Ex post efficiency in the buyer's bid double auction when demand can be arbitrarily larger than supply (Q5937321)

The aim of the paper is to investigate the efficiency of the equilibrum state of the the market when the demand overgrows the supply. The authors base on the buyers bid double auction model. Namely, there are two groups of players - buyers and sellers, each trading one unit. Having each one bid, the uniform transaction price \(p\) is chosen. Here, \(p\) is the biggest price such that all sellers requests on the level lower than \(p\) and all buyers requests on the level higher than \(p\) are fulfilled. The requests on the level \(p\) may be fulfilled partially. The gain of a player is the difference between the uniform market price \(p\) and his individual base price \(c\) (\(p-c\) for sellers and \(c-p\) for buyers) if he trades and 0 otherwise.NEWLINENEWLINENEWLINEThe equilibrium is due to the gain. The players choose a strategy to maximize it.NEWLINENEWLINENEWLINEThe efficiency is measured with respect to the volume of the transactions.NEWLINENEWLINENEWLINEThe main result of the paper is to show that when the numbers of buyers \(m\) and sellers \(n\) (\(m \geq \beta n\), for \(\beta >1\)) tend to infinity then the expected efficiency tends to the maximal possible one.