8 - Beyond Nash Equilibrium: Solution Concepts for the 21st Century

Summary

Abstract

Nash equilibrium is the most commonly-used notion of equilibrium in game theory. However, it suffers from numerous problems. Some are well known in the game theory community; for example, the Nash equilibrium of the repeated prisoner's dilemma is neither normatively nor descriptively reasonable. However, new problems arise when considering Nash equilibrium from a computer science perspective: for example, Nash equilibrium is not robust (it does not tolerate ‘faulty’ or ‘unexpected’ behaviour), it does not deal with coalitions, it does not take computation cost into account, and it does not deal with cases where players are not aware of all aspects of the game. Solution concepts that try to address these shortcomings of Nash equilibrium are discussed.

Introduction

Nash equilibrium is the most commonly-used notion of equilibrium in game theory. Intuitively, a Nash equilibrium is a strategy profile (a collection of strategies, one for each player in the game) such that no player can do better by deviating. The intuition behind Nash equilibrium is that it represents a possible steady state of play. It is a fixed-point where each player holds correct beliefs about what other players are doing, and plays a best response to those beliefs. Part of what makes Nash equilibrium so attractive is that in games where each player has only finitely many possible deterministic strategies, and we allow mixed (i.e., randomised) strategies, there is guaranteed to be a Nash equilibrium [Nash, 1950a] (this was, in fact, the key result of Nash's thesis).