Upload
calais
View
42
Download
2
Embed Size (px)
DESCRIPTION
Metagame Strategies of Nation-States, with Application to Cross-Strait Relations. Alex Chavez and Jun Zhang* Dept. of Psychology, University of Michigan *AFOSR. Standard solution concept. Nash equilibrium (NE): NE often fails descriptively. Common knowledge of rationality. - PowerPoint PPT Presentation
Citation preview
Metagame Strategies of Nation-States, with Application
to Cross-Strait Relations
Alex Chavez and Jun Zhang*Dept. of Psychology, University of Michigan
*AFOSR
Standard solution concept• Nash equilibrium (NE):• NE often fails descriptively.
– Common knowledge of rationality.
• Limited # of steps of iterated thinking (Camerer, 2003).
– Utility misspecifications.
• Altruism, inequality aversion (Fehr & Schmidt, 1998), social norms (Bicchieri, 2006).
– Strategy space?
Cooperate Defect
Cooperate 3, 3 0, 5
Defect 5, 0 1, 1
Why?
MetagamesMetagames describe situations where players
recursively predict each other’s conditional strategies.
• Base game: where P = set of players, S = strategy
space, π = payoff functions.• Metagame: Iteratively replace Si with
• Each metagame is identified by its title, the order in which the Si* are constructed.
• E.g., some metagames for P = {1, 2} are:
Metagames• Example: 21Γ for Γ = Prisoner’s Dilemma• Player 1:
Level-1Level-2
• Player 2:
f1
If Player 2 Then
Cooperate Cooperate
Defect Cooperate
f3
If Player 2 Then
Cooperate Defect
Defect Cooperate
f2
If Player 2 Then
Cooperate Cooperate
Defect Defect
f4
If Player 2 Then
Cooperate Defect
Defect Defect
g1
If Player 1 Then
f1 Cooperate
f2 Cooperate
f3 Cooperate
f4 Cooperate
g2
If Player 1 Then
f1 Cooperate
f2 Defect
f3 Cooperate
f4 Cooperate
g16
If Player 1 Then
f1 Defect
f2 Defect
f3 Defect
f4 Defect
. . .
Metagames• Metagames strategies resolve as base game strategies.
f2
If Player 2 Then
Cooperate Cooperate
Defect Defect
g2
If Player 1 Then
f1 Cooperate
f2 Defect
f3 Cooperate
f4 Cooperate
Γ(c,c) (c,d)(d,c) (d,d)
21Γ
Metagames• Metagames strategies resolve as base game strategies.
f2
If Player 2 Then
Cooperate Cooperate
Defect Defect
g2
If Player 1 Then
f1 Cooperate
f2 Defect
f3 Cooperate
f4 Cooperate
Γ(c,c) (c,d)(d,c) (d,d)
21Γ
Metagames• Metagames strategies resolve as base game strategies.
f2
If Player 2 Then
Cooperate Cooperate
Defect Defect
g2
If Player 1 Then
f1 Cooperate
f2 Defect
f3 Cooperate
f4 Cooperate
Γ(c,c) (c,d)(d,c) (d,d)
21Γ
Metagames• Metagames strategies resolve as base game strategies.
f2
If Player 2 Then
Cooperate Cooperate
Defect Defect
g2
If Player 1 Then
f1 Cooperate
f2 Defect
f3 Cooperate
f4 Cooperate
Γ(c,c) (c,d)(d,c) (d,d)
21Γ
Metagames• Metagames strategies resolve as base game strategies.
Γ(c,c) (c,d)(d,c) (d,d)
21Γ
Metagames• Metagames strategies resolve as base game strategies.
Γ(c,c) (c,d)(d,c) (d,d)
21Γ
Metagames• Metagames strategies resolve as base game strategies.
Γ(c,c) (c,d)(d,c) (d,d)
21Γ
Metagames• Metagames strategies resolve as base game strategies.
• Resolution is easy. Finding Nash equilibria is not.– E.g., 24 x 232 x 2512 outcomes in the 3-player game we study.
• Luckily, it is easy to find metaequilibria, outcomes in the base game which the Nash equilibria in the metagame game project to.
Γ(c,c) (c,d)(d,c) (d,d)
21Γ
Three useful theorems• (Identification). Howard (1971) provides a theorem for
identifying the set of all metaequilibria.– Requires optimization over certain strategy subspaces of the
base game.
• (Reducilibility). Repetitions in the title may be deleted.
• (Nestedness). Metaequilibria are nested in larger titles.
Application: cross-Strait relations
• 1949 Communist party take power of mainland China after civil war with nationalists, who setup a government in Taiwan.
• 1979 U.S. recognition of communist China and passage of Taiwan Relations Act, which protects Taiwan against Chinese attack
• Recent years:• Taiwan indicates desire of official independence
from mainland China.• China threatens to use force to prevent this.• The U.S. may have a pro-Taiwan or pro-China
stance.
Taiwan Taiwan
No Ind. Ind. No Ind. Ind.
ChinaNo War A B E F
War C D G H
U.S.: Support U.S.: No support
(A) Status quo (E) Isolated Taiwan without independence
(B) U.S.-recognized independent Taiwan
(F) U.S.-unrecognized independent Taiwan
(C) Taiwan gives in despite U.S. support
(G) Unification without resistance
(D) All-out war (H) Unification w/resistance
Results• G, forceful unification without
resistance, is a metaequilibrium in every metagame by the nesting property.
• The status quo, A, is a metaequilibrium in certain level-2 metagames and in all level-3 metagames.
Results• Brute force -> all Nash equilibria of cΓ.• E.g., for G:
– Taiwan does not declare independence,– The U.S. does not support Taiwan, and – China threatens to go to war if either Taiwan or the
U.S. unilaterally changes strategies.
Summary and Future Directions• Metagames
– Applied to multinational conflict.– Useful for highly sophisticated players.
• Open questions– Robustness to payoff assumptions– Computation of Nash equilibria– Real challenge: qualitatively describing the
many Nash equilibria associated with one metaequilibrium
• Thanks. questions?
1
2 3
2131
12
32 13
23
321231
312
132 213
123