Sampling dynamics and stable mixing in hawk-dove games

TL;DR

This paper investigates how sampling-based learning dynamics in hawk-dove games can lead populations to converge to inefficient mixed equilibria, contrasting with traditional convergence to pure equilibria.

Contribution

It demonstrates that sampling dynamics can cause global convergence to mixed equilibria, challenging existing results about convergence to pure strategies in hawk-dove games.

Findings

Sampling dynamics induce convergence to mixed equilibria.

Traditional models predict convergence to pure equilibria.

Sampling behavior can sustain inefficient mixed states.

Abstract

The hawk-dove game admits two types of equilibria: an asymmetric pure equilibrium in which players in one population play hawk and players in the other population play dove, and an inefficient symmetric mixed equilibrium, in which hawks are frequently matched against each other. The existing literature shows that populations will converge to playing one of the pure equilibria from almost any initial state. By contrast, we show that plausible sampling dynamics, in which agents occasionally revise their actions by observing either opponents' behavior or payoffs in a few past interactions, can induce the opposite result: global convergence to one of the inefficient mixed stationary states.