Fairness Norms Can Explain the Emergence of Specific Cooperation Norms in the Battle of the Prisoner's Dilemma

Abstract

Cooperation norms often emerge in situations, where the long term collective benefits help to overcome short run individual interests, for instance in repeated Prisoner's Dilemma (PD) situations. Often, however, there are different paths to cooperation, benefiting different kinds of actors to different degrees. This leads to payoff asymmetries even in the state of cooperation, and consequently can give rise to normative conflicts about which norms should be in place. This norm coordination problem will be modeled as a Battle of the Sexes game (BoS) with different degrees of asymmetry in payoffs. I combine the PD and the BoS to the 3 × 3 Battle of the Prisoner's Dilemma (BOPD) with several asymmetric cooperative and 1 noncooperative equilibria. Game theoretical and “behavioral” predictions are derived about the kind of norms that are likely to emerge under different shadows of the future and degrees of asymmetry and tested in a lab experiment. The experimental data show that game theory fairly well predicts the basic main effects of the experimental manipulations but “behavioral” predictions perform better in describing the equilibrium selection process of emerging norms.

Keywords:

• experiment
• norms
• social dilemmas

ACKNOWLEDGMENTS

This article benefitted from comments made by Werner Güth, Heiko Rauhut, Gerd Gigerenzer, Ryan Murphy, and the IMPRS Workshop 2011 at the MPI for Human Development in Berlin, Germany.

Notes

¹In this sense, TRIGGER should be understood as a form of punishment, an important feature in many other definitions of social norms. It does not require, though, an internalization of the norm.

²It is often assumed that (T + S)/2 < R in PD. This is, however, an unnecessary limitation of the PD.

Note. PD = Prisoner's Dilemma; BOPD = Battle of the Prisoner's Dilemma.

Note. All models are random effects logistic regressions controlling for correlated errors on the subject level (see equation 4). The first model on the left predicts the general degree of cooperation (i.e., non-D choices). The second model investigates the joint probabilities of turn taking between two choices, whereas the model on the right predicts cooperation in pure strategies. The “sign” columns list the theoretically expected signs. Confidence intervals are based on 1,000 bootstraps. Bootstrapped 95% confidence intervals in brackets.

*p < 0.05. ** p < 0.01. *** p < 0.001.

Note. PD = Prisoner's Dilemma; BOPD = Battle of the Prisoner's Dilemma. Different forms of cooperation are likely to emerge in different games. All models are random effects logistic regressions. The first two models on the left predict the general degree of cooperation (i.e., non-D choices). The second block of models investigates the joint probabilities of turn taking between two choices, whereas the two models on the right predict cooperation in pure strategies. The “sign”-columns list the theoretically expected signs. Bootstrapped 95% confidence intervals in brackets (1,000 bootstraps).

*p < 0.05. **p < 0.01. ***p < 0.001.

³We ran the same regressions with and without competitive players and the results are robust.

Note. Different forms of cooperation are likely to emerge for different types of actors. All models are random effects logistic regressions. The model on the left predicts the general degree of cooperation (i.e., non-D choices) among prosocial and maximizing types. The second model investigates the joint probabilities of turn taking between two choices, given the fairness types. The third model on the right predicts cooperation in pure strategies for the two types. The “sign”-columns list the expected signs as predicted by “behavioral” theory. Bootstrapped 95% confidence intervals in brackets (1,000 bootstraps).

*p < 0.05. **p < 0.01. ***p < 0.001.