PapersAbstract This paper develops an extended set of results for signaling games under weak conditions. A weak order theoretic notion of single crossing is used; unlike Spence-Mirrlees single crossing, the usual assumption in theoretical work, it is implied by supermodularity, and typically satisfied in applications. Differentiability and continuity of payoffs, and strictness of monotonicity, are also relaxed. Generalized results include existence of separating equilibria and a dominant separating equilibrium, uniqueness of separating equilibrium with a continuum of types, and selection of the dominant separating equilibrium by the D1 refinement. Also the set of separating equilibria and the dominant separating equilibria are continuous with respect to the type space as it becomes a continuum. Continuity of both with respect to the payoff function is a new result. Also signaling games are shown to have strong comparative statics properties, and conditions are found for strategies to be increasing in a parameter, and for value functions to be supermodular, and for the increase and supermodularity to be bounded. These results allow for the analysis of signaling within larger dynamic games. Signaling and Reputation in Repeated GamesAbstract In a repeated interaction, if the actions of an agent signal a private characteristic, or type, they will influence howhe is expected to act in future, giving reputational incentives. If the signaler’s type can change over time, these incentives can persist. A general model of repeated signaling is presented. The type space is finite or a continuum, and players have arbitrary supermodular payoffs. There is a unique equilibrium with continual (minimal) separation of types. It is selected by a recursive version of the equilibrium refinement D1. The equilibrium is calculable, showing a quantitative dependence of reputation on patience, the length of the game, and the random process on types. Abstract This paper studies continually separating equilibria of repeated signaling games, extending Roddie (2011b) to study stationary equilibria in infinite horizon games. Reputational incentives arise because current actions influence future expectations of actions via type-beliefs. In a long game with a continuum of persistent types, if the signaler is patient he gains Stackelberg leadership, subject to separating from the lowest type. This remains true if the respondent cares directly about the signaler’s type in addition to his actions. If the signaler has additively separable utility and is is impatient, his actions maximize a discounted form of Stackelberg payoffs. In contrast to the usual theoretical approach to reputation there is no reliance on behavioral types. Research projectsJoint reputation and reciprocation via repeated signaling
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