The Equivalence of Contests

We use a Tullock-type contest model to show that intuitively and structurally different contests can be strategically and revenue equivalent to each other. We consider a two-player contest, where outcome-contingent payoffs are linear functions of prizes, own effort, and the effort of the rival. We identify strategically equivalent contests that generate the same family of best response functions and, as a result, the same revenue. However, two strategically equivalent contests may yield different equilibrium payoffs. Finally, we discuss possible contest design applications and avenues for future theoretical and empirical research.rent-seeking, contest, spillover, equivalence, revenue equivalence, contest design

A generalized Tullock contest

We construct a generalized Tullock contest under complete information where contingent upon winning or losing, the payoff of a player is a linear function of prizes, own effort, and the effort of the rival. This structure nests a number of existing contests in the literature and can be used to analyze new types of contests. We characterize the unique symmetric equilibrium and show that small parameter modifications may lead to substantially different types of contests and hence different equilibrium effort levels.rent-seeking, contest, spillover

The hidden perils of affirmative action: Sabotage in handicap contests

Contests are ubiquitous in economic, organizational and political settings. Contest designers often use tools to make a contest among asymmetric contestants more even, in order to either elicit higher effort levels, or for ethical reasons. Handicapping – in which stronger participants are a priori weakened – is one successful tool that is widely used in sports, promotional tournaments and procurement auctions. In this study we show theoretically that participants may also increase their destructive effort, and sabotage their rivals’ performance, when handicapping is employed. We empirically verify this prediction using data on 19,635 U.K. horse-races in 2011 and 2012. Our results suggest that while a level field may be conducive to heightened positive effort in general, in a setting where both handicapping and sabotage are present it also lays the ground for greater destruction

An experimental investigation of Colonel Blotto games

This article examines behavior in the two-player, constant-sum Colonel Blotto game with asymmetric resources in which players maximize the expected number of battlefields won. The experimental results support all major theoretical predictions. In the auction treatment, where winning a battlefield is deterministic, disadvantaged players use a “guerilla warfare” strategy which stochastically allocates zero resources to a subset of battlefields. Advantaged players employ a “stochastic complete coverage” strategy, allocating random, but positive, resource levels across the battlefields. In the lottery treatment, where winning a battlefield is probabilistic, both players divide their resources equally across all battlefields. -- Dieser Artikel untersucht das Verhalten von Individuen in einem „constant-sum Colonel Blotto“-Spiel zwischen zwei Spielern, bei dem die Spieler mit unterschiedlichen Ressourcen ausgestattet sind und die erwartete Anzahl gewonnener Schlachtfelder maximieren. Die experimentellen Ergebnisse bestätigen alle wichtigen theoretischen Vorhersagen. Im Durchgang, in dem wie in einer Auktion der Sieg in einem Schlachtfeld deterministisch ist, wenden die Spieler, die sich im Nachteil befinden, eine „Guerillataktik“ an, und verteilen ihre Ressourcen stochastisch auf eine Teilmenge der Schlachtfelder. Spieler mit einem Vorteil verwenden eine Strategie der „stochastischen vollständigen Abdeckung“, indem sie zufällig eine positive Ressourcenmenge auf allen Schlachtfeldern positionieren. Im Durchgang, in dem sich der Gewinn eines Schlachtfeldes probabilistisch wie in einer Lotterie bestimmt, teilen beide Spieler ihre Ressourcen gleichmäßig auf alle Schlachtfelder auf.Colonel Blotto,conflict resolution,contest theory,multi-dimensional,resource allocation,rent-seeking,experiments

“Small, yet Beautiful”: Reconsidering the optimal design of multi-winner contests

We reconsider whether a grand multi-winner contest elicits more equilibrium effort than a collection of sub-contests. Fu and Lu (2009) employ a sequential winner-selection mechanism and find support for running a grand contest. We show that this result is completely reversed if a simultaneous winner-selection mechanism or a sequential loser-elimination mechanism is implemented. We then discuss the optimal allocation of players and prizes among sub-contests

An Experimental Investigation of Colonel Blotto Games

This article examines behavior in the two-player, constant-sum Colonel Blotto game with asymmetric resources in which players maximize the expected number of battlefields won. The experimental results support all major theoretical predictions. In the auction treatment, where winning a battlefield is deterministic, disadvantaged players use a “guerilla warfare” strategy which stochastically allocates zero resources to a subset of battlefields. Advantaged players employ a “stochastic complete coverage” strategy, allocating random, but positive, resource levels across the battlefields. In the lottery treatment, where winning a battlefield is probabilistic, both players divide their resources equally across all battlefields.Colonel Blotto, conflict resolution, contest theory, multi-dimensional resource allocation, rent-seeking, experiments

An experimental investigation of colonel blotto games

This article examines behavior in the two-player, constant-sum Colonel Blotto game with asymmetric resources in which players maximize the expected number of battlefields won. The experimental results support all major theoretical predictions. In the auction treatment, where winning a battlefield is deterministic, disadvantaged players use a guerilla warfare strategy which stochastically allocates zero resources to a subset of battlefields. Advantaged players employ a stochastic complete coverage strategy, allocating random, but positive, resource levels across the battlefields. In the lottery treatment, where winning a battlefield is probabilistic, both players divide their resources equally across all battlefields

Overbidding and Heterogeneous Behavior in Contest Experiments: A Comment on the Endowment Effect

We revisit the meta-analysis of Sheremeta (2013) on overbidding in contest experiments and focus on the effect of endowment on overbidding. Whereas Sheremeta (2013) assumes, and finds evidence of, an increasing linear relationship between endowment and overbidding in his meta-analysis, Quantal Response Equilibrium (QRE) predicts an increasing concave relationship, and Baik et al. (2016) find an inverted-U shaped relationship in their analysis of a single experiment. We use the same data as in Sheremeta (2013), but employ a different econometric model which leads to support for both QRE and the inverted-U shaped relationship. Following Baik et al. (2016) we posit that the inverted-U relationship may be interpreted in terms of a wealth effect

Linking individual and collective contests through noise level and sharing rules

We propose the use of Nitzan’s (1991) sharing rule in collective contests as a tractable way of modelling individual contests. This proposal (i) tractably introduces noise in Tullock contests when no closed form solution in pure strategies exists, (ii) satisfies the important property of homogeneity of degree zero, (iii) can be effort or noise equivalent to a standard Tullock contest

Group Contests with Internal Conflict and Power Asymmetry

We investigate situations in which players make costly contributions as group members in a group conflict, and at the same time engage in contest with fellow group members to appropriate the possible reward. We introduce within group power asymmetry and complementarity in members' efforts, and analyze how each group's internal conflict in-fluences its chance of winning in the external conflict. We find that a more symmetric group may expend more effort in external conflict when the (common) collective action technology exhibits a high degree of complementarity. Furthermore, depending on the degree of complementarity, the stronger player's relative contribution to external conflict may be higher in a more asymmetric group and, as a result, it is possible for the weaker player to earn a higher payoff. In absence of any complementarity, the rent-dissipation is non-monotonic with the within-group power asymmetry