On Rent Dissipation in Dynamic Multi-battle Contests

TL;DR

This paper analyzes how contest structures influence incentives and rent dissipation in dynamic multi-battle contests, highlighting the role of exchangeability and environmental volatility.

Contribution

It identifies a structural property called exchangeability that affects rent dissipation and provides a condition for almost-full rent dissipation in such contests.

Findings

Discouragement effects prevent full rent dissipation in certain contests.

Exchangeability is a key structural property influencing rent dissipation.

Environmental volatility can sustain incentives and lead to almost-full rent dissipation.

Abstract

We study dynamic multi-battle contests and examine how the contest structure shapes dynamic incentives and determines the extent of rent dissipation. A discouragement effect often arises -- such as in tug-of-war and best-of-$K$ contests -- preventing full rent dissipation even when the series can extend infinitely. We identify a structural property, exchangeability, that contributes to the effect. Leveraging this insight, we establish a necessary and sufficient condition for almost-full rent dissipation. As an application, we introduce the iterated incumbency contest, which illustrates how volatility in the surrounding environment sustains dynamic incentives and generates almost-full rent dissipation, and thus offers insights into various competitive phenomena.