Interconnected Battles

We study a model of multibattle contest with two players and spillovers of efforts between battles. The players distribute their costly efforts across the battles. Each battle receives effort assigned to it directly (real efforts) as well as spillovers of efforts assigned to the other battlefield (effective efforts). The probability of winning a battle is determined by a contest success function and depends on the effective efforts assigned to it by the players. Winning a battle has a common value to each of the players.

We show uniqueness of Nash equilibria in the model and we characterize the equilibrium efforts. We also uncover a surprising feature of the equilibria: network invariance of equilibrium payoffs and probabilities of success. We also show that equilibrium efforts satisfy a generalization of the property of neighbourhood inclusion.