The graph structure of two-player games.

ABSTRACT: In this paper, we analyse two-player games by their response graphs. The response graph has nodes which are strategy profiles, with an arc between profiles if they differ in the strategy of a single player, with the direction of the arc indicating the preferred option for that player. Response graphs, and particularly their sink strongly connected components, play an important role in modern techniques in evolutionary game theory and multi-agent learning. We show that the response graph is a simple and well-motivated model of strategic interaction which captures many non-trivial properties of a game, despite not depending on cardinal payoffs. We characterise the games which share a response graph with a zero-sum or potential game respectively, and demonstrate a duality between these sets.

SUBMITTER: Biggar O 

PROVIDER: S-EPMC9892046 | biostudies-literature | 2023 Feb

REPOSITORIES: biostudies-literature