Reseach

Waiting and Preemption in Public Good Contributions

We study threshold public-good provision when two players gradually learn the quality of a common project. The first contribution serves two strategic roles: its timing conveys information about the first mover’s learning status, while its amount allocates the funding burden between the first mover and the follower. With an exogenously prescribed first contribution, we establish a separating equilibrium, in which only players with good news contribute first, and a preemption equilibrium, in which uninformed players contribute at the outset. We also establish a gradual contribution equilibrium, in which uninformed contribution occurs over time before eventually giving way to separation. We identify a distinct form of strategic delay in the pooling equilibrium: a player who receives good news optimally waits until the same contribution becomes sufficiently credible to induce completion, at which point uninformed players also contribute with positive probability. Finally, we show that the size of the first contribution can serve as a design instrument: by choosing it appropriately, the fundraiser can eliminate the welfare-inferior equilibrium paths and attain the first-best welfare benchmark achieved by a centralized decision maker.

Learning Private Values in Public Good Contributions, with Simona Fabrizi and Steffen Lippert

We study voluntary contributions to a threshold public good by two players who learn about their private valuations through private signals. Only bad signals can arrive. The absence of signals makes players increasingly optimistic about their own valuations, whereas a prolonged history of no contribution makes them increasingly pessimistic about the other player’s willingness to contribute. We characterize the unique symmetric perfect Bayesian equilibrium. We show that equilibrium behavior evolves from waiting to partial contribution and ultimately to full contribution by a single player. Private-value learning can eventually eliminate free-riding in the private provision of public goods.

Prize Sharing in Dynamic Discovery Races, with Vladimir Smirnov

We analyze a two-player dynamic discovery race in which participants undertake a costly search for a prize whose location is unknown, and a fixed rule determines how the prize is divided between the discoverer and the non-discoverer. Because an unsuccessful search rules out explored regions, effort today changes both the probability of discovery and the opportunities available for future search. We characterize the payoff-dominant symmetric Markov-perfect equilibrium, in which the search path is determined endogenously. We show that greater patience can accelerate search and make both players worse off. We also show that a winner-take-all rule need not maximize value. Concentrating the reward on the discoverer strengthens incentives to search first but can generate inefficient preemption, whereas greater prize sharing mitigates preemption but encourages free riding. A social planner seeking to improve efficiency, therefore, chooses the sharing rule to balance these forces, rather than simply maximizing search effort or minimizing the time to discovery.