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Auctions with Limited Commitment

Author

Listed:
  • Qingmin Liu
  • Konrad Mierendorff
  • Xianwen Shi

Abstract

We study auction design in the standard symmetric independent private values environment, where the seller lacks the commitment power to withhold an unsold object off the market. The seller has a single object and can conduct an infinite sequence of standard auctions with reserve prices to maximize her expected profit. In each period, the seller can commit to a reserve price for the current period but cannot commit to future reserve prices. We analyze the problem with limited commitment through an auxiliary mechanism design problem with full commitment, in which an additional constraint reflects the sequential rationality of the seller. We characterize the maximal profit achievable in any perfect Bayesian equilibrium in the limit as the period length vanishes. The static full commitment profit is not achievable but the seller can always guarantee the profit of an efficient auction. If the number of buyers exceeds a cutoff which is small for many distributions, the efficient auction is optimal. Otherwise, the efficient auction is not optimal, and we give conditions under which the optimal solution consists of an initial auction with a non-trivial reserve price followed by a continuously decreasing price path. The solution is described by a simple ordinary differential equation. Our analysis combines insights from bargaining, auctions, and mechanism design.

Suggested Citation

  • Qingmin Liu & Konrad Mierendorff & Xianwen Shi, 2013. "Auctions with Limited Commitment," Working Papers tecipa-504, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-504
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    File URL: https://www.economics.utoronto.ca/public/workingPapers/tecipa-504.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

    Auctions; Commitment; Bargaining; Mechanism Design; Coase Conjecture;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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