Indeterminacy of reputation effects in repeated games with contracts

We study whether allowing players to sign binding contracts governing future play leads to reputation effects in repeated games with long-run players. We proceed by extending the analysis of Abreu and Pearce (2007) by allowing for the possibility that different behavioral types may not be immediately distinguishable from each other. Given any prior over behavioral types, we construct a modified prior with the same total weight on behavioral types and a larger support under which almost all efficient, feasible, and individually rational payoffs are attainable in perfect Bayesian equilibrium. Thus, whether reputation effects emerge in repeated games with contracts depends on details of the prior distribution over behavioral types other than its support.