Networks preserving evolutionary equilibria and the power of randomization

We study a natural extension of classical evolutionary game theory to a setting in which pairwise interactions are restricted to the edges of an undirected graph or network. We generalize the definition of an evolutionary stable strategy (ESS), and show a pair of complementary results that exhibit the power of randomization in our setting: subject to degree or edge density conditions, the classical ESS of any game are preserved when the graph is chosen randomly and the mutation set is chosen adversarially, or when the graph is chosen adversarially and the mutation set is chosen randomly. We examine natural strengthenings of our generalized ESS definition, and show that similarly strong results are not possible for them. Categories and Subject Descriptors J.4 [Social and Behavioral Sciences]: Economics General Terms Economics, Theory Keywords Game Theory, Evolutionary Stable Strategy, Networks

• Type: Conference
• Year: 2006
• Where: SIGECOM
• Authors: Michael S. Kearns, Siddharth Suri
• Keywords: Classical Evolutionary Game, Evolutionary Stable Strategy, Game Theory, SIGECOM 2006