The fixed price offer mechanism in Trade Me online auctions

Abstract

The fixed-price-offer (FPO) mechanism in Trade Me auctions allows sellers to make a take-it-or-leave-it offer at the conclusion of an unsuccessful auction. Weinvestigate the effects of the FPO option on strategies and outcomes in independent-value auctions. The FPO option induces some bidders with a value above the seller's reserve to wait for an FPO instead of bidding. Overall, the FPO option increases the probability of sale but reduces expected seller revenue compared with a standard auction. The impact of the FPO option is reduced when the number of bidders increases.

Keywords:

• fixed-price offer
• private value auction
• online auction
• optimal reserve price
• second-chance offer

Acknowledgements

The authors would like to warmly thank our editor Matthew Ryan, the anonymous referee, Vivienne Groves, Phil Gunby, Simon Loertscher, Ian MacDonald, Andrew McLennan, Phil Meguire, Ilke Onur, Alan Woodfield, seminar participants at Victoria University of Wellington and the University of Auckland and conference participants at CEA 2009 (Toronto), AETW 2010 (Melbourne) and EARIE 2010 (Istanbul) for their comments. Laura Meriluoto gratefully acknowledges funding from University of Canterbury, College of Business and Economics Research Committee. This paper builds on the 2008 Honours project of Hamish Kidd and the 2009 Honours project of Andrew Smith.

Notes

1. See, for example, Menezes and Ryan (2005) for a discussion on commitment value of reserve prices.

2. See, for example, Krishna (2002) for a definition of a standard versus non-standard auction.

3. In the former case on Trade Me auctions, a yellow flag appears by the start price indicating that the reserve will be met after the first bid.

4. This result as it is well-known from Vickrey (1961) and the subsequent auction theory literature.

5. As a convention, we assume that bidders indifferent between the two strategies will play strategy W. This is just for expositional convenience. With a continuous distribution ofbidders' valuations, the choice of strategy when indifferent has no impact on any of the equilibrium variables derived in the paper.

6. See Hogan and Meriluoto (2011) for a proof of the equivalence between equations (13) and (14).

7. The number of bidders in Grant et al. is stochastic. By an increase in n in their model, therefore, we mean a shift in the distribution of possible n to a stochastically dominating distribution.

8. The formula for the maximised expected revenue is not shown here but is trivially derived.