Algorithmic Rationality: Game Theory with Costly Computation

TL;DR

This paper introduces a game-theoretic framework accounting for costly computation by strategic agents, explaining observed behaviors and establishing conditions for equilibrium existence.

Contribution

It extends traditional game theory to include computational costs, providing explanations for behavior and conditions for equilibrium in complex strategic settings.

Findings

Traditional equilibria may not exist with costly computation.

The framework explains behaviors in repeated prisoner's dilemma and rock-paper-scissors.

Conditions for equilibrium existence are identified.

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 of 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.