Mathematical Analysis
The theory of unique bid auctions has been the subject of mathematical investigation. In a 2007 paper Bruss, Louchard and Ward proposed a technique for calculating game-theoretic probabilistic optimal strategies for unique bid auctions, given a small set of extra assumptions about the nature of the auction. Another paper by Raviv and Gabor in the same year made theoretical predictions and compared their results to the results of real-world unique bid auctions. Another paper by Rapoport et. al. compared theoretical results to the results of experimental auctions.
Further work by Bruss et al. and a number of other researchers including Gallice, and Rapoport and Otsubo has continued to develop the theory on this subject.
In a 2012 study Pigolotti et.al. conducted a thorough study of the unique bid auction in the grand canonical ensemble, finding a theoretical expression for the Nash equilibrium distribution and showing that real-world players play according to this distribution when the number of players in the auction is low.
Read more about this topic: Unique Bid Auction
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