Coordination Games on Directed Graphs

TL;DR

This paper investigates coordination games on directed graphs, revealing their computational complexity and identifying classes where strong equilibria can be efficiently computed.

Contribution

It demonstrates the NP-completeness of equilibrium existence and provides linear-time algorithms for specific classes of these games.

Findings

Existence of pure Nash equilibria is not guaranteed.

Determining equilibrium existence is NP-complete.

Strong equilibria can be found in linear time for certain classes.

Abstract

We study natural strategic games on directed graphs, which capture the idea of coordination in the absence of globally common strategies. We show that these games do not need to have a pure Nash equilibrium and that the problem of determining their existence is NP-complete. The same holds for strong equilibria. We also exhibit some classes of games for which strong equilibria exist and prove that a strong equilibrium can then be found in linear time.