Study of Complex Auction Dynamics Through Mean Field Theory
http://iopscience.iop.org/article/10.1088/1367-2630/17/9/093003/pdf
This paper studies the approach of using methods from statistical and nonlinear physics to study a unique class of auctions, the lowest unique bid auction (LUBA), which has recently emerged as a form of online auctions. Lowest unique bid auctions work by having bidders bid on an item and the bidder with the lowest unique bid having the option to claim the item being bidded on by paying the price that they bid. These auctions typically make money through means of having the bidders pay a small entrance fee. Though hypothetically, items normally worth thousands of dollars can be sold for pennies, the entrance fee paid by the many bidders drawn in by the low prices make up for the deficit. Using empirically collected bidding price distributions for these types of auctions, a general feature of these distributions was able to be determined. An inverted J-shaped function was found to fit the empirical data, with an exponential decay function modeling the behavior of bids in the large-price regime. Researchers developed a model based on this insight in which multiple agents places stochastic bids in the field of the winner’s attractiveness. Using this model, they were able to accurately predict distribution functions for the bids of other LUBAs and hope to be able to further apply this model to achieve quantitative insights into complex socio-economic phenomena.
The inspiration for using statistical mechanics to model auctions comes is because for systems with many agents interacting with one another, one can make an analogy between the macroscopic properties of bidders in a lowest unique bid auction and the microscopic behavior of particles. Fully formulating this analogy allows one to use the rigor and framework of statistical mechanics to abstract away all the specific details of the macroscopic problem to make predictions, and then reinterpret the microscopic results into macroscopic phenomena. This has been applied before in many fields, from studying biological systems with statistical mechanics to the development of simulated annealing in optimization problems in computer science.
The most important result that this model draws is that for a large enough group of people (even though the people themselves may be different) as long as the demographics of people were sampled similarly, participating in a LUBA, will generate a stable equilibrium price that their model has shown to be universal. This is significant because even though LUBA is a very niche socio-economic phenomena, it is a proof of concept that statistical mechanics can be used to apply to people and predict their mean behavior in a certain scenario. This is interesting because we are able to use the topic of statistical mechanics to make a statement that is universally true for human behavior in auctions and it applies to the topics that we learned in lecture, albeit a different kind of auction.