Biased contests for symmetric players

In a biased contest, one of the players has an advantage in the winner determination process. We characterize a novel class of biased contest success functions pertaining to such contests and provide necessary and sufficient conditions for zero bias to be a critical point of arbitrary objectives satisfying certain symmetry restrictions. We, however, challenge the common wisdom that unbiased contests are always optimal when contestants are symmetric ex ante or even ex post. We show that contests with arbitrary favorites, i.e., biased contests of symmetric players, can be optimal in terms of various objectives such as expected aggregate effort, the probability to reveal the stronger player as the winner or expected effort of the winner

Biased contests for symmetric players

In a biased contest, one of the players has an advantage in the winner determination process. We characterize a novel class of biased contest success functions pertaining to such contests and provide necessary and sufficient conditions for zero bias to be a critical point of arbitrary objectives satisfying certain symmetry restrictions. We, however, challenge the common wisdom that unbiased contests are always optimal when contestants are symmetric ex ante or even ex post. We show that contests with arbitrary favorites, i.e., biased contests of symmetric players, can be optimal in terms of various objectives such as expected aggregate effort, the probability to reveal the stronger player as the winner or expected effort of the winner

A Micro- Foundation for Non-Deterministic Contests of the Logit Form

In models of non-deterministic contest, players exert irreversible effort in order to increase their probability of winning a prize. The most prominent functional form of the win probability in the literature is the so-called “logit” contest success function. We provide a simple micro-foundation of this function for the two contestant case. In this setting the contest administrator is a rational decision maker whose optimal choice is deterministic. However, from the point of view of the contestants the outcome of the contest is probabilistic because of an underlying uncertainty about the type of the administrator.Contests, Contest Success Function, Effort levels, Endogenous Contest.

Multi-Item Contests

Contests are games in which the players compete for a valuable prize by exerting effort or using resources so as to increase their probability of winning. This paper examines two player multi-item contests, a class of games in which players are faced with a decision about how much of a given resource to devote to an entire collection or sequence of different contests. Applications include multi-item rent-seeking behavior, multi-good marketing and advertising, multi-jurisdictional political contests. In these games, even when the (uncertain) outcomes in each contest are assumed to be mutually statistically independent, equilibrium efforts can exhibit strong interdependencies. Changes in either the contest success function or value of the prize in one contest usually alter the equilibrium amount of resources devoted to all contests by both players. We unify and extend results from marketing and political science, and also derive conditions under which both players exert zero effort in equilibrium in some subset of contests.

The Collective Wisdom of Beauty Contests

This note uses techniques developed for aggregate games to characterize the set of equilib- ria for a beauty contest or prediction game in which the experts’ preferences are quadratic, but with an otherwise unrestricted information structure for private signals and the state variable. We show that, on aggregate, the experts’ collective estimate of the unknown parameter to be estimated is unbiased for every equilibrium.Aggregate games, beauty contests, prediction games

FOUNDATIONS FOR CONTEST SUCCESS FUNCTIONS

We examine two approaches to contest success functions. In the first we analyze the implications of contestants´ incomplete information concerning the `type´ of the contest administrator. While in the case of two contestants this approach can rationalize prominent contest success functions, we show that it runs into difficulties when there are more agents. Our second approach interprets contest success functions as sharing rules and establishes a connection to bargaining and claims problems which is independent of the number of contestants. Both approaches provide foundations for popular contest success functions and guidelines for the definition of new ones.

Commitment in R&D Tournaments via Strategic Delegation to Overoptimistic Managers

This paper shows that it is profitable for a firm to hire an overoptimistic manager to commit to a certain investment strategy in an R&D tournament situation. In the unique symmetric equilibrium, all firms delegate to overoptimistic managers, where the optimal degree of overoptimism depends on the riskiness of the tournament. In these situations a manager’s type may serve as a substitute for delegation via contracts. By delegating to overoptimistic managers, firms can escape the rat race nature of R&D tournaments

Aggregate Representations of Aggregate Games

An aggregate game is a normal-form game with the property that each player’s payoff is a function only of his own strategy and an aggregate function of the strategy profile of all players. Aggregate games possess a set of purely algebraic properties that can often provide simple characterizations of equilibrium aggregates without first requiring that one solves for the equilibrium strategy profile. The defining nature of payoffs in an aggregate game allows one to project the n-player strategic analysis of a normal form game onto a lower-dimension aggregate-strategy space, thereby converting an n-player game to a simpler object – a self-generating single-person maximization program. We apply these techniques to a number of economic settings including competition in supply functions and multi-principal common agency games with nonlinear transfer functions.Aggregate games, common agency, asymmetric informa- tion, menu auctions

Endogenous group formation in experimental contests

We study endogenous group formation in tournaments employing experimental three-player contests. We find that players in endogenously formed alliances cope better with the moral hazard problem in groups than players who are forced into an alliance. Also, players who are committed to expending effort above average choose to stand alone. If these players are forced to play in an alliance, they invest even more, whereas their co-players choose lower effort. Anticipation of this exploitation may explain their preference to stand alone

Endogenous strength in conflicts

In this paper we study a two stage contest where the strength of players in the second stage depends on the result of the contest in the first stage. We show that this contest displays properties that are not present in one shot contests. Non-symmetric players make different efforts in the first stage and rent dissipation in the first period may be large. We study the conditions under which the discouragement effect holds. In addition, new issues emerge like the evolution of the strengths and the shares of the prize during the game.