Testing Game-Theoretic Comparative Statics Using Bayesian Model Selection

Abstract

Aksoy and Weesie (2013) propose a formal-game-theoretic model that yields comparative statics predictions about the behavior of actors and actors’ expectations about behaviors of others in nonrepeated Prisoner's Dilemma games. They consider five competing specifications of this model. In this note, we present a Bayesian statistical method to test these five competing specifications, taking the hierarchical nature of the data into account. While this paper is a follow-up to Aksoy and Weesie (2013), the method we discuss is suitable to test multiple comparative statics and is, thus, useful to asses the fit of other game-theoretic models.

Keywords:

• Bayesian inference
• cooperation
• methodology

ACKNOWLEDGMENTS

We thank Herbert Hoijtink for his comments on AW13 which resulted in this paper.

Notes

¹There is also a frequentist, albeit not widely used literature on “combining p values” (see, e.g., Won, Morris, Lu, & Elston, 2009).

²The t_j values are rescaled to be between 0 and 10 for all of the five specifications such that the above priors remain uninformative.

³For the games with the same threshold values, any switch is counted as a Gutmann error. The more lenient approach of not counting switches in tied games as errors yielded the same conclusions.

⁴We experienced convergence problems when predicting expectations, especially for parameters related to error. Plugging in estimates from the models predicting behavior did not solve the convergence issue. As a result, for expectations we fitted “.” To ensure γ > 0, we imposed a Gamma(1000,1000) prior for γ. This specification is a reparametrized version of the specification in Eq. (1) where β₁ is assumed to be zero. Further alternative specifications, such as assuming a log-normal distribution for γ, yielded the same results.