Time and the Prisoner's Dilemma

TL;DR

This paper explores how computational constraints influence cooperation in the repeated Prisoner's Dilemma, proposing a new game variant and using competitive analysis to understand strategic choices under resource limitations.

Contribution

It introduces a minimal computational bound for cooperation and a variant with an opt-out option, applying competitive analysis to bounded rationality in game theory.

Findings

Computational bounds can enable cooperation in repeated Prisoner's Dilemma.

A game variant with an opt-out option promotes cooperative strategies.

Sub-optimal strategies may be optimal for resource-bounded players.

Abstract

This paper examines the integration of computational complexity into game theoretic models. The example focused on is the Prisoner's Dilemma, repeated for a finite length of time. We show that a minimal bound on the players' computational ability is sufficient to enable cooperative behavior. In addition, a variant of the repeated Prisoner's Dilemma game is suggested, in which players have the choice of opting out. This modification enriches the game and suggests dominance of cooperative strategies. Competitive analysis is suggested as a tool for investigating sub-optimal (but computationally tractable) strategies and game theoretic models in general. Using competitive analysis, it is shown that for bounded players, a sub-optimal strategy might be the optimal choice, given resource limitations.