Formation of Teams in Contests: Tradeoffs Between Inter- and Intra-Team Inequalities (with Hideo Konishi (Boston College) and Chen-Yu Pan (National Chengchi University)) (JMP link)
In a team contest players make efforts to compete with other teams for a prize, and players of the winning team divide the prize according to a prize-sharing rule. Players' efforts in a team are aggregated into team effort, and the winning probabilities of teams are determined by a Tullock probability success function of team efforts. Thus, players in a team have free-riding incentives, and prize-sharing rules matter in generating members' efforts and attracting players from outside.
Assuming that players differ in their abilities to contribute to a team and their abilities are common knowledge, we analyze which team structure
realizes by allowing players to move across teams. This inter-team mobility is achieved via head-hunting: a team leader can offer one of the positions to an outside player. We say that it is a successful head-hunting if the player is better off by taking the position, and the team's winning probability is improved. A team structure is stable if there is no successful head-hunting opportunity. We show that if all teams employ the egalitarian sharing rule, then the complete sorting of
players according to their abilities occurs, and inter-team inequality becomes the largest. In contrast, if all teams employ a substantially unequal sharing rule, there is a stable team structure with a small inter-team inequality and a large intra-team inequality. This result illustrates a trade-off between intra-team inequality and inter-team inequality in the formation of teams.
Equilibrium Player Choices in Team Contests with Multiple Pairwise Battles (link) - with the editor for publication (GEB) ( link)
We consider a setting in which two teams compete in a sequence of pairwise battles. Unlike the famous work of Konrad and Kovenoch (2006), here each player on each team only gets to participate in a single battle. We assume that the players have different abilities and we model each individual battle as a Tullock contest. A natural example here comes from tennis tournaments. Typically, the two coaches have to announce an ordered list of their players before the tournament begins. The matches are then carried out sequentially according to the corresponding submitted player orders (the first players on each are matched first, then the second players, etc). The team that wins more than half the games also wins the tournament.. We consider both the one-shot choice problem, but also a sequential battle-by-battle player choice problem. In the latter, each coach selects one player only, then the match is carried out. The coaches then select the next players conditionally on the observed history.
We show that as long as the number of players on each team is the same as the number of battles, the equilibrium winning probability of a team in a multi-battle contest is independent of player assignments' being one-shot or battle-by-battle sequential. This equilibrium winning probability and ex ante expected total effort coincide with the ones when the matching of players is chosen totally randomly with an equal probability lottery by the contest organizer. Indeed, they key to showing this equivalence is the fact that perfectly equal randomization is a Nash Equilibrium in the one-shot game, and a Nash Equilibrium in every subgame of the sequential choice game. The second statement is quite surprising as each subgame consists of differing subsets of players. At the core of the results is the history-independence of winning probabilities that endogenously arises in equilibrium as long as the contest success function in each round is homogeneous of degree 0.
Efficiency and Incentives in Group Contests with Heterogeneous Agents ( link)
This paper focuses on the analysis of collective action, group efficiency, and incentive mechanisms in a team contest for an endogenously determined and divisible prize. Each team is represented by a team leader who tries to maximize the performance of her group. The individual contributions of team members are not observable and so the team leader has to carefully devise a prize-sharing rule within the team. The shares that she assigns to group members are dependent on their heterogeneous characteristics, modeled as individual abilities, as well as on the observable level of team performance. Both the abilities and the allocation rules are modeled as private information within each team.
Using subgame perfect equilibrium, a CES effort aggregator, and constant elasticity marginal cost of effort, I focus the analysis on non-wasteful allocation rules. I derive the optimal allocation mechanism which rewards agents according to a general-logit specification based on their relative ability. I show that as long as the degree of effort complementarity and the elasticity of the marginal cost of effort are not too high, then a team's performance is most sensitive to the ability of its highest-skill members, and a higher spread in the distribution of ability has a positive effect on group performance.
Finally, I study the incentives for free-riding and the group-size paradox. I obtain a very novel result that unifies much of the existing literature on free-riding in teams. I show that free-riding can be completely eliminated for some agents as long as their share of the prize does not decline too fast relative to the team's aggregate performance.
Student Matching with Vouchers: the Inefficiency of the DC School System