Motives for Cooperation in the One-Shot Prisoner’s Dilemma

Abstract

We investigate the motives for cooperation in the one-shot Prisoner’s Dilemma (PD). A prior study finds that cooperation rates in one-shot PD games can be ranked empirically by the social surplus from cooperation. That study employs symmetric payoffs from cooperation in simultaneous PD games. Hence, in that setting, it is not possible to discern the motives for cooperation since three prominent social welfare criteria, social surplus (efficiency) preferences, Rawlsian maximin preferences, and inequity aversion make the same predictions. In the present paper, we conduct an experiment to identify which of these social preferences best explains differences in cooperation rates and to study the effects of the risk of non-cooperation.

Keywords:

• Experiment
• cooperation
• social preferences
• risk
• strategic interaction

Acknowledgement

We thank Megan Luetje for recruiting experimental participants, and the Economic Science Institute at Chapman University for their financial support. We also thank Jack Stecher, Nat Wilcox, and workshop participants at the Society for the Advancement of Economic Theory, Economic Science Association, and Chapman University for their helpful comments.

Notes

1 The following strict rankings of cooperation rates implicitly assume that the distribution of social preference parameters is such that at least one player in the sample has parameter values that imply $U\left(6,6\right)>U(6,4)$ (for conditional efficiency, Rawlsian, and inequity-averse preferences) and that at least one player in the sample has parameter values such that $U\left(4,4\right)>U(6,4)$ for inequity aversion.

2 An alternative design choice would be to present each of the six games one at a time instead of presenting all six games at one time. There are tradeoffs in this presentation choice: sequential choices can introduce unanticipated order effects, while simultaneous choices may cause players to consider differences in games otherwise unnoticed. Given that all six games were explicitly showed in the instructions before participants made choices, we opted to show all games at once.

3 We solicit beliefs after choices were made to avoid affecting cooperation. Other studies examining the prisoner’s dilemma game find that participants were significantly less likely to cooperate in a prisoner’s dilemma game where their beliefs about what others would do were first elicited than never elicited (Croson 2000). In the next part of our experiment, participants made choices conditional on knowing their partner moved first and cooperated or knowing their partner moved first and defected, which theoretically is independent of beliefs about their partner’s cooperation.

4 A new version of the cognitive reflection test (CRT) was used because the original version of Frederick (2005) and the more recent extension of Toplak et al. (2014) have been used in other experiments at the laboratories and may be familiar to the participants in the subject pool.

5 A decision in the simultaneous game or the second-mover game conditional upon first-mover cooperation was consistent for a type when the participant’s decision to cooperate for the pair of games met the criteria in Table 6.