Payoff Shares in Two-Player Contests

In contest models with symmetric valuations, equilibrium payoffs are positive shares of the value of the prize. In contrast to a bargaining situation, these shares sum to less than one because a share of the value is lost due to rentdissipation. We ask: can every such division into payoff shares arise as the outcome of the unique pure-strategy Nash equilibrium of a simple asymmetric contest in which contestants differ in the effectiveness of their efforts? For two-player contests the answer is shown to be positive

Payoff shares in two-player contests

In imperfectly discriminating contests with symmetric valuations, equilibrium payoffs are positive shares of the value of the prize. In contrast to a bargaining situation, players’ shares sum to less than one because a residual share of the value is lost due to rent dissipation. In this paper, we consider contests with two players and investigate the relationship between these equilibrium shares and the parameters of a class of asymmetric Tullock contest success functions. Our main finding is that any players’ shares that sum up to less than one can arise as the unique outcome of a pure-strategy Nash equilibrium for appropriate parameters

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

Top guns may not fire:Best-shot group contests with group-specific public good prizes

We analyze a group contest in which n groups compete to win a group-specific public good prize. Group sizes can be different and any player may value the prize differently within and across groups. Players exert costly efforts simultaneously and independently. Only the highest effort (the best-shot) within each group represents the group effort that determines the winning group. We fully characterize the set of equilibria and show that in any equilibrium at most one player in each group exerts strictly positive effort. There always exists an equilibrium in which only the highest value player in each active group exerts strictly positive effort. However, perverse equilibria may exist in which the highest value players completely free-ride on others by exerting no effort. We provide conditions under which the set of equilibria can be restricted and discuss contest design implications

Collective Production and Incentives

We analyse incentive problems in collective production environments where contributors are compensated according to their observed and ranked efforts. This provides incentives to the contributors to choose first best efforts

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 Attack-and-Defense Group Contests: Best-shot versus Weakest-link

This study analyzes a group contest in which one group (defenders) follows a weakest-link whereas the other group (attackers) follows a best-shot impact function. We fully characterize the Nash and coalition-proof equilibria and show that with symmetric valuation the coalition-proof equilibrium is unique up to the permutation of the identity of the active player in the attacker group. With asymmetric valuation it is always an equilibrium for one of the highest valuation players to be active; it may also be the case that the highest valuation players in the attacker group free-ride completely on a group-member with a lower valuation. However, in any equilibrium, only one player in the attacker group is active, whereas all the players in the defender group are active and exert the same effort. We also characterize the Nash and coalition-proof equilibria for the case in which one group follows either a best-shot or a weakest-link but the other group follows an additive impact function