Abstract
In this paper, the auction problem of a kind of continuous homogeneous divisible goods is studied and a uniform price auction mechanism is presented based on three conditions, i.e. the auctioneer’s supply is variable, every bidder submits multiple rounds continuous linear bidding, and every bidder’s valuation to per unit of the goods is independent private information. Concretely, two key problems, i.e. the bidders’ asymptotic strategic behaviours and forming process and composition of equilibrium points are explored. The conclusion is drawn that different bidders’ bidding order and different starting points of initial bidding would not cause different local equilibrium points, and if the equilibrium points exist, then the equilibrium point is unique.
Highlights
With the development of auction market of the emission rights, treasury and spectrum, multi-object auctions become one of the most active research areas in auction theory in recent years
With the improvement of auctioneer’s strategies as its main line, the elimination of low price equilibrium as its core, the induction of the ideal equilibrium as its keynote, this paper presents a uniform price auction mechanism with variable supply based on multiple rounds linear bidding
We explore the bidders’ asymptotic strategic behaviours and discuss the formation process of the desired equilibrium in theory, and answer the question that whether the equilibrium excursion exists in our uniform price auction mechanism
Summary
With the development of auction market of the emission rights, treasury and spectrum, multi-object auctions become one of the most active research areas in auction theory in recent years. Wilson (1979) was the first to consider uniform price auctions of divisible goods He showed there is an equilibrium in which the asset is sold for half of its value in several settings. Klemperer (1989) generalized this result by showing that any low price can be supported in equilibrium Based on these results, Back and Zender (1993) demonstrated how such a uniform-price auction can yield sensible results, consider the strategic difference between unit-demand and divisible goods auctions, and compare uniform-price and discriminatory auctions. Groves (2011) studied a charity auction with multiple goods and showed that the highest-losing bid uniform price auction revenue dominates its lowest-winning bid counterpart These are all the important research results in uniform price auctions theory in the past few years.
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