Evolutionarily stable networks

Abstract

This paper studies the evolution of behavior governing strategic network formation. I first propose a general framework of evolutionary selection in non-cooperative games played in heterogeneous groups under assortative matching. I show that evolution selects strate-gies that (i) execute altruistic actions towards others in the interaction group with rate of altruism equal to the rate of assortative matching and (ii) are stable against pairwise coali-tional deviations under two qualifications: pairs successfully coordinate their deviations with probability equaling the rate of assortative matching and externalities are taken into account with the same weight. I then restrict the domain of interaction games to strategic network formation and define a new stability concept for networks called ‘evolutionarily stable networks’. The concept fuses ideas of solution concepts used by evolutionary game theory and network formation games. In a game of communication, evolutionarily stable networks prescribe equal information access. In the classic co-authorship game only the least efficient network, the complete network, is evolutionarily stable. Finally, I present an evolutionary model of homophilistic network formation between identity groups and show that extreme high degrees of homophily may persist even in groups with virtually no preference for it; thus societies may struggle to eliminate segregation between identity groups despite becoming increasingly tolerant.

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Reference

Péter Bayer, “Evolutionarily stable networks”, TSE Working Paper, n. 23-1487, November 2023.