Discrimination in Heterogeneous Games

TL;DR

This paper analyzes how individuals in heterogeneous games choose to discriminate based on opponent types, revealing equilibrium conditions and limits in anti-coordination versus coordination games, with implications for psychological behavior.

Contribution

It introduces a theoretical framework for understanding discrimination in heterogeneous games, highlighting the existence and limits of symmetric Nash equilibria.

Findings

Discrimination occurs in anti-coordination games but not in coordination games.

Maximum of three groups can be discriminated in equilibrium.

Theoretical results relate to observed psychological behaviors.

Abstract

In this paper, we consider coordination and anti-coordination heterogeneous games played by a finite population formed by different types of individuals who fail to recognize their own type but do observe the type of their opponent. We show that there exists symmetric Nash equilibria in which players discriminate by acting differently according to the type of opponent that they face in anti-coordination games, while no such equilibrium exists in coordination games. Moreover, discrimination has a limit: the maximum number of groups where the treatment differs is three. We then discuss the theoretical results in light of the observed behavior of people in some specific psychological contexts.