COMMENT

Heuristic Game Theory

Joachim I. KruegerBrown University

Colman, Pulford, and Lawrence, in the current issue of this journal, present theory anddata to advance a psychologically informed approach to game theory. While supportingtheir project, I respond to their critique of projection theory, question their overlyflexible way of evaluating alternative proposals, and note that two of these alternatives,team reasoning and Stackelberg reasoning, cannot get off the ground without assumingsocial projection. Lastly, I note that the empirical data Colman et al. present providestronger support for so-called Level-1 reasoning than the authors acknowledge.

Keywords: game theory, social dilemmas, decision heuristics

Classic Game Theory (CGT) is a great intellec-tual achievement, which has stimulated theory andresearch in many disciplines (von Neumann &Morgenstern, 1944). Yet, many social scientistsare troubled by the theory’s failure to explaincollective action. The assumptions of commonknowledge and instrumental rationality cast a longshadow. In many collective games, where coop-eration matters, CGT predicts tragedy worthy ofAischylos (Hardin, 1968).

Noting widespread cooperation (Kropotkin,1902) and variation over individuals and con-texts, behavioral scientists have struggled toarticulate theories that fit these data. AndrewColman and his collaborators are among thosewho have searched for a psychologically plau-sible game theory (Colman, 2003; see also VanLange, Joireman, Parks, & Van Dijk, 2013). Asingle, dominant theory has not emerged. Per-haps people approach different strategic gameswith a toolbox of heuristics, each of whichshortcuts the strict assumptions of CGT whileyielding more socially (and personally) desir-

able results. This possibility suggests itself inthe common-interest games, which Colman,Pulford, and Lawrence (this issue) address intheir article.

In the High-Low (i.e., Hi-Lo) game, two play-ers win a high payoff if they both choose strategyH, and both receive a low payoff if they bothchoose L. If they choose different strategies, nei-ther gets anything. Colman et al. show that classictheory fails to predict behavior because it boaststhree Nash equilibria (two pure and one mixed),but no way to choose among them.

How do ordinary people solve such a coor-dination problem? Colman et al. reject the prin-ciple of indifference because it leads to questionbegging. For player 1 to assume that player 2throws darts without realizing that player 1knows this would be to violate the commonknowledge assumption. Yet, Colman et al. useassumptions of CGT to refute an alternativetheory, a point worth remembering.

The next alternative is social projection the-ory, which predicts that a player in the Hi-Logame will choose H, assuming that the otherplayer will probably come to the same decision(Krueger, DiDonato, & Freestone, 2012). Noinferences about other players’ thought pro-cesses are necessary. Colman et al. raise twoobjections. First, they note that projectionworks only inasmuch as players are ignorant ofeach other’s motives, intention, or preferences.Usually people do have some knowledge aboutothers, which dilutes any contribution their own

Joachim I. Krueger, Department of Cognitive, Linguistic,& Psychological Sciences, Brown University.

I thank Leonard Chen for comments on a draft of thisarticle.

Correspondence concerning this article should be ad-dressed to Joachim I. Krueger, Department of Cognitive,Linguistic, & Psychological Sciences, Brown University,190 Thayer Street, Providence, RI 02912. E-mail:Joachim@brown.edu

Decision © 2014 American Psychological Association2014, Vol. 1, No. 1, 59–61 2325-9965/14/$12.00 DOI: 10.1037/dec0000002

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choice might make when predicting the choiceof another. The same argument was broughtagainst Dawes’s (1989) reformulation of the“false consensus effect” in rational Bayesianterms. Empirical work has since shown thatself-related information dominates (in part be-cause there is more of it; Krueger & Clement,1994), but also that projection decreases whenmore other-related information becomes avail-able (Robbins & Krueger, 2005). In experimen-tal games, the players’ mutual anonymity isoften stressed, which creates the condition un-der which projection works best.

Second, Colman et al. question whether pro-jection theory can be applied to contemplatedchoice. The theory assumes that before makinga decision, players consider the inferential im-plications of each strategy. If they play H, theywill have to rationally assume that most othersalso choose H; if they play L, they must inferthat most others also choose L. In the absence ofany countervailing reason, why would they thennot choose H? Colman et al. argue (withoutproof) that contemplated choice has less induc-tive power than actual choice. However, theBayesian calculus knows no difference betweencontemplation and action. The resistance to thestatistical equivalence of contemplated and ac-tual choice probably stems from a metaphysicalcommitment to free will (Krueger et al., 2012).Players are supposed to make their choicesfreely and independently. That is true enough,but because they are cut from the same biolog-ical and cultural cloth and because they arefacing the same task, two randomly pickedplayers will more likely agree than disagree.Social projection theory exploits this brute fact.

Colman et al. then discuss three other ap-proaches. The first is cognitive hierarchy the-ory. Here, “Level-1” players are of particularinterest; they assume that other players chooserandomly (throw darts), which allows them, theLevel-1 players, to choose a payoff-maximizingstrategy. This works in the Hi-Lo game but failsto predict the high levels of cooperation seen inassurance games and prisoner’s dilemmas. Col-man et al. are also concerned about the asym-metries that arise when most players believethey are deeper thinkers than others. A finalproblem is that player 1’s assumption thatplayer 2 chooses randomly is the same thatColman et al. already rejected when discussingthe principle of indifference. If the common-

knowledge axiom is used to exclude one alter-native to game theory, why not use it to excludeanother? If one agrees, however, that playerschoose strategies heuristically, the assumptionof common knowledge need not trouble anyexplanatory effort.

The second contender is the theory of teamreasoning. Its key idea is that individuals reasonon behalf of the group, asking what they can doto maximize the collective payoff. In the Hi-Logame, a team reasoner finds that choosing strat-egy H is necessary, though not sufficient, torealize the Hi-Hi payoff. There are three prob-lems. One is that the assumption that a player’sown contribution is necessary for collective suc-cess breaks down in large-N public-goodsgames or problems of collective action, such asvoting. In large-N games, one would have toadd an assumption of positive social identity orthe idea that people feel good about being partof a successful collective even if their owncontribution is negligible (Tajfel & Turner,1979). Social projection theory does not requirethis additional assumption (Acevedo &Krueger, 2004).

Another problem is that the theory of teamreasoning itself concedes that it will work onlyif there is “a belief that the other player(s) willdo likewise” (p. 42). Although Colman et al.note that “this should be distinguished fromsocial projection theory” (p. 42), they do not sayhow. They offer that team reasoning assumes aparameter omega to represent “the probabilitythat a player will adopt the team-reasoningmode” (p. 42). Social projection theory uses sucha parameter as well, provides a theoretical ratio-nale for it, and guides its empirical measurement.The final problem is that in some games, self-interest and collective interest are identical. In theHi-Lo game, a methodological individualist sim-ply asks, “What do I want, and what is necessaryfor me to do to achieve it?”

Finally, Colman et al. introduce strong Stack-elberg reasoning. Stackelberg retains the gametheoretic axioms of common knowledge andindividual rationality, but adds that players actas if their choices were obvious to others. Tosay that player 1’s intentions are transparent toplayer 2 implies the inverse. One might say thatplayer 1 knows what player 2 will do andchooses the best reply. This raises the questionof how any player knows what another playerwill do. Colman et al. assert that players are not

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omniscient but that they “choose strategies as ifthey believed that their coplayers could antici-pate their choices” (p. 43). In the Hi-Lo game,player 1 chooses H, as if believing that player 2knows that he would choose H, and that player2 therefore chooses H. Each player’s choice isthe best reply to the other’s best reply to one’sown. . .—it does look circular. Stackelberg rea-soning has players expect each other to chooseas they themselves do. Social projection theoryarrives at the same conclusion but describeshow players arrive at probabilistic predictions.Yet, in games that are not payoff-dominant,theoretical predictions diverge. Like CGT,Stackelberg reasoning predicts mutual defectionin the prisoner’s dilemma, whereas projectioncorrectly predicts widespread cooperation.

If cognitive hierarchy theory, team reason-ing, and Stackelberg reasoning are potentialsolutions to game-theoretic challenges, oneneeds to know which type of reasoning cap-tures the intuitions and ruminations of ordi-nary people. In two experiments, Colman etal. turn to asymmetric games, carefully de-signed to pit the three theories against oneanother. Social projection, having been criti-cally reviewed in the introduction, is no lon-ger in the mix. It has nothing to offer inasymmetric games. The data suggest thatLevel-1 reasoning is the clear winner. Table 1(p. 48) shows that Level-1 reasoning predictsthe results in 9 of 12 cases. The binomialprobability of this result, or a more extremeoutcome, is .004 (with p � 1/3 to score a hitin given game). Team reasoning and Stackel-berg each make only 3 correct predictions(binomial p � .82 for this result or a betterone). Although it appears that only Level-1reasoning beat chance, verbal protocols sug-gested that some players reasoned for theteam or like Stackelberg.

To conclude, current work to find new waysto study social dilemmas and experimentalgames may benefit from the view that peoplemake judgments and decisions by using heuris-tics (Hertwig, Hoffrage, & the ABC ResearchGroup, 2013). Full rationality may neither benecessary nor desirable. Social projection andLevel-1 reasoning hold promise for further de-velopment, whereas team and Stackelberg rea-

soning may also play a role once their boundaryconditions are properly understood.

References

Acevedo, M., & Krueger, J. I. (2004). Two egocen-tric sources of the decision to vote: The voter’sillusion and the belief in personal relevance. Po-litical Psychology, 25, 115–134. doi:10.1111/j.1467-9221.2004.00359.x

Colman, A. M. (2003). Cooperation, psychologicalgame theory, and limitations of rationality in socialinteraction. Behavioral and Brain Sciences, 26,139–153. doi:10.1017/S0140525X03000050

Dawes, R. M. (1989). Statistical criteria for establish-ing a truly false consensus effect. Journal of Ex-perimental Social Psychology, 25, 1–17. doi:10.1016/0022-1031(89)90036-X

Hardin, G. (1968). Tragedy of the commons. Science,162, 1243–1248. doi:10.1126/science.162.3859.1243

Hertwig, R., Hoffrage, U., & the ABC ResearchGroup. (2013). Simple heuristics in a social world.New York, NY: Oxford University Press.

Kropotkin, P. A. (1902). Mutual aid: A factor ofevolution. New York, NY: McClure, Philips & Co.

Krueger, J., & Clement, R. W. (1994). The truly falseconsensus effect: An ineradicable and egocentricbias in social perception. Journal of Personalityand Social Psychology, 67, 596–610. doi:10.1037/0022-3514.67.4.596

Krueger, J. I., DiDonato, T. E., & Freestone, D.(2012). Social projection can solve social dilem-mas. Psychological Inquiry, 23, 1–27. doi:10.1080/1047840X.2012.641167

Robbins, J. M., & Krueger, J. I. (2005). Social pro-jection to ingroups and outgroups: A review andmeta-analysis. Personality and Social Psychol-ogy Review, 9, 32– 47. doi:10.1207/s15327957pspr0901_3

Tajfel, H., & Turner, J. (1979). An integrative theoryof intergroup conflict. In W. G. Austin & S.Worchel (Eds.), The social psychology of inter-group relations (pp. 33– 48). Monterey, CA:Brooks/Cole.

Van Lange, P. A. M., Joireman, J., Parks, C. D., &Van Dijk, E. (2013). The psychology of socialdilemmas: A review. Organizational Behavior andHuman Decision Processes, 120, 125–141. doi:10.1016/j.obhdp.2012.11.003

von Neumann, J., & Morgenstern, O. (1947). Theoryof games and economic behavior. Princeton, NJ:Princeton University Press.

Received April 30, 2013Revision received May 24, 2013

Accepted May 29, 2013 �

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