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Prospect dynamics and loss dominance

Ryoji Sawa,Jiabin Wu

Published 2018 in Games Econ. Behav.

ABSTRACT

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 2 x 2 coordination game. When an agent revises her strategy, she compares the payoff from each strategy to a reference point which is endogenously formed. Based on the comparison, she makes a (possibly stochastic) choice. We call the resulting dynamics prospect dynamics. Three types of endogenous reference points are examined: social average, expectations and status-quos. We find that risk-dominance is no longer sufficient to guarantee stochastic stability under prospect dynamics with any type of reference points. Therefore, we propose a stronger concept, loss-dominance: a strategy is loss-dominant if it is both risk-dominant strategy and the maximin strategy. This concept captures people's psychological needs to avoid not only risks but also losses. We show that it serves as a natural selection refinement for games with loss-averse agents. 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 also characterize the precise conditions for stochastic stability in games with no loss-dominant strategy.

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