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Learning, Mean Field Approximations, and Phase Transitions in Auction Models

Author

Listed:
  • Juan Pablo Pinasco

    (Greenmap - Global REnewable ENergy Mass Adoption Program
    Universidad de Buenos Aires
    CONICET - Consejo Nacional de Investigaciones Científicas y Técnicas)

  • Nicolas Saintier

    (Universidad de Buenos Aires
    CONICET - Consejo Nacional de Investigaciones Científicas y Técnicas)

  • Martin Kind

    (Greenmap - Global REnewable ENergy Mass Adoption Program)

Abstract

In this paper, we study an agent-based model for multi-round, pay as bid, sealed bid reverse auctions using techniques from partial differential equations and statistical mechanics tools. We assume that in each round a fixed fraction of bidders is awarded, and bidders learn from round to round using simple microscopic rules, adjusting myopically their bid according to their performance. Agent-based simulations show that bidders coordinate in the sense that they tend to bid the same value in the long-time limit. Moreover, this common value is the true cost or the ceiling price of the auction, depending on the level of competition. A discontinuous phase transition occurs when half of the bidders win. We establish the corresponding rate equations, and we obtain a system of ordinary differential equations describing the dynamics. Finally, we derive formally the kinetic equations modeling the dynamics, and we study the asymptotic behavior of solutions of the corresponding first-order, nonlinear partial differential equation satisfied by the distribution of agents.

Suggested Citation

  • Juan Pablo Pinasco & Nicolas Saintier & Martin Kind, 2024. "Learning, Mean Field Approximations, and Phase Transitions in Auction Models," Dynamic Games and Applications, Springer, vol. 14(2), pages 396-427, May.
    • Handle: RePEc:spr:dyngam:v:14:y:2024:i:2:d:10.1007_s13235-023-00508-9
    DOI: 10.1007/s13235-023-00508-9
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