Information Design in Allocation with Costly Verification: Multiple Agents

Abstract

We study optimal information design on top of the allocation problem with costly verification à la Ben-Porath et al. (2014) and extend the analysis of Chen et al. (2024) to the multiple-agent case. Each agent learns a private signal about the allocation value to the principal from a signal distribution which is influenced by an information designer. The principal designs a mechanism to maximize her net value based upon the designed information. We identify (i) the agent-optimal information which maximizes the total probability of agents getting the object and (ii) the principal-optimal information. Unlike the single-agent case where any agent-optimal information is principal-worst, when there multiple agents, some agent-optimal information may not be principal-worst (though some remain to be). Moreover, we characterize when agent-optimal information design strictly increases the probability of allocation. Finally, through identifying the principal-worst information, we obtain an optimal robust allocation mechanism for the principal.

Keywords: information design, mechanism design, costly verification, robust mechanism design