Robust equilibria: Normal-form, extensive-form, and repeated games

Rachel C Hemphill, Purdue University

Abstract

This work continues previous work done with William Geller, in which we introduced the concepts of ϵ-dominance, most-dominance, the ϵ-robust equilibrium, and the globally ϵ-robust equilibrium. These were developed in response to certain "paradoxes" in the literature, where the Nash equilibrium predictions differ strikingly from intuition and experimental results. The problem games studied here include Centipede, Traveler's Dilemma, extreme forms of the games Stag Hunt and Chicken, and a restricted-strategy finitely-repeated Prisoner's Dilemma. For finite normal-form games, ϵ-robust equilibrium and globally ϵ-robust equilibrium are refinements of Radner's ϵ-equilibrium and when ϵ = 0 are refinements of Nash equilibrium. I will discuss the different criteria used in the definition of ϵ-robust equilibrium for normal-form games. I expand ϵ-dominance, most-dominance, the ϵ-robust equilibrium, and the globally ϵ-robust equilibrium to finite extensive-form games and to finitely-repeated games. For finite extensive-form games, ϵ-robust equilibrium and globally ϵ-robust equilibrium are refinements of ϵ-subgame-perfect equilibrium and when ϵ = 0 are refinements of subgame-perfect Nash equilibrium. For finitely-repeated games, ϵ-robust equilibrium and globally ϵ-robust equilibrium are refinements of contemporaneous perfect ϵ-equilibrium and when ϵ = 0 are refinements of contemporaneous perfect Nash equilibrium.

Degree

Ph.D.

Advisors

Geller, Purdue University.

Subject Area

Mathematics

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