Learning, mean field approximations, and phase transitions in auction models (Q6556815)

In this article, the authors 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 under the assumption 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.\N\NThe problem of an unadvertised agreement between buyers of non-exclusive rights at a spectrum auction for the agreed formation of price bids is considered from the viewpoint of game theory and operations research. The simulations show that bidders coordinate in the sense that they tend to bid the same value in the long-time limit. In Section 6 the authors analyze the case of a heterogeneous cost distribution among the bidders showing that the phase transition at \(\rho = 2\) persists in this more general setting. When \(\rho = 2\), an exact formula for the final mean price involving the cost distribution is obtained heuristically building on the intuition developed so far, and which agrees very well with the simulations.