Incentive Design in Competitive Resource Allocation: Exploiting Valuation Asymmetry in Tullock Contests

TL;DR

This paper analyzes how a central coordinator can strategically manipulate reported valuations in multi-player Tullock contests to gain an advantage, providing equilibrium characterizations and optimal strategies.

Contribution

It characterizes the Nash equilibrium in multi-player Tullock contests and derives optimal valuation manipulation strategies for the coordinator.

Findings

Equilibrium bids depend on valuations and costs.

Optimal valuation reports can be computed for two subordinates.

The solution structure extends to any number of subordinates.

Abstract

In competitive resource allocation, a central coordinator may seek to gain an advantage not by directly controlling subordinate agents, but by strategically manipulating the information they receive. We study this problem within the framework of multi-player Tullock contests, where the coordinator influences subordinate players by designing their reported valuations of the contested prize, a mechanism that preserves the Tullock structure of the subordinates' objectives and thereby enables tractable equilibrium analysis. We first characterize the Nash equilibrium of the general multi-player Tullock contest, establishing how valuations and per-unit costs jointly determine equilibrium bids and payoffs. We then derive the optimal reported valuations for a coordinator managing two subordinates against a single opponent, and show that the structure of the optimal solution extends to contests with an arbitrary number of subordinates, reducing the coordinator's optimization to a two-variable problem regardless of system size.