The path player game

We introduce the path player game, a noncooperative network game with a continuum of mutually dependent set of strategies. This game models network flows from the point of view of competing network operators. The players are represented by paths in the network. They have to decide how much flow shall be routed along their paths. The competitive nature of the game is due to the following two aspects: First, a capacity bound on the overall network flow links the decisions of the players. Second, edges may be shared by several players which might have conflicting goals. In this paper, we prove the existence of feasible and pure-strategy equilibria in path player games, which is a nontrivial task due to noncontinuity of payoff functions and the infinite, mutually dependent strategy sets. We analyze different instances of path player games in more detail and present characterizations of equilibria for these cases.