Network-formation games with regular objectives

Unlike the case of reachability objectives, here the paths selected by the players need not be simple, thus a player may traverse some edges several times. Edge costs are shared by the players with the share being proportional to the number of times the edge is traversed. We study the existence of a pure Nash equilibrium (NE), the inefficiency of a NE compared to a social-optimum solution, and computational complexity problems in this setting.