title: Four classes of interactions for evolutionary games.
abstract: The symmetric four-strategy games are decomposed into a linear combination of 16 basis games represented by orthogonal matrices. Among these basis games four classes can be distinguished as it is already found for the three-strategy games. The games with self-dependent (cross-dependent) payoffs are characterized by matrices consisting of uniform rows (columns). Six of 16 basis games describe coordination-type interactions among the strategy pairs and three basis games span the parameter space of the cyclic components that are analogous to the rock-paper-scissors games. In the absence of cyclic components the game is a potential game and the potential matrix is evaluated. The main features of the four classes of games are discussed separately and we illustrate some characteristic strategy distributions on a square lattice in the low noise limit if logit rule controls the strategy evolution. Analysis of the general properties indicates similar types of interactions at larger number of strategies for the symmetric matrix games.
authors.affiliation: Institute of Technical Physics and Materials Science, Centre for Energy Research, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary.
authors.forename: György
authors.initials: G
authors.lastname: Szabó
authors.affiliation: Budapest University of Technology and Economics, Budafoki t 8, H-1111 Budapest, Hungary.
authors.forename: Kinga S
authors.initials: KS
authors.lastname: Bodó
authors.affiliation: Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, Massachusetts 02138, USA.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Allen
authors.affiliation: Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, Massachusetts 02138, USA.|Department of Mathematics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Martin A
authors.initials: MA
authors.lastname: Nowak
mesh_terms: D003198:Computer Simulation; D005716:Game Theory; D016014:Linear Models; D009010:Monte Carlo Method