We introduce the path player game, a noncooperative networkgame with a continuum of mutually dependent set of strategies. This gamemodels network flows from the point of view of competing network oper-ators. The players are represented by paths in the network. They have todecide how much flow shall be routed along their paths. The competitive na-ture of the game is due to the following two aspects: First, a capacity boundon the overall network flow links the decisions of the players. Second, edgesmay be shared by several players which might have conflictinggoals. Inthis paper, we prove the existence of feasible and pure-strategy equilibriain path player games, which is a non-trivial task due to non-continuity ofpayoff functions and the infinite, mutually dependent strategy sets. We an-alyze different instances of path player games in more detailand presentcharacterizations of equilibria for these cases.
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