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

Juan Pablo Pinasco (), Nicolas Saintier () and Martin Kind ()
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Juan Pablo Pinasco: Greenmap - Global REnewable ENergy Mass Adoption Program
Nicolas Saintier: Universidad de Buenos Aires
Martin Kind: Greenmap - Global REnewable ENergy Mass Adoption Program

Dynamic Games and Applications, 2024, vol. 14, issue 2, No 7, 396-427

Abstract: 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.

Keywords: Auctions; Agent-based models; Learning; Kinetic models; 91A22; 91A26; 91A40 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13235-023-00508-9

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