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Metagame Strategies of Nation-States, with Application to Cross-Strait Relations

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.

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Metagame Strategies of Nation-States, with Application to Cross-Strait Relations

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  1. Metagame Strategies of Nation-States, with Application to Cross-Strait Relations Alex Chavez and Jun Zhang* Dept. of Psychology, University of Michigan *AFOSR

  2. 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? Why?

  3. Metagames Metagames 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:

  4. Metagames Example: 21Γ for Γ = Prisoner’s Dilemma Player 1: Level-1 Level-2 Player 2: . . .

  5. Metagames Metagames strategies resolve as base game strategies.

  6. Metagames Metagames strategies resolve as base game strategies.

  7. Metagames Metagames strategies resolve as base game strategies.

  8. Metagames Metagames strategies resolve as base game strategies.

  9. Metagames Metagames strategies resolve as base game strategies.

  10. Metagames Metagames strategies resolve as base game strategies.

  11. Metagames Metagames strategies resolve as base game strategies.

  12. 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.

  13. 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.

  14. 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.

  15. 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

  16. 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.

  17. 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?

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