Market Instability in a Stackelberg Duopoly

m

-period duopoly model with inventory costs, where each firm chooses when to produce. We find that, in contrast to most existing works concerning endogenous roles of the firms, no pure strategy equilibrium exists when m is strictly larger than two. This result indicates that no stable pattern of allocation of roles exists except for a two-period model; thus the leader-follower relationship inevitably becomes instable.