Equilibrium Bidding without the Independence Axiom: A Graphical Analysis
- 59 Downloads
In this paper we examine optimal bidding without the independence axiom in a unified framework which allows for a clear graphical representation. Thus, we can show very simply the independence axiom to be a necessary and sufficient condition on preferences for strategical equivalence of the two first-price and second-price auctions, respectively, and for the second-price sealed-bid auction to be demand revealing. The analysis reveals that the betweenness property is necessary and sufficient for the ascending-bid auction to be demand revealing while optimal bids exceed (are less than) bidders' valuations, iff preferences are quasiconcave (quasiconvex). Furthermore, it can be shown that fanning out (fanning in) leads to a higher (lower) selling-price in open than in sealed-bid auctions.
Unable to display preview. Download preview PDF.
- Coppinger, V.M., Smith, V.L. and Titus, J.A. (1980), Incentives and Behavior in English, Dutch and Sealed-Bid Auctions, Economic Inquiry 43: 1–22.Google Scholar
- Cox, J., Roberson, B. and Smith, V. (1982), Theory and Behavior of Single Object Auctions, in V.L. Smith, (ed.), Research in Experimental Economics, Greenwich: JAI Press, 1–43.Google Scholar
- Holt, C.A. (1986), Preference Reversals and the Independence Axiom, American Economic Review 76: 508–515.Google Scholar
- Kagel, J.H. (1995), Auctions: A Survey of Experimental Research, in J.H. Kagel and Roth A.E. (eds.), The Handbook of Experimental Economics, Princeton, 501–585.Google Scholar
- Kagel, J.H., Harstad, R.M. and Levin, D. (1987), Information Impact and Allocation Rules in Auctions with Affiliated Private Values: A Laboratory Study, Econometrica 55: 1275–1304.Google Scholar
- Karni, E. (1986), Revelations in Auctions and the Structure of Preferences, Working Paper No. 175, The John Hopkins University, Baltimore.Google Scholar
- Karni, E. (1988), On the Equivalence between Descending Bid Auctions and First Price Sealed Bid Auctions, Theory and Decision 25: 211–217.Google Scholar
- Karni, E. and Safra Z. (1989a), Dynamic Consistency, Revelations in Auctions and the Structure of Preferences, Review of Economic Studies 56: 421–434.Google Scholar
- Karni, E. and Safra, Z. (1989b), Ascending Bid Auctions with Behaviorally Consistent Bidders, Annals of Operations Research 19: 435–446.Google Scholar
- Machina, M.J. (1982), Expected Utility Analysis Without the Independence Axiom, Econometrica, 50: 393–405.Google Scholar
- Schmidt, U. (2000), Alternatives to Expected Utility: Some Formal Theories, in S. Babera, P.J. Hammond and C. Seidl (eds.), Handbook of Utility Theory, Vol. II, Dordrecht (forthcoming).Google Scholar
- Weber, R. (1982), The Allais Paradox, Dutch Auctions and Alpha-Utility Theory, Working Paper No. 536, Kellog Graduate School of Management, Northwestern University, Evanston.Google Scholar