Behavior in Repeated Prisoner's Dilemma Games with Shifted Outcomes Analyzed with a Statistical Learning Model

ABSTRACT

We address whether cooperative behavior in a repeated Prisoner's Dilemma (PD) is more easily achieved under “good circumstances” (all payoffs in the constituent PD are positive), “bad circumstances” (payoffs are negative), or “mixed circumstances.” To analyze the behavior in these repeated PDs, we developed and applied a learning model that improves upon standard learning models in two ways: (1) It allows for statistical tests of the parameter estimates, and (2) it allows for the incorporation of independent variables (e.g., subject or game characteristics). The model is applied to the data of the repeated PD experiment in van Assen and Snijders (2004 2005). Our findings demonstrate that our model can be used to identify and test how learning differs across persons and across different circumstances.

Keywords:

• prisoner's dilemma
• collective action
• learning
• learning models
• risk
• risk preferences

Notes

²The PD with Δ = 0 and S = −5 was treated as a positive PD because according to standard game-theoretic predictions only the values of T, R, and P matter, and not the value of S (Raub and Snijders, 1997; van Assen, 1998).

³The goodness of fit test comparing observed and predicted proportions yielded a chi-square value of 3.24. This result is not even significant for 1 degree of freedom, even though many more (dependent) proportions are fitted.

⁴That is, each of β₀₀ and β₁₁ is cancelled out by each of β₁₀ and β₀₁.

¹See van Assen and Snijders (2004) for details of the experiment.