Research and Development (R&D): Stochastic All-Pay Auctions

Abstract

Research and development (R&D) competition generates innovation but can also produce socially wasteful duplication of effort. In our thesis, we model this dynamic through a stochastic all-pay auction, where firms make sunk-cost investments to increase their chances of obtaining a technological prize. Equilibrium and welfare properties are then analyzed for deterministic all-pay auctions, proportional (Chinese) auctions, and a broader class of stochastic “share-of-score’’ mechanisms. The analysis derives equilibrium bidding behavior, welfare bounds, and approximate Price of Anarchy guarantees, and identifies conditions under which total social welfare asymptotically increases with greater competition and more firms. Policy interventions are then studied from the perspective of a social planner seeking to reduce inefficient investment while preserving innovation incentives. Transfers, predictive information about firm valuations, and incentive-compatible reporting mechanisms are examined as coordination tools. Finally, computational methods — including multi-agent reinforcement learning, numerical approximation, and differentiable mechanism design — are used to approximate equilibria and explore welfare-improving mechanisms in environments without closed-form solutions. Taken together, these results provide the crucial theoretical and computational tools for understanding how institutional design shapes incentives and efficiency in R&D, providing hope for a more socially-optimal future allocation of scientific resources and investment.