Auctions Where Incomes are Private Information and Preferences (Non Quasi-Linear) are Common Knowledge

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Kobe University and at the 10th SAET conference in Singapore. The usual disclaimer applies. Terms of use: Documents in AbstractWe consider a two good world where an individual i with income m i has utility function u (x, y), where x ∈ [0, ∞) and y ∈ {0, 1}. We first derive the valuation (maximum price that he is willing to pay for the object) for good y as a function of his income. Then we consider the following problem. Suppose good x is available in a store at a fixed price 1. Good y can be obtained in an auction. In such a situation we show that bidding ones own valuation is an equilibrium in a second-price auction. With risk neutral bidders and high enough incomes we derive the symmetric equilibrium in first-price and all-pay auctions and show that revenue equivalence fails to hold. With risk neutrality we also show that under mild restrictions, the revenue maximising reserve price is zero for all the three auctions and the all-pay auction with zero reserve price fetches the highest expected revenue. With low enough incomes, we show that under some restrictions, bidding ones own valuation is a symmetric equilibrium even for first-price and all-pay auctions. Here also, the expected revenue is the highest with all-pay auctions.Journal of Economic Literature classification number D44

Reserve Price When Bidders are Asymmetric

“…While there are other papers in the literature that find the same result (e.g. Englebrecht-Wiggans (1987), McAfee and McMillan (1987), and Lu (2010)), they all assume that symmetric bidders have to pay some participation (or information) cost/fee before entering the auction or non quasi linear utility functions (Dastidar (2010)). In our model, asymmetric bidders do not have cost of participation nor do they buy information.…”

“…Then, the seller would not set an effective reserve price. Englebrecht-Wiggans (1987), by assuming that bidders have a cost to participate in the auction, and Dastidar (2010), by assuming a model with non-quasi linear utility functions, show that the optimal reserve price will be equal to zero (effectively no reserve price). Also, McAfee and McMillan (1987) and Lu (2010) show that sellers may not use reserve price but the "endogenous number" of bidders have to buy information/pay entry fee.…”