Theory and Decision

, Volume 49, Issue 4, pp 361–374 | Cite as

Equilibrium Bidding without the Independence Axiom: A Graphical Analysis

  • Veronika Grimm
  • Ulrich Schmidt


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.

Auctions Non-expected utility 


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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Veronika Grimm
    • 1
  • Ulrich Schmidt
    • 1
  1. 1.Department of EconomicsHumboldt–University at BerlinBerlinGermany

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