Contests with a Stochastic Number of Players

We study Tullock's (1980) n-player contest when each player has an independent probability 0Contests, Stochastic number of players, Over-dissipation.

Continuois Time Contests

This paper introduces a contest model in which each player decides when to stop a privately observed Brownian motion with drift and incurs costs depending on his stopping time. The player who stops his process at the highest value wins a prize. Applications of the model include procurement contests and competitions for grants. We prove existence and uniqueness of the Nash equilibrium outcome, even if players have to choose bounded stopping times. We derive the equilibrium distribution in closed form. If the noise vanishes, the equilibrium outcome converges to - and thus selects - the symmetric equilibrium outcome of an all-pay auction. For two players and constant costs, each player’s profits increase if costs for both players increase, variance increases, or drift decreases. Intuitively, patience becomes a more important factor for contest success, which reduces informational rents

Multi-Stage Contests with Stochastic Ability

We consider the properties of perfectly discriminating contests in which players’ abilities are stochastic, but become common knowledge before efforts are expended. Players whose expected ability is lower than that of their rivals may still earn a positive expected payoff from participating in the contest, which may explain why they participate. We also show that an increase in the dispersion of a player’s own ability generally benefits this player. It may benefit or harm his rival, but cannot benefit the rival more than it benefits himself. We also explore the role of stochastic ability for sequential contests with the same opponent (multi-battle contests) and with varying opponents (elimination tournaments) and show that it reduces the strong discouragement effects and hold-up problems that may otherwise emerge in such games. High own ability dispersion selects such players into the contest and favors them in elimination contests.All-Pay Auctions ; Elimination Tournament ; Contest ; Race ; Conflict ; Multi-Stage ; Random Ability ; Discouragement

Gambling in Contests

This paper presents a strategic model of risk-taking behavior in contests. Formally, we analyze an n-player winner-take-all contest in which each player decides when to stop a privately observed Brownian Motion with drift. A player whose process reaches zero has to stop. The player with the highest stopping point wins. Contrary to the explicit cost for a higher stopping time in a war of attrition, here, higher stopping times are riskier, because players can go bankrupt. We derive a closed-form solution of the unique Nash equilibrium outcome of the game. In equilibrium, the trade-off between risk and reward causes a non-monotonicity: highest expected losses occur if the process decreases only slightly in expectation

Spanish Football

The authors analyze the financial situation of the Spanish football industry. They first argue that a relevant analysis of the industry's financial results relies on a careful description of how historical and cultural factors have influenced its organization. Moreover, they stress the important relationship between the industry and television. The authors suggest that the situation of the Spanish football industry suffers from some structural weaknesses in its accounts. However, the situation seems less severe than in other major European football leagues, partly because local authorities in Spain have strong incentives to back football teams.Publicad

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." (author's abstract)"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." (Autorenreferat

Asymmetric Conflicts with Endogenous Dimensionality

This article examines a two-stage model of asymmetric conflict based on the classic Colonel Blotto game in which players have, in the first stage, the ability to increase the number of battlefields contested. It thereby endogenizes the “dimensionality” of conflict. In equilibrium, if the asymmetry in the players’ resource endowments exceeds a threshold, the weak player chooses to add battlefields, while the strong player never does. Adding battlefields spreads the strong player’s forces more thinly, increasing the incidence of favorable strategic mismatches for the weak player.Asymmetric Conflict, Multi-battle Conflict, Colonel Blotto Game, Stochastic Guerilla Warfare, Endogenous Dimensionality