Difference-Form Group Contests

Abstract

Contests are situations in which a set of agents compete for a valuable object, rent or award. The present paper analyzes difference-form group contests, that is, contests fought among groups and where their probability of victory depends on the difference of their effective efforts. First, we show that the non-existence of pure-strategy equilibria and the monopolization results obtained in previous analysis of difference-form contests rest critically on the assumption of a linear cost of effort. Under exponential costs, we show that pure strategy equilibria exist in a large set of cases and that more than one group can expend positive effort in equilibrium. Second, we show that inequality of valuations of victory within groups hinders their chances of prevailing in the contest. If possible; members may find beneficial to engage in progressive redistribution within their group.JEL Codes: D31, D63, D72, D74

An axiomatization of difference-form contest success functions

“…In addition, this form implies the separability of contender groups, leading to dominant strategy equilibria when impacts are linear. We explore these issues in a companion paper (Cubel and Sanchez-Pages, 2014). …”

Difference-form group contests

“…Unfortunately, the techniques they employ there cannot be applied to the difference-form contests studied here. We have been able to make only some small progress on that front for the n player version of our contest game (Cubel and Sanchez-Pages 2021). Secondly, mixed strategy equilibria are especially hard to characterize in group contests; we are aware of just a few group contest papers investigating this (Barbieri et al 2014;, although they study all-pay auctions rather than probabilistic contests like the one we explore here.…”

“…2 Difference-form success functions appear also in rank-order tournaments with random noise, from the seminal Lazear and Rosen (1981) to more recent contributions such as Drugov and Ryvkin (2017). Cubel and Sanchez-Pages (2021) explore the connection between tournaments à la Lazear and Rosen (1981) and probabilistic difference-form contests of the type studied here. 3 This feature relates the group contests we study here with the group contests under all-pay auction format studied in Barbieri and Malueg (2016), and Barbieri et al (2019).…”

“…5 Baik (1998) and Che and Gale (2000) were among the first to study two-player probabilistic differenceform contests. Recently, Skaperdas et al (2016) and Cubel and Sanchez-Pages (2021) generalized these contests to non-linear impact functions. The latter also considered strictly convex costs and more than two players.…”

Inequality and conflict outbreak

“…There are other papers that explore the relation between conflict and inequality from a materialistic view point. Cubel and Sanchez-Pages (2014) analyze equilibrium behavior in a contest between coalitions (or groups) of players, identifying a link between the inequality of the distribution of resources within groups and their relative win probabilities via a free-riding effect. The functional form they employ to represent win probabilities belongs to the class axiomatically characterized in Münster (2009), and the measure of inequality that links to their model is the well-known Atkinson index.…”