Abstract
Can search engines increase revenues by changing their position auctions? In this paper, I analyze position auctions with general pricing rules to answer this question. In these auctions, there are several items that are commonly ranked by bidders with unit demand. I show that revenues remain the same for position auctions with regular pricing rules where the price for an item depends on the bids of agents who win lower-ranked items. In addition, all of the bidders have the same ex post payoffs. I also show that regularity is a necessary condition to get ex post payoff equivalence.
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Notes
For a brief history of the GSP auctions, see Edelman et al. (2007).
In a subsequent work, Babaioff and Roughgarden (2010) analyze a special case of my model when different auction formats can be used depending on the search query, which is contrary to the practice.
The results remain the same if there is also an advertiser-specific multiplier in the click probability. However, the separability of the click probability into the position and advertiser-specific components is questioned in recent work, for example, Jeziorski and Segal (2009). This assumption is made in most of the literature including Edelman et al. (2007), Varian (2007), Hashimoto (2010).
With some abuse of notation, I denote the strategy profile \((\sigma _1(v_1),\ldots ,\sigma _{k}(v_k))\) by \((\sigma _i(v_i),\sigma _{-i}(v_{-i}))\).
Here, let \(v_{i(n+1)}=0\) for all \(i\).
It is worth mentioning here that whether the VCG is in this class or not is a moot question since the VCG is a static auction. What I show is the equivalence of a class of dynamic auctions to the VCG auction, which is static.
See Chapter 8.B of Mas-Colell et al. (1995) for the relevant game theoretic definitions.
To be more precise, the statement holds for all values perhaps except a set of measure zero.
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The author acknowledges the financial support of the SIEPR Leonard W. Ely & Shirley R. Ely Graduate Student Fellowship at Stanford University.
I am indebted to Alexander Frankel, Michael Ostrovsky, Daniel Taylor, and Robert Wilson for comments and support. This paper is a part of my dissertation submitted to the Stanford University.
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Yenmez, M.B. Pricing in position auctions and online advertising. Econ Theory 55, 243–256 (2014). https://doi.org/10.1007/s00199-013-0748-0
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DOI: https://doi.org/10.1007/s00199-013-0748-0