bipartite graphs as models of population structures in evolutionary multiplayer games一式两份的图作为模型的人口结构进化的多人游戏.pdfVIP

Bipartite Graphs as Models of Population Structures in Evolutionary Multiplayer Games ˜ ¤a ¤b Jorge Pena* , Yannick Rochat Institute of Applied Mathematics, Faculty of Social and Political Sciences, University of Lausanne, Lausanne, Switzerland Abstract By combining evolutionary game theory and graph theory, ‘‘games on graphs’’ study the evolutionary dynamics of frequency-dependent selection in population structures modeled as geographical or social networks. Networks are usually represented by means of unipartite graphs, and social interactions by two-person games such as the famous prisoner’s dilemma. Unipartite graphs have also been used for modeling interactions going beyond pairwise interactions. In this paper, we argue that bipartite graphs are a better alternative to unipartite graphs for describing population structures in evolutionary multiplayer games. To illustrate this point, we make use of bipartite graphs to investigate, by means of computer simulations, the evolution of cooperation under the conventional and the distributed N-person prisoner’s dilemma. We show that several implicit assumptions arising from the standard approach based on unipartite graphs (such as the definition of replacement neighborhoods, the intertwining of individual and group diversity, and the large overlap of interaction neighborhoods) can have a large impact on the resulting evolutionary dynamics. Our work provides a clear example of the importance of construction procedures in games on graphs, of the suitability of bigraphs and hypergraphs for computational modeling, and of the importance of concepts from social network analysis such