Distributional Competition

TL;DR

This paper develops a general framework for distributional competition in which symmetric players choose probability distributions over a one-dimensional performance index and pay convex production costs. Existence of symmetric pure-strategy equilibria is established despite tie-induced discontinuities, and equilibria are shown to be atomless under natural tie-breaking assumptions with a first-order characterization for both equilibrium and the planner’s problem. The author then specializes the model to rank-order contests, risky R&D, and quality and price-quantity competition, deriving welfare-relevant comparisons: more unequal prizes raise mean and dispersion of effort, competition accelerates discovery in risky R&D relative to the planner, and quality competition tends to overprovide quality relative to social optimum; in price-quality competition, convergence to marginal-cost pricing in large markets depends on cost-structure steepness and may imply no product differentiation under certain conditions. Overall, the paper clarifies how endogenous distributional choices interact with competition to shape effort, design, and welfare across diverse settings.

Abstract

I study symmetric competitions in which each player chooses an arbitrary distribution over a one-dimensional performance index, subject to a convex cost. I establish existence of a symmetric equilibrium, document various properties it must possess, and provide a characterization via the first-order approach. Manifold applications--to R&D competition, oligopolistic competition with product design, and rank-order contests--follow.

Theorems & Definitions (63)

• Proposition 3.1
• Lemma 3.2
• Lemma 3.4
• Lemma 3.5
• Proposition 3.6
• Proposition 3.7
• Proposition 3.8
• Proposition 3.10
• Lemma 4.2
• Theorem 4.3