New paper shows how to exploit valuation asymmetry in Tullock contests

In competitive resource allocation, a central coordinator often cannot directly control subordinate agents but can influence their behavior by manipulating the information they receive. A new paper from researchers Diaz-Garcia, Paarporn, and Marden examines this problem within multi-player Tullock contests—a classic model where players bid for a prize, with each player's probability of winning proportional to their bid relative to total bids. The coordinator designs the reported valuations of the prize for each subordinate, preserving the Tullock structure and enabling tractable equilibrium analysis.

The authors first characterize the Nash equilibrium for general multi-player Tullock contests, showing how valuations and per-unit costs jointly determine equilibrium bids and payoffs. They then derive the optimal reported valuations for a coordinator managing two subordinates against a single opponent, and show that the optimal solution structure extends to an arbitrary number of subordinates—reducing the coordinator's optimization to a two-variable problem regardless of system size. This work has implications for auction design, resource allocation in networks, and any scenario where a central planner can indirectly shape competition through information asymmetry.