical case for two systems of reasoning. Psychological bulletin,
119(1):3.
Stern, S. M. (2005). The Week the World Stood Still: Inside the Secret Cuban Missile
Crisis. Stanford: Stanford University Press.
Taubman, W. (2003). Khrushchev: The Man and His Era. New York: W.W. Nortion.
Thayer, B. A. (2004). Darwin and international relations: On the evolutionary origins of
war and ethnic conflict. University Press of Kentucky.
Tingley, D. (2011). The Dark Side of the Future: An Experimental Test of Commitment
Problems in Bargaining. International Studies Quarterly, 55(2):521–544.
42
Tingley, D. and Walter, B. (2011a). Can cheap talk deter? an experimental analysis.
Journal of Conflict Resolution, 55(6):994–1018.
Tingley, D. and Walter, B. (2011b). The effect of repeated play on reputation building:an
experimental approach. International Organization.
Tingley, D. and Wang, S. (2010). Belief updating in sequential games of two-sided in-
complete information: An experimental study of a crisis bargaining model. Quarterly
Journal of Political Science, 5(3):243–255.
Tomz, M. (2007). Domestic audience costs in international relations: An experimental
approach. International Organization, 61(4):821–840.
VanderWeele, T. J., Valeri, L., and Ogburn, E. L. (2012). The role of measurement
error and misclassification in mediation analysis. Epidemiology (Cambridge, Mass.),
23(4):561.
Van’t Wout, M., Kahn, R., Sanfey, A., and Aleman, A. (2006). Affective state and
decision-making in the ultimatum game. Experimental Brain Research, 169(4):564–
568.
Welch, D. (2003). Culture and emotion as obstacles to good judgment. In Good Judgment
in Foreign Policy: Theory and Application, pages 483–507. Rowman & Littlefield.
Welch, D. A. (1995). Justice and the Genesis of War. Cambridge University Press, New
York, NY.
White, M. J. (1992). Belligerent beginnings: John f. kennedy on the opening day of the
cuban missile crisis. The Journal of Strategic Studies, 15(1):30–49.
Winter, D. G. (2007). The role of motivation, responsibility, and integrative complexity
in crisis escalation: comparative studies of war and peace crises. Journal of Personality
and Social Psychology, 92(5):920–937.
Woodward, B. (2002). Bush at War. New York: Simon and Schuster.
43
A Model of Commitment Problems
To see how power shifts can lead to conflict we provide a brief sketch of a simple two
period bargaining model.21 The basic intuition is that when one player expects to be
disadvantaged in the future, they have an incentive to start a conflict in order to forestall
the shift in bargaining power. There are two players, A and B. In each period there is a
resource with value 10. This resource may be divided between the players. The bargaining
protocol is as follows. In the first period player A makes a demand, x1A, to player B.
This leaves player B with 10− x1A. If the demand is accepted, then in the second period
there is another bargaining stage, where player A makes a demand x2A. If the first period
demand is rejected then both players play a war lottery, with probability p1 player A
wins. One player wins the resource for period 1, but both players pay costs cA = cB. The
winner of the lottery obtains the entire resource in period 2. If the resource is rejected in
the second period, both players pay the cost and play a war lottery, with probability p2
player A wins.
To analyze the complete information game we use backwards induction. We begin
with the second period decision by actor B. In Period 2 player B is indifferent between
demand x2A and lottery if (1 − p2) × 10 − cB = 10 − x2A. Thus if x2A = 10p2 + cB then
actor B is indifferent and by assumption accepts the demand. In period 2 player A’s
expected utility from the lottery is 10p2 − cA. Hence A will prefer to make a demand
x2A = 10p2 + cB if p2 + cB > p2− cA. This holds because cB = cA. They can’t make more
than this demand because then it will be rejected. So, the optimal demand in the second
period is x∗2A = 10p2 + cB. In the SmallShift condition this amounts to a demand of 7.1
and in the BigShift condition a demand of 9.
Now consider period 1. B’s utility from rejecting the lottery in period 1 is 10× (1−
p1)− cB + δ10× (1− p1), where δ represents the discount rate for the second period, or
the likelihood that the second period is played. We assume that δ = 1 for any numerical
calculations. Player B’s utility from accepting a demand x1A is equal to 10−x1A + δ(10×
(1− p2)− cB).
21This is simply a two period version of the model in Fearon (1995).
45
Thus player B will reject the demand x1A if
10× (1− p1)− cB + δ10× (1− p1) > 10− x1A + δ(10× (1− p2)− cB)
x1A > 10p1 + δ10p1 − δ10p2 + cB − δcB
Hence they will be indifferent if x1A = 10p1 + δ10p1 − δ10p2 + cB − δcB,
Now consider A’s expected utility in period 1. If they have the lottery rejected they get
10p1−cA+δ10p1. If they have some demand x1A accepted then they get x1A+δ(10p2+cB).
They will want their first period demand accepted if
x1A + δ(10p2 + cB) ≥ 10p1 − cA + δ10p1
x1A ≥ 10p1 + δ10p1 − δ10p2 − cA − δcB
Now note that the RHS of this is almost identical to what will make B indifferent,
except that it is slightly smaller (−cA instead of cB).
Hence A will make demand x∗1A = 10p1 + δ10p1− δ10p2 + cB − δcB. In the SmallShift
condition this will be a demand of 4.7. Hence offers over 5.3 in the first round will be
accepted.
The key question is when the first period demand will be rejected. This will occur
when x∗1A is less than 0. That is, when player A can not offer (demand little) enough to
make player B accept the demand in light of what they expect to get in period 2. This
holds when we have 0 > 10p1 + δ10p1− δ10p2 + cB − δcB. Assuming δ = 1 this reduces to
p2 − 2p1 > 0. Thus as p2 gets larger and/or p1 gets smaller, this condition is more likely
to hold.
In the experiment that follows, our BigShift condition has p1 = .3 and p2 = .7 and
our SmallShift condition has p1 = .49 and p2 = .51. In the BigShift condition p2−2p1 > 0
holds and so we expect preventive war, but in the SmallShift condition this condition does
not hold. Demands less than 4.7 should be accepted.
46