Repeated Signalling and Reputation

The one-shot monotonic signalling game can be solved under the refinement Dw, selecting the Riley equilibrium. This paper adapts the refinement to the repeated signalling game, selecting a dynamic version of the Riley equilibrium, defined iteratively, in which types minimally separate in each period. This model provides an alternative framework for studying reputation, generating under appropriate limits a modified Stackelberg property: each type above the lowest takes the action that maximizes Stackelberg payoffs, subject to separating from the lowest type. In contrast to the usual approach to reputation there are no behavioral types. It can be solved under arbitrary discount factors of both players: if the signaller discounts, the result above holds with the signaller’s Stackelberg payoffs replaced by simply defined "discounted Stackelberg" payoffs. If the respondent has preferences not only over the actions but also over the type of the signaller, a differential equation characterizes the limit, combining reputational and pure type-signalling motives.

For more information, contact Philipp Kircher.