Finite population trust game replicators

Abstract

Our previous work introduced the N player trust game and examined the dynamics of this game using replicator dynamics for an infinite population. In finite populations, quantization becomes a necessity that introduces discontinuity in the trajectory space, which can impact the dynamics of the game differently. In this paper, we present an analysis of replicator dynamics of the N player trust game in finite populations. The analysis reveals that, quantization indeed introduces fixed points in the interior of the 2-simplex that were not present in the infinite population analysis. However, there is no guarantee that these fixed points will continue to exist for any arbitrary population size; thus, they are clearly an artifact of quantization. In general, the evolutionary dynamics of the finite population are qualitatively similar to the infinite population. This suggests that for the proposed trust game, trusters will be extinct if the population contains an untrustworthy player. Therefore, trusting is an evolutionary unstable strategy.