Limited capacity in project selection: competition through evidence production

An organization must decide which of two proposals to fund. In evaluating the proposals, the organization relies on the agents applying for funding to produce evidence about the merits of their own proposals. When the organization can fund all proposals, each agent engages in an independent game of Bayesian persuasion with the organization, choosing information strategies that maximize the probability of producing evidence in favor of funding. When the organization has limited capacity to implement proposals, the game becomes one of competitive Bayesian persuasion. Producing favorable evidence is not enough to secure funding; an agent must also produce more-favorable evidence than the other agent. We show that an organization’s limited capacity leads agents to produce more (Blackwell) informative evidence than they do when the organization is unconstrained. We fully characterize the unique equilibrium under unlimited and limited capacity, and show that unless the prior strongly favors accepting both proposals, the funding organization is better off when its capacity is limited. The analysis highlights similarities between competitive Bayesian persuasion games and all-pay auctions and generalized Colonel Blotto games.