Ranking Auctions: a Cooperative Approach

In this paper, we deal with situations arising from markets where an Internet search service provider offers a service of listing firms in decreasing order according to what they have bid. We call these ranking auction situations and introduce the corresponding TU-games. The core, as well as the two friendly solutions for the corners of the market, in this class of games can be easily described using a related assignment game. We study the Alexia value and the Shapley value of this type of games. Using these solutions, we show which circumstances in the game are in favor of the provider and which are beneficial to the bidders.

[1]  R. Branzei,et al.  Two Classes of Cooperative Games Related to One-Object Auction Situations , 2006 .

[2]  Agnieszka Wiszniewska-Matyszkiel,et al.  Game theory and mathematical economics , 2006 .

[3]  R. Branzei,et al.  Convex Games versus Clan Games , 2008 .

[4]  Philip Wolfe,et al.  Contributions to the theory of games , 1953 .

[5]  Shigeo Muto,et al.  On Big Boss Games , 1988 .

[6]  Christopher S. Tang,et al.  An auction model arising from an Internet search service provider , 2006, Eur. J. Oper. Res..

[7]  D. Graham,et al.  Collusive Bidder Behavior at Single-Object Second-Price and English Auctions , 1987, Journal of Political Economy.

[8]  L. Shapley,et al.  The assignment game I: The core , 1971 .

[9]  Vito Fragnelli,et al.  On Cooperative Games Related to Market Situations and Auctions , 2009, IGTR.

[10]  Pradeep Dubey,et al.  Totally balanced games arising from controlled programming problems , 1984, Math. Program..

[11]  Thomas A. Weber,et al.  A Model of Search Intermediaries and Paid Referrals , 2006, Inf. Syst. Res..

[12]  L. Shapley.  A Value for n-person Games , 1988 .

[13]  A. Atkinson.  On the measurement of inequality , 1970 .

[14]  Vito Fragnelli,et al.  Tree-connected peer group situations and peer group games , 2002, Math. Methods Oper. Res..

[15]  René van den Brink,et al.  Null or nullifying players: The difference between the Shapley value and equal division solutions , 2007, J. Econ. Theory.

[16]  Ester Camiña,et al.  A generalized assignment game , 2006, Math. Soc. Sci..

[17]  J. Richard,et al.  Differential Payments within a Bidder Coalition and the Shapley Value , 1990 .

[18]  Zsolt Katona,et al.  The Race for Sponsored Links: Bidding Patterns for Search Advertising , 2010, Mark. Sci..