Fourier decomposition of payoff matrix for symmetric three-strategy games

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

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

In spatial evolutionary games the payoff matrices are used to describe pair interactions among neighboring players located on a lattice. Now we introduce a way how the payoff matrices can be built up as a sum of payoff components reflecting basic symmetries. For the two-strategy games this decomposition reproduces interactions characteristic to the Ising model. For the three-strategy symmetric games the Fourier components can be classified into four types representing games with self-dependent and cross-dependent payoffs, variants of three-strategy coordinations, and the rock-scissors-paper (RSP) game. In the absence of the RSP component the game is a potential game. The resultant potential matrix has been evaluated. The general features of these systems are analyzed when the game is expressed by the linear combinations of these components.

Original languageEnglish
Article number042811
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume90
Issue number4
DOIs
Publication statusPublished - Oct 20 2014

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games
Game
decomposition
Decompose
matrices
Potential Games
Evolutionary Game
Dependent
rocks
Interaction
Ising Model
Strategy
Linear Combination
Ising model
Symmetry
interactions
symmetry

ASJC Scopus subject areas

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

Cite this

Fourier decomposition of payoff matrix for symmetric three-strategy games. / Szabó, G.; Bodó, Kinga S.; Allen, Benjamin; Nowak, Martin A.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 90, No. 4, 042811, 20.10.2014.

Research output: Contribution to journalArticle

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