Beyond Nash equilibrium: Solution concepts for the 21st century

Abstract

An often useful way to think of security is as a game between an adversary and the "good" participants in the protocol. Game theorists try to understand games in terms of solution concepts; essentially, this is a rule for predicting how the game will be played. The most commonly used solution concept in game theory is Nash equilibrium. 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 represent 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., randomized) strategies, there is guaranteed to be a Nash equilibrium [11] (this was, in fact, the key result of Nash's thesis). © 2011 Springer-Verlag.