Contests between two groups for a group-specific public-good/bad prize

We study contests between groups for a group-specific public-good/bad prize in which the contest success function for a group can be represented by a continuous function in each group's effort level, where each group's effort level equals the sum of effort levels that the individual players in that group expend. The players expend their effort simultaneously and independently to win the prize or not to win it (or both). Obtaining the pure-strategy Nash equilibrium, we establish that, in each group, only the player with the highest valuation and the player with the lowest valuation may be active. We further establish that there are only two active players, either in the same group or in different groups, and the rest expend zero effort. (c) 2023 Elsevier B.V. All rights reserved.