Testing rational hypotheses in signaling games

Abstract

We introduce a solution concept for signaling games, called Rational Hypothesis Testing Equilibrium (RHTE). Beliefs are updated via Ortoleva’s (2012) Hypothesis Testing model, allowing for conditioning on information sets off the path. Hypotheses are conjectures by the uninformed player about opponent’s strategies that rationalize sending an unexpected message. Each RHTE is a Perfect Bayesian Equilibrium, but not vice versa. RHTE features a number of desirable properties: First, beliefs are structurally consistent in the spirit of Kreps and Wilson (1982). Second, beliefs are consistent with mutual knowledge of rationality. Third, RHTE can be related to the prominent refinement concepts, including the Intuitive Criterion, strategic stability, and undefeated equilibrium. In the Spence game, RHTE restricts the admissible wages, significantly reducing the number of equilibria. Finally, we show that our equilibrium notion offers an alternative explanation for the experimental results in Brandts and Holt (1992, 1993).