The Max-Min Group Contest

We investigate a group all-pay auction with weakest-link impact function and group-specific public good prize. Since only the minimum effort exerted among all group members represents the group effort and the group with the maximum group effort wins the contest, this is termed as the `Max-Min group contest'. Examples of such structure include various sporting events, territorial conicts, negative product or political campaigns etc. We fully characterize equilibria for the case of two groups and show that a continuum of pure strategy equilibria exist, in which all (active) players exert the same effort. A semi-pure strategy equilibrium may also exist in which all the members of one group play the same pure strategy whereas all the members of the other group play the same mixed strategy. There are two types of non-degenerate mixed strategy equilibria - with and without continuous supports. When either type of such equilibrium exists, it exhibits the same support and effort distribution of group members. We also fully characterize pure strategy equilibria for a general case of n groups and specify candidates for mixed strategy equilibria.