Game Theory with Costly Computation

TL;DR

This paper introduces a game-theoretic framework that accounts for costly computation, explaining observed behaviors and establishing conditions for equilibrium existence, while linking cryptographic and game-theoretic approaches to protocol security.

Contribution

It develops a novel framework for strategic agents with costly computation, providing new insights into equilibrium existence and connecting cryptography with game theory.

Findings

Traditional equilibria may not exist with costly computation.

The framework explains behaviors in well-known games.

Cryptographic security notions relate to game-theoretic implementation.

Abstract

We develop a general game-theoretic framework for reasoning about strategic agents performing possibly costly computation. In this framework, many traditional game-theoretic results (such as the existence of a Nash equilibrium) no longer hold. Nevertheless, we can use the framework to provide psychologically appealing explanations to observed behavior in well-studied games (such as finitely repeated prisoner's dilemma and rock-paper-scissors). Furthermore, we provide natural conditions on games sufficient to guarantee that equilibria exist. As an application of this framework, we consider a notion of game-theoretic implementation of mediators in computational games. We show that a special case of this notion is equivalent to a variant of the traditional cryptographic definition of protocol security; this result shows that, when taking computation into account, the two approaches used for dealing with "deviating" players in two different communities -- Nash equilibrium in game theory and zero-knowledge "simulation" in cryptography -- are intimately related.