Deviations, Dynamics, and Equilibrium Refinements

Refinements of Nash Equilibrium

In game theory, “refinement” refers to the selection of a subset of equilibria, typically on the grounds that the selected equilibria are more plausible than other equilibria. These notes are a brief, largely informal, survey of some of the most heavily used refinements. Throughout, “equilibria” means Nash equilibria (NE), unless I state otherwise explicitly. And throughout, I assume that the g...

Learning and Equilibrium Refinements in Signalling Games∗

We propose two new signalling-game refinements that are microfounded in a model of patient Bayesian learning. Agents are born into player roles and play the signalling game against a random opponent each period. Inexperienced agents know their opponents’ payoff functions but not the prevailing distribution of opponents’ play. One refinement corresponds to an upper bound on the set of possible l...

Counterfactuals, belief changes, and equilibrium refinements

Refinements of Nash equilibrium in potential games

A strategic-form game is a potential game if the incentive of all players to change their strategy can be expressed in one global function, called the game’s potential. Potential games have many applications in Economics and other disciplines (cf. Rosenthal 1973, Monderer and Shapley 1996, Ostrovsky and Schwarz 2005, Armstrong and Vickers 2001, Myatt and Wallace 2009, inter alia). Potential gam...

On equilibrium refinements in supermodular games

We show that supermodular games satisfying sequential better-reply security possess a pure strategy perfect equilibrium and a strategically stable set of pure strategy equilibria. We illustrate that in continuous supermodular games, perfect equilibria may contain weakly dominated actions. Moreover, in discontinuous supermodular games satisfying sequential better-reply security, perfect equilibr...