Strategic rationing in Stackelberg games

Abstract

This paper examines Stackelberg price-quantity competition with imperfectly substitutable products. Under general cost and demand conditions, we establish existence of a subgame-perfect Nash equilibrium and provide a full characterization of the set of subgame-perfect Nash equilibria. In each equilibrium, the leader rations part of its clientele. Assuming linear demand and cost functions, first- and second-mover advantages are shown to critically depend on the degree of spillover demand, i.e., how many of the unserved customers visit the follower. We identify the presence of a spillover demand paradox. The leader may be the bigger firm and make more profit, but only when a sufficiently large part of its unmet demand shifts to the follower.