Time Consistency in Games of Timing

This paper tackles the issue of choosing roles in duopoly games. First, it is shown that the two necessary (and sufficient, if both satisfied) conditions for sequential play to emerge at equilibrium are that both leader and follower are at least weakly better off than under simultaneous play. Second, by means of a two-stage game of vertical differentiation, it is shown that if firms can commit to their respective timing decisions, there may exists a case where the leader is not necessarily better off than in the simultaneous equilibrium. Finally, in the absence of any commitment devices, it is proved that the timing choice can be time inconsistent if it is taken before firms proceed to play in both stages taking place in real time