Bayesian Inference and Non-Bayesian Prediction and Choice: Foundations and an Application to Entry Games with Multiple Equilibria

As a central motivating example, we consider a policy maker facing a cross-section of markets in which …rms play an entry game. Her theory is Nash equilibrium and it is incomplete because there are multiple equilibria and she does not understand how equilibria are selected. This leads to partial identi…cation of parameters when drawing inferences from realized outcomes in some markets and to ambiguity when considering (policy) decisions for other markets. We model both her inference and choice. The central component of the model is a generalization of de Finetti’s exchangeable Bayesian model to accommodate ambiguity. Boston University, [email protected]. We gratefully acknowledge the …nancial support of the National Science Foundation (awards SES-0917740 and SES-0918248) and discussions with Soo Hong Chew, Marc Henry, Hiro Kaido, Peter Klibano¤ and Minjae Song. We also thank three referees, and seminar participants at Harvard, Warwick, Northwestern, Austin, Yale, Cal Tech, Wisconsin and University of Technology Sydney. Some of the material in this paper was formerly contained in the paper “A de Finetti Theorem for Capacities,”originally circulated in 2009, which no longer exists as a separate paper.