Cooperation, but No Reciprocity: Individual Strategies in the Repeated Prisoner’s Dilemma

Abstract

A recent advance in our understanding of repeated PDs is the detection of a threshold δ at which laboratory subjects start to cooperate predictively. This threshold is substantially above the classic threshold "existence of Grim equilibrium" and has been characterized axiomatically by Blonski, Ockenfels, and Spagnolo (2011, BOS). In this paper, I derive its behavioral foundations. First, I show that the threshold is equivalent to existence of a "Semi-Grim" equilibrium σ cc > σ cd = σ dc > σ dd . It is cooperative (σ cc > 0.5), non-reciprocal (σ cd = σ dc ), and robust to imperfect monitoring ("belief-free"). Next, I show that the no-reciprocity condition σ cd = σ dc also follows from robustness to random-utility perturbations (logit equilibrium). Finally, I re-analyze strategies in four recent experiments and find that the majority of subjects indeed plays Semi-Grim when it is an equilibrium strategy, which explains δ 's predictive success.JEL-Codes: C72, C73, C92

The Influence of Trust Score on Cooperative Behavior

“…In the repeated game, trust potentially accrues as both players react to their partner's past behavior in subsequent rounds. To our knowledge, the theoretical analysis for participant behavior in the infinitely repeated trust game is still an open question [Breitmoser 2015;Bruttel and Kamecke 2012]. However, we note that the two players experience consequence at different times.…”

“…Though related, they are not the same constructs [Fetchenhauer and Dunning 2009]. Consistent with [Breitmoser 2015], we consider reputation as the collective opinion of a community regarding a particular participant, while trust is the specific relationship between a pair of participants. Participant reputation is a global value, while trust in a participant is a personal value and differs by partners [Hoelz and Ralha 2015].…”

The Evolution of Cooperation: The Role of Costly Strategy Adjustments

“…2 Our work contributes to three strands of literature. First, we contribute to the growing experimental research that investigates conditions under which cooperation arises in repeated prisoner's dilemma games (Dal Bó 2005;Duffy and Ochs 2009;Camera and Casari 2009;Stahl 2011;Dal Bó and Fréchette 2011;Bruttel and Kamecke 2012;Friedman and Oprea 2012;Fudenberg, Rand, and Dreber 2012;Stahl 2013;Honhon and Hyndman 2015;Bigoni et al 2015;Breitmoser 2015;Peysakhovich and Rand 2016;Cason, Lau, and Mui 2017;Dal Bó and Fréchette 2016;Embrey, Fréchette, and Yuksel 2017;and Romero and Rosokha 2018). Dal Bó and Fréchette (2018) provides a review of the literature on repeated prisoner's dilemma games.…”

The Evolution of Cooperation: The Role of Costly Strategy Adjustments

“…2 Our work contributes to three strands of literature. First, we contribute to the growing experimental research that investigates conditions under which cooperation arises in repeated prisoner's dilemma games (Dal Bó 2005;Duffy and Ochs 2009;Camera and Casari 2009;Stahl 2011;Dal Bó and Fréchette 2011;Bruttel and Kamecke 2012;Friedman and Oprea 2012;Fudenberg, Rand, and Dreber 2012;Stahl 2013;Honhon and Hyndman 2015;Bigoni et al 2015;Breitmoser 2015;Peysakhovich and Rand 2016;Cason, Lau, and Mui 2017;Dal Bó and Fréchette 2016;Embrey, Fréchette, and Yuksel 2017;and Romero and Rosokha 2018). Dal Bó and Fréchette (2018) provides a review of the literature on repeated prisoner's dilemma games.…”