Rationalization and Robustness in Dynamic Games with Incomplete Information: Extended Abstract

In the game theoretic environment, there is a clear tension between the strength of a solution concept and its robustness to misspecification. In other words, if the analyst wants his model to be resilient to small errors in the parameters, then he must weaken the predictive power of the model. In fact, this tension can be made formal; under a richness assumption (loosely speaking, for every strategy there is a state such that it is dominant), structure theorems place clear limits to the predictive power of robust solution concepts (Weinstein and Yildiz, 2007; Penta, 2012). Intuitively, a similar tension arises when considering a solution concept and its epistemic demands. To make sharper predictions, the modeler must place more stringent requirements on the structure of the understanding of agents (at least insofar as to adhere to the requirements of the solution concept). Informally, this observation suggests a possible link between the epistemic demands of a solution concept and it’s robustness. The first aim of this paper is to formalize this connection. We show that particular notions of robustness can be thought of as epistemic concerns. In particular, we examine a solution concept’s robustness to the misspecification of players’ beliefs, the underlying space of payoff uncertainty, and to the joint misspecification of both. In each case, we show that reasonable and common notions of robustness can be described entirely though the epistemic characterization of the solution concept. Most commonly, robustness has been defined with respect to misspecification of players beliefs; in particular via the upper-hemicontinuity (henceforth, UHC) of the solution concept in question. UHC dictates that if a strategy is ruled out for some type then there is a neighborhood of nearby types for which the strategy is also ruled out. In the absence of UHC, approximations ∗University of Pittsburgh,[email protected] †Universitat Rovira i Virgili, [email protected] 1Informally, epistemic demand refer to the restrictions placed on players beliefs regarding payoff uncertainty, opponents strategies, and the higher order beliefs over these objects. A more formal, but my no means complete, explanation is found in Section 2.