The Computation of Perfect and Proper Equilibrium for Finite Games via Simulated Annealing

This paper exploits an analogy between the “trembles” that underlie the functioning of simulated annealing and the player “trembles” that underlie the Nash refinements known as perfect and proper equilibrium. This paper shows that this relationship can be used to provide a method for computing perfect and proper equilibria of n-player strategic games. This paper also shows, by example, that simulated annealing can be used to locate a perfect equilibrium in an extensive form game.Game Theory

Coalition-Stable Equilibria in Repeated Games

It is well-known that subgame-perfect Nash equilibrium does not eliminate incentives for joint-deviations or renegotiations. This paper presents a systematic framework for studying non-cooperative games with group incentives, and offers a notion of equilibrium that refines the Nash theory in a natural way and answers to most questions raised in the renegotiation-proof and coalition-proof literature. Intuitively, I require that an equilibrium should not prescribe in any subgame a course of action that some coalition of players would jointly wish to deviate, given the restriction that every deviation must itself be self-enforcing and hence invulnerable to further self-enforcing deviations. The main result of this paper is that much of the strategic complexity introduced by joint-deviations and renegotiations is redundant, and in infinitely-repeated games with discounting every equilibrium outcome can be supported by a stationary set of optimal penal codes as in Abreu (1988). In addition, I prove existence of equilibrium both in stage games and in repeated games, and provide an iterative procedure for computing the unique equilibrium-payoff setCoalition, Renegotiation, Game Theory

On dominance solvable games and equilibrium selection theories

Game Theory;Equilibrium Theory

Computing Perfect Stationary Equilibria in Stochastic Games

The notion of stationary equilibrium is one of the most crucial solution concepts in stochastic games. However, a stochastic game can have multiple stationary equilibria, some of which may be unstable or counterintuitive. As a refinement of stationary equilibrium, we extend the concept of perfect equilibrium in strategic games to stochastic games and formulate the notion of perfect stationary equilibrium (PeSE). To further promote its applications, we develop a differentiable homotopy method to compute such an equilibrium. We incorporate vanishing logarithmic barrier terms into the payoff functions, thereby constituting a logarithmic-barrier stochastic game. As a result of this barrier game, we attain a continuously differentiable homotopy system. To reduce the number of variables in the homotopy system, we eliminate the Bellman equations through a replacement of variables and derive an equivalent system. We use the equivalent system to establish the existence of a smooth path, which starts from an arbitrary total mixed strategy profile and ends at a PeSE. Extensive numerical experiments further affirm the effectiveness and efficiency of the method