Martin Kaae Jensen
() and Alexandros Rigos
Martin Kaae Jensen: School of Economics, University of Surrey, Postal: School of Economics, Ground Floor AD Building, University of Surrey, Guildford, Surrey GU2 7XH, UK
Alexandros Rigos: Department of Economics, Lund University, Postal: Department of Economics, School of Economics and Management, Lund University, Box 7082, S-220 07 Lund, Sweden
Abstract: This study considers evolutionary games with non-uniformly random matching when interaction occurs in groups of n >= 2 individuals using pure strategies from a finite strategy set. In such models, groups with different compositions of individuals generally co-exist and the reproductive success (fitness) of a specific strategy varies with the frequencies of different group types. These frequencies crucially depend on the matching process. For arbitrary matching processes (called matching rules), we study Nash equilibrium and ESS in the associated population game and show that several results that are known to hold for population games under uniform random matching carry through to our setting. In our most novel contribution, we derive results on the efficiency of the Nash equilibria of population games and show that for any (fixed) payoff structure, there always exists some matching rule leading to average fitness maximization. Finally, we provide a series of applications to commonly studied normal-form games.
29 pages, First version: September 28, 2017. Revised: March 6, 2018.
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