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Strategic rationing in Stackelberg games

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  • Yousefimanesh, Niloofar
  • Bos, Iwan
  • Vermeulen, Dries

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.

Suggested Citation

  • Yousefimanesh, Niloofar & Bos, Iwan & Vermeulen, Dries, 2023. "Strategic rationing in Stackelberg games," Games and Economic Behavior, Elsevier, vol. 140(C), pages 529-555.
    • Handle: RePEc:eee:gamebe:v:140:y:2023:i:c:p:529-555
    DOI: 10.1016/j.geb.2023.05.001
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    More about this item

    Keywords

    Price-quantity competition; Rationing; Spillover demand; Stackelberg models;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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