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Dynamic Conflict on a Network

Players are endowed with resources. A player can engage in conflict with others to enlarge his resources. The set of potential conflicts is defined by a contiguity network. Players are farsighted and aim to maximize their resources. They decide on whether to wage war or remain peaceful. The winner of a war takes control of the loser's node and resources; he then decides on whether to wage war against other neighbours, or to stay peaceful. The game ends when either all players choose to be peaceful or when only one player is left. We study the influence of the technology of conflict and the structure of the network on war and peace. Our first result identifies a threshold property in the technology of conflict: above this threshold, every ruler wishes to wage war and, eventually, there is a hegemon. Below the threshold, resources and networks determine the prospects for peace and the number of kingdoms. We develop sufficient conditions for war and provide examples with lasting peace.