A Reputation for Honesty (with D. Fudenberg and H. Pei)
Journal of Economic Theory, 2022
Abstract: We analyze situations where players build reputations for honesty rather than for playing particular actions. A patient player faces a sequence of short-run opponents. Before players act, the patient player announces their intended action after observing both a private payoff shock and a signal of what actions will be feasible that period. The patient player is either an honest type who keeps their word whenever their announced action is feasible, or an opportunistic type who freely chooses announcements and feasible actions. Short-run players only observe the current-period announcement and whether the patient player has kept their word in the past. We provide sufficient conditions under which the patient player can secure their optimal commitment payoff by building a reputation for honesty. Our proof introduces a novel technique based on concentration inequalities.
Abstract: We consider the disclosure problem of a sender who wants to use hard evidence to persuade a receiver towards higher actions. When the receiver hopes to make inferences based on the distribution of the data, the sender has an incentive to drop observations to mimic the distributions observed under better states. We use a continuum model to predict optimal play when datasets are large and find that, in the big-data limit, it is optimal for senders to play an imitation strategy, under which they submit evidence imitating the natural distribution under some desirable target state. Relative to full information, the partial pooling equilibrium with voluntary disclosure generates a loss in welfare to senders who either have little data or a favorable state, who optimally disclose their full dataset, but a benefit to senders with access to large datasets, who can profitably drop observations under low states.