The robustness of ‘enemy-of-my-enemy-is-my-friend’ alliances

We examine a three-player, three-stage game of alliance formation followed by multi-battle conflict. There are two disjoint sets of battlefields, each of which is associated with a player who competes only within that set. The common enemy competes in both sets of battlefields. An ‘enemy-of-my-enemy-is-my-friend’ alliance forms when the two players facing the common enemy agree on a pre-conflict transfer of resources among themselves. We examine the case in which the players may commit to binding ex post transfers (alliances with full commitment) and the case in which ex post transfers are not feasible (self-enforcing alliances). Models that utilize the lottery contest success function typically yield qualitatively different results from those arising in models with the auction contest success function. However, under both contest success functions, alliances with full commitment result in identical alliance transfers for all parameter configurations, and self-enforcing alliances yield identical transfers over a subset of the parameter space. Our results, thus, provide a partial robustness result for ‘enemy-of-my-enemy-is-my-friend’ alliances.