The Best-Shot All-Pay (Group) Auction with Complete Information∗

We analyze an all-pay group contest problem in which individual members’ efforts are aggregated via the best-shot technology and the prize is a public good for the winning group. The interplay of within-group free-riding and across-group competition allows for a wide variety of equilibria, according to how well groups are able to overcome internal free-riding. In a symmetric model we derive equilibria in which multiple agents per group are active, in contrast with the existing literature. Our findings differ qualitatively from those of the individualistic all-pay auction: rents are not necessarily dissipated in equilibrium, total expected efforts vary across equilibria, and participation is expected to be greater. Moreover, equilibria with greater symmetry of behavior within a group are shown to have more “wasted” effort but also greater payoffs as overall efforts are lower. In contrast to many results in the literature, free-riding can be beneficial for players as it reduces competition among groups. Examples of asymmetric group contests are also studied. JEL Codes: H41, D61, D82