In this paper, we consider a prize-sharing rule design problem in a group contest with effort complementarities within groups by employing a CES effort aggregator function.We derive the conditions for a monopolization rule that dominates an egalitarian rule if the objective of the rule design is to maximize the group's winning probability. We find conditions under which the monopolization rule maximizes the group's winning probability, while the egalitarian rule is strictly preferred by all members of the group. Without effort complementarity, there cannot be such a conflict of interest.

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