Strategic rationing in Stackelberg games

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. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).