Asymmetric All-Pay Auctions with Spillovers

TL;DR

This paper analyzes asymmetric all-pay auctions incorporating spillovers, revealing how effort-reward linkages can lead to counterintuitive payoff outcomes in competitive scenarios.

Contribution

It introduces a general model of asymmetric all-pay auctions with spillovers, highlighting novel effects on equilibrium behavior and payoff distribution.

Findings

Higher-cost, lower-value players can sometimes secure larger payoffs.

Spillovers significantly influence effort and reward dynamics in competitive settings.

The model applies to lobbying, warfare, R&D, and marketing contexts.

Abstract

When opposing parties compete for a prize, the sunk effort players exert during the conflict can affect the value of the winner's reward. These spillovers can have substantial influence on the equilibrium behavior of participants in applications such as lobbying, warfare, labor tournaments, marketing, and R&D races. To understand this influence, we study a general class of asymmetric, two-player all-pay auctions where we allow for spillovers in each player's reward. The link between participants' efforts and rewards yields novel effects -- in particular, players with higher costs and lower values than their opponent sometimes extract larger payoffs.