Abstract

We prove the existence of a trembling-hand perfect equilibrium within a class of compact, metric, and possibly discontinuous games. Our conditions for existence are easily verified in a variety of economic games.

Highlights

  • A Nash equilibrium is trembling-hand perfect if it is robust to the players’ choice of unintended strategies through slight trembles

  • In a world where agents make slight mistakes, trembling-hand perfection requires that there exist at least one perturbed model of low-probability errors with an equilibrium that is close to the original equilibrium, which is thought of as an approximate description of “slightly constrained” rational behavior, or what could be observed if the players were to interact within the perturbed game

  • A Nash equilibrium that is not trembling-hand perfect cannot be a good prediction of equilibrium behavior under any “conceivable” theory of imperfect choice

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Summary

Introduction

A Nash equilibrium is trembling-hand perfect if it is robust to the players’ choice of unintended strategies through slight trembles. By adapting arguments from Carbonell-Nicolau [11], this paper addresses the issue of existence for an infinite-game extension of Selten’s [1] original notion of trembling-hand perfection This extension corresponds to Simon and Stinchcombe’s [10] strong approach when the universe of games is restricted by continuity of the players’ payoffs. We show that this condition gives payoff security of certain Selten perturbations (Lemma 2) We combine this finding with known results to establish the existence of a trembling-hand perfect equilibrium in discontinuous games (Theorem 2).

Perturbed Games and Perfect Equilibria
The mixed extension of G is the game
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