A dynamical view of different solution paradigms in two-person symmetric games: Nash vs co-action equilibria

TL;DR

This paper offers a dynamical systems perspective on two solution concepts in symmetric two-player games, highlighting differences between Nash and co-action equilibria through analysis of classic games.

Contribution

It introduces a dynamical framework to compare Nash and co-action equilibria, providing equilibrium refinement and insights into strategy quality in symmetric games.

Findings

Dynamical view refines Nash equilibria, resolving multiple solutions.

Co-action equilibria often lead to more cooperative strategies.

Analysis of Prisoner's Dilemma, Chicken, and Stag-Hunt illustrates differences.

Abstract

The study of games and their equilibria is central to developing insights for understanding many socio-economic phenomena. Here we present a dynamical systems view of the equilibria of two-person, payoff-symmetric games. In particular, using this perspective, we discuss the differences between two solution concepts for such games - namely, those of Nash equilibrium and co-action equilibrium. For the Nash equilibrium, we show that the dynamical view can provide an equilibrium refinement, selecting one equilibrium among several possibilities, thereby solving the issue of multiple equilibria that appear in some games. We illustrate in detail this dynamical perspective by considering three well known 2-person games namely the Prisoner's Dilemma, game of Chicken and the Stag-Hunt. We find that in all of these cases, co-action equilibria tends to correspond to `nicer' strategies than those corresponding to Nash equilibria.