A Tree Formulation for Signaling Games

Abstract:     
We provide a detailed presentation and complete analysis of the sender/receiver Lewis signaling game using a game theory extensive form, decision tree formulation. The analysis employs well established game theory ideas and concepts. We establish the existence of four perfect Bayesian equilibria in this game. We explain which equilibrium is the most likely to prevail. Our explanation provides an essential step for understanding the formation of a language convention. Further, we discuss the informational content of such signals and estabish a distinction between a truthful and a correct signal in terms of the payoffs of the sender and the receiver.

Number of Pages in PDF File: 19

Keywords: signals, signaling games, actions, states of nature, language convention, rational expectations equilibrium, information set, games, imperfect information, Nash equilibrium, Perfect Bayesian equilibrium, beliefs updating

JEL Classification: C70, C72

working papers series