Fourier decomposition of payoff matrix for symmetric three-strategy games.
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.
Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary and Regional Knowledge Centre, Eötvös University, Irányi Dániel u. 4, H-8000 Székesfehérvár, Hungary.
György
G
Szabó
Roland Eötvös University, Institute of Physics, Pázmány P. sétány 1/A, H-1117 Budapest, Hungary.
Kinga S
KS
Bodó
Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, Massachusetts 02138, USA.
Benjamin
B
Allen
Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, Massachusetts 02138, USA and Department of Mathematics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138, USA.
Martin A
MA
Nowak
D005583:Fourier Analysis; D005716:Game Theory