Contests with rank-order spillovers

Abstract

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.We are grateful to two referees for exceptionally lucid and helpful reports. We have also benefited from conversations with

The effect of fight cost structure on fighting behaviour

“…It consists of the true energetic cost of the investment (such as performing a complex manoeuvre in an aerial contest between birds), the potential for getting hurt by an animal's own actions (typically, the more complex the manoeuver, the more things could go wrong and the animal could end up seriously injured even if the other individual does not fight) and the potential for getting hurt by the actions of the opponent. However, in such a full generality, the mathematics would be intractable, and we thus consider a symmetrical cost function (note that it is possible to find solutions for linear asymmetric functions, as shown in Baye et al (2012)). The symmetrical cost function that we use is defined by…”

“…Alternatively, more complex contests can take more time, and that time be a function of s + p. The cost paid could then be a function of the time spent; for example in lost opportunities, or predation risk through being in an exposed area. We note that Baye et al (2005Baye et al ( , 2012 consider many possible cost functions, including conventional functions (each pays its own costs) and less conventional ones (each pays some Fig. 1: Scheme of the game.…”

Conflicts with Multiple Battlefields

“…8 We follow Lizzeri and Persico's focus on the case of a zero-one infrastructure technology that, when employed, provides a uniform level of force across all of the battlefields. However, our results may be directly extended to allow for a more general lumpy, or discrete, infrastructure technology.…”

“…, x B,n +Iι I ) and (ii) for any n-tuple of effective forces there exists a unique cost-minimizing combination of the targetable force and the infrastructure investment, it will be convenient to state player B's mixed strategy in terms of his n-tuple of effective forces. 8 Because the model in Lizzeri and Persico (2001) assumes a continuum of voters, mixed strategies are unidimensional. A variation of this game with a finite set of voters and multidimensional mixed strategies is examined in Roberson (2008).…”

Tournaments and piece rates revisited: a theoretical and experimental study of output-dependent prize tournaments

“…The same is true for the 'share contests' analysed by Falluchi et al (2013) and for the compensation mechanism studied by Chowdhury et al (2014). Chowdhury and Sheremeta (2011) and Baye et al (2012) analyse contests where the prize to be awarded is fixed, but where additionally the own output and the rival's output enter the winning agent's payoff function. Hence, similarly to our model, agent payoff is influenced by (firm) performance.…”