On the NP-completeness of Finding an Optimal Strategy in Games with Common Payoffs

TL;DR

This paper proves that finding an optimal joint strategy in simple, common-payoff games is NP-complete, highlighting computational complexity even in straightforward game scenarios.

Contribution

It establishes the NP-completeness of determining the existence of a joint strategy with a specified expected payoff in simple, common-interest games.

Findings

NP-complete problem of strategy existence

Complexity holds even in simple game structures

Implications for computational game theory

Abstract

Consider a very simple class of (finite) games: after an initial move by nature, each player makes one move. Moreover, the players have common interests: at each node, all the players get the same payoff. We show that the problem of determining whether there exists a joint strategy where each player has an expected payoff of at least r is NP-complete as a function of the number of nodes in the extensive-form representation of the game.