The optimal sorting of players in contests between groups

Sorting and communication in weak-link group contests

“…Lee (2012) characterizes the set of equilibria present in group contests with weak-link aggregation and linear costs of effort, but does not consider the question of sorting which is relevant to our study. Rather, the optimal sorting of heterogeneous players in group contests was first explored by Ryvkin (2011). Provided the cost function of effort is not "too steep," Ryvkin (2011) theoretically shows that when within-group efforts are perfectly substitutable and the probability of winning is given by the lottery contest success function (CSF) (Tullock, 1980), the optimal sorting is the one that minimizes the variance in ability across groups, i.e., the most "balanced" sorting.…”

“…Rather, the optimal sorting of heterogeneous players in group contests was first explored by Ryvkin (2011). Provided the cost function of effort is not "too steep," Ryvkin (2011) theoretically shows that when within-group efforts are perfectly substitutable and the probability of winning is given by the lottery contest success function (CSF) (Tullock, 1980), the optimal sorting is the one that minimizes the variance in ability across groups, i.e., the most "balanced" sorting. Extending these results to group contests with arbitrary levels of within-group complementarity, Brookins, Lightle and Ryvkin (2015b) show that the optimal sorting may be either balanced or unbalanced, and depends on both the degree of complementarity of efforts within groups and steepness of the effort cost function.…”

Intra-group heterogeneity in collective contests

“…By properties (a) and (b) of the share functions, we can see that 12 Ryvkin (2011) uses another approach to derive existence and uniqueness of equilibrium for a contest model similar to ours. But his proof seems to critically depend on the restriction that the limit of the marginal effort cost at the zero effort level is not positive, i.e.…”

“…22 We could refer to two articles mentioned in the introduction. Also, Ryvkin (2011) uses the property in examining how to sort individuals in competing groups to maximize the total effort. See Esteban andRay (1999, 2011a) on other important applications of this assumption.…”

Optimal sorting in group contests with complementarities

“…For example, for certain parameters, there are intermediate levels of complementarity, such as a Cobb-Douglas aggregation function, where balanced sorting is optimal, even though unbalanced sorting is optimal at either extreme. In order to explore the effect of sorting on output, similar to Ryvkin (2011), we use the quadratic approximation to the true equilibrium efforts and develop an expansion of output in the moments of the distribution of abilities. Within the quadratic approximation, we describe all possible cases for how optimal sorting depends on within-group effort complementarity, and provide an example of each case.…”