Evolutionary games on graphs

Abstract

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by non-mean-field-type social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.

Combination with anti-tit-for-tat remedies problems of tit-for-tat

“…In many studies, reciprocity is a particularly important idea to explain cooperation between rational players. In the iterated version of the Prisoner's Dilemma (IPD) game, the repetition makes it profitable for each player to cooperate because one has to take the other's reaction into account [1,2,3,4,5,6]. As long as both are sufficiently patient and free from error, therefore, the players cooperate from the first encounter and this continues forever.…”

Does mobility decrease cooperation?

“…The onset and sustainability of cooperation in social and non social populations is still an open and challenging problem [3,7,26,35,48] that has been tackled with tools from different fields, ranging from psychological and social sciences to statistical physics. Although involving a cost to the performer, cooperative behavior is ubiquitous in biological populations.…”

Competing associations in bacterial warfare with two toxins

“…In any traditional analysis of the spatial Rock-ScissorsPaper game identical invasion rates are assumed (for a survey see the reviews by Tainaka, 2001;Szabo´and Fa´th, 2007). Detailed investigations have proven later that the introduction of different invasion rates does not modify the basic conclusions significantly.…”