Prospect Dynamic and Loss Dominance

This paper investigates the role of loss-aversion in affecting the long-run equilibria of stochastic evolutionary dynamics. We consider a finite population of loss-averse agents who are repeatedly and randomly matched to play a symmetric two-player normal form game. When an agent revises her strategy, she compares the payoff from each strategy to a reference point. Based on the comparison, she makes a (possibly stochastic) choice. Under the resulting dynamics, called prospect dynamics, risk-dominance is no longer sufficient to guarantee stochastic stability in 2 by 2 coordination games. We propose a stronger concept, loss-dominance: a strategy is loss-dominant if it is both a risk-dominant strategy and a maximin strategy. This concept captures people's psychological needs to avoid not only risks but also losses. In a 2 by 2 coordination game, the state in which all agents play the loss-dominant strategy (if exists) is uniquely stochastically stable under prospect dynamics for any degree of loss-aversion and all types of reference points. We generalize the concept for symmetric two-player normal form games and show that generalized loss-dominance gives a sufficient condition for stochastic stability with loss-averse agents.