Four classes of interactions for evolutionary games

G. Szabó, Kinga S. Bodó, Benjamin Allen, Martin A. Nowak

Research output: Contribution to journalArticle

23 Citations (Scopus)

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.

Original languageEnglish
Article number022820
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume92
Issue number2
DOIs
Publication statusPublished - Aug 27 2015

Fingerprint

Evolutionary Game
games
Game
Interaction
interactions
matrices
Class
Potential Games
Matrix Game
Orthogonal matrix
Logit
Evolution Strategies
Dependent
Symmetric matrix
Square Lattice
Parameter Space
Linear Combination
low noise
Strategy

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Four classes of interactions for evolutionary games. / Szabó, G.; Bodó, Kinga S.; Allen, Benjamin; Nowak, Martin A.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 92, No. 2, 022820, 27.08.2015.

Research output: Contribution to journalArticle

Szabó, G. ; Bodó, Kinga S. ; Allen, Benjamin ; Nowak, Martin A. / Four classes of interactions for evolutionary games. In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2015 ; Vol. 92, No. 2.
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