Rent-seeking for a public good with additive contributions

We analyze rent-seeking for a public good with two groups, where the provision of a public good is decided in the all-pay contest where "the winner takes all". We assume that the valuation of the public good varies across groups, but is the same for all members within a group. Free-riding in such situation was predicted by Baik et al. (J Public Econ 82(3):415-429, 2001). We describe a continuum of equilibria where all players make contributions. There is room for substantial payoff asymmetry, which ranges from equal payoffs to all group members to a zero payoff for the player who makes a contribution and positive payoffs for free-riders. The results generalize for the case where the prize has both a private and a public component.