Respect, Iterative Admissibility, and Equilibrium Refinements

Abstract Much of the literature on international environmental agreements (IEA) considers the case of identical countries. There is a much smaller literature concerning the more complex but more realistic case of country heterogeneity. This paper involves modifying the standard static homogeneous country model of international environmental agreements. In particular, we consider two types of countries, differing in size as well as in marginal damage from pollution. Although the IEA does not have a unique size in this case, we do introduce two equilibrium refinements and explore the implications for coalition size. The two refinements include one based on efficiency and one based on equity.

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Information, rational beliefs and equilibrium refinements

Ricerche Economiche ◽

10.1016/0035-5054(94)90018-3 ◽

1994 ◽

Vol 48 (1) ◽

pp. 23-43

Author(s):

Giacomo Bonanno

Keyword(s):

Rational Beliefs ◽

Equilibrium Refinements

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Smoothing Method for Approximate Extensive-Form Perfect Equilibrium

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2017/42 ◽

2017 ◽

Cited By ~ 2

Author(s):

Christian Kroer ◽

Gabriele Farina ◽

Tuomas Sandholm

Keyword(s):

Nash Equilibrium ◽

Imperfect Information ◽

Large Scale ◽

Nash Equilibria ◽

Convex Polytope ◽

Solution Concept ◽

Extensive Form ◽

Game Tree ◽

Equilibrium Refinements ◽

Perfect Equilibria

Nash equilibrium is a popular solution concept for solving imperfect-information games in practice. However, it has a major drawback: it does not preclude suboptimal play in branches of the game tree that are not reached in equilibrium. Equilibrium refinements can mend this issue, but have experienced little practical adoption. This is largely due to a lack of scalable algorithms.Sparse iterative methods, in particular first-order methods, are known to be among the most effective algorithms for computing Nash equilibria in large-scale two-player zero-sum extensive-form games. In this paper, we provide, to our knowledge, the first extension of these methods to equilibrium refinements. We develop a smoothing approach for behavioral perturbations of the convex polytope that encompasses the strategy spaces of players in an extensive-form game. This enables one to compute an approximate variant of extensive-form perfect equilibria. Experiments show that our smoothing approach leads to solutions with dramatically stronger strategies at information sets that are reached with low probability in approximate Nash equilibria, while retaining the overall convergence rate associated with fast algorithms for Nash equilibrium. This has benefits both in approximate equilibrium finding (such approximation is necessary in practice in large games) where some probabilities are low while possibly heading toward zero in the limit, and exact equilibrium computation where the low probabilities are actually zero.

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