Abstract

We introduce simple guilt into a generic prisoner’s dilemma (PD) game and solve for the equilibria of the resulting psychological game. It is shown that for all guilt parameters, it is a pure strategy equilibrium that both players defect. But if the guilt parameter surpasses a threshold, a mixed strategy equilibrium and a pure strategy equilibrium in which both players cooperate emerge. We implement three payoff constellations of the PD game in a laboratory experiment and find in line with our equilibrium analysis that first- and second-order beliefs are highly correlated and that the probability of cooperation depends positively on these beliefs. Maximum likelihood estimations of a model of noisy introspection reveal that experimental data is best fitted with positive guilt levels and that omission of guilt results in a substantial increase in the noise parameters.

۱٫ Introduction

The observation that individual (expected) payoff maximization may lead to a socially undesirable (Pareto inefficient) outcome is the key insight of the Prisoner’s Dilemma (PD) game. But by now it is also well-established that a non-negligible fraction of subjects participating in laboratory experiments decides to cooperate in the PD game even though they should not do so from a purely materialistic point of view (see, Chaudhuri, 2011, for an overview). Rationalizations of this behavior include other regarding preferences—among which we would like to highlight models of altruism (cf. Andreoni, 1990, inequality aversion (cf. Bolton & Ockenfels, 2000; Fehr & Schmidt, 1999) and preferences for efficiency (cf. Engelmann & Strobel, 2004)—, intentions/reciprocity (cf. Cox et al., 2007; Dufwenberg & Kirchsteiger, 2004; Falk & Fischbacher, 2006; Rabin, 1993), and emotions (cf. Eisenberg, 2000; Elster, 1998).

The literature in social psychology (cf. Baumeister et al., 1994) emphasizes the role of guilt for the maintenance, protection, and strengthening of interpersonal relationships. This emotion motivates individuals in particular to exhibit pro-social behavior. In the economic literature, Battigalli and Dufwenberg (2007, 2009) define simple guilt as the degree by which player ? suffers from letting another player ? down towards her payoff expectation. Since the payoff expectations of player ? depend on her first-order beliefs about the strategy of player ?, the expected let-down of player ? towards player ? is related to ?’s second-order beliefs. That is, the utility function of the players depend on second-order beliefs.