Sequential Formation of Alliances in Survival Contests

Abstract

We consider a sequential formation of alliances à la Bloch (1996) and Okada (1996) followed by a two-stage contest in which alliances first compete with each other, and then the members in the winning alliance compete again for an indivisible prize. In contrast to Konishi and Pan (2019) which adopted an open-membership game as the alliance formation process, alliances are allowed to limit their memberships (excludable alliances). We show that if members' efforts are strongly complementary to each other, there will be exactly two asymmetric alliances the larger alliance is formed first and then the rest of the players form the smaller one. This result contrasts with the one under open membership, where moderate complementarity is necessary to support a two-alliance structure. It is also in stark contrast with Bloch et al. (2006), where they show that a grand coalition is formed in the same game if the prize is divisible and a binding contract is possible to avoid further conflicts after an alliance wins the prize.