Separation or Not: A Critique of "Appearance-Based" Selection Criteria

We examine the foundations of traditional equilibrium selection rules that choose a separating equilibrium in a signaling model. With an example from the entry deterrence model of Milgrom and Roberts (1982). where the players are forced to reveal their private information in the post-entry game. we show that a separating equilibrium might not survive some forward induction argument (Kohlberg and Mertens 1986), and that the resulting equilibrium has many intuitive properties. If the players are not forced to reveal their private information in the post-entry game. the forward induction criterion selects the Pareto efficient separating equilibrium. We assert that in contrast to forward induction. "appearance-based" equilibrium selection criteria can provide misleading implications on the value of complete information in the post-entry game.