Evolution of Preferences in Multiple Populations
Yu-Sung Tu, Wei-Torng Juang
TL;DR
This paper extends the indirect evolutionary approach to evolve preferences to a multi-population, asymmetric matching framework with $n$ populations, where each player’s realized fitness is given by a material payoff and observability of opponents’ preferences is governed by $p\in[0,1]$. It develops a stability analysis across perfect, no, and partial observability, introducing a configuration $(\mu,b)$ with post-entry mutations and focal equilibria, and showing that stability requires Pareto-efficient outcomes under perfect observability, with two-population results extending to three or more populations via the concept of strict union Nash equilibrium. Under no observability, aggregate outcomes must be Nash equilibria of the objective game, and materialist preferences may gain a fitness advantage; under partial observability, robustness results show that almost-perfect observability weakens efficiency requirements and that observed outcomes can shift toward weaker Pareto notions. Overall, the work clarifies how asymmetry and degrees of observability influence which preference types can persist and how efficiency notions relate to stability in multi-population evolutionary settings.
Abstract
We study the evolution of preferences in multi-population settings that allow matches across distinct populations. Each individual has subjective preferences over potential outcomes, and chooses a best response based on his preferences and the information about the opponents' preferences. Individuals' realized fitnesses are given by material payoff functions. Following Dekel et al. (2007), we assume that individuals observe their opponents' preferences with probability $p$. We first derive necessary and sufficient conditions for stability for $p=1$ and $p=0$, and then check the robustness of our results against small perturbations on observability for the case of pure-strategy outcomes.