This paper presents a unified framework for characterizing symmetric equilibrium in simultaneous move, two-player, rank-order contests with complete information, in which each player's strategy generates direct or indirect affine "spillover" effects that depend on the rank-order of her decision variable. These effects arise in natural interpretations of a number of important economic environments, as well as in classic contests adapted to recent experimental and behavioral models where individuals exhibit inequality aversion or regret. We provide the closed-form solution for the symmetric Nash equilibria of this class of games, and show how it can be used to directly solve for equilibrium behavior in auctions, pricing games, tournaments, R&D races, models of litigation, and a host of other contests.

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Keywords Auctions, Contests, Spillovers
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Journal Economic Theory
Baye, M.R, Kovenock, D, & de Vries, C.G. (2012). Contests with rank-order spillovers. Economic Theory, 51(2), 315–350. doi:10.1007/s00199-009-0489-2