On Expressing Value Externalities in Position Auctions

We introduce a bidding language for expressing negative value externalities in position auctions for online advertising. The unit-bidder constraints (UBC) language allows a bidder to condition a bid on its allocated slot and on the slots allocated to other bidders. We introduce a natural extension of the Generalized Second Price (GSP) auction, the expressive GSP (eGSP) auction, that induces truthful revelation of constraints for a rich subclass of unit-bidder types, namely downward-monotonic UBC. We establish the existence of envy-free Nash equilibrium in eGSP under a further restriction to a subclass of exclusion constraints, for which the standard GSP has no pure strategy Nash equilibrium. The equilibrium results are obtained by reduction to equilibrium analysis for reserve price GSP (Even-Dar et al. 2008). In considering the winner determination problem, which is NP-hard, we bound the approximation ratio for social welfare in eGSP and provide parameterized complexity results.

[1]  Dimitrios M. Thilikos,et al.  Invitation to fixed-parameter algorithms , 2007, Comput. Sci. Rev..

[2]  Jeffrey B. Sidney,et al.  Decomposition Algorithms for Single-Machine Sequencing with Precedence Relations and Deferral Costs , 1975, Oper. Res..

[3]  Clyde L. Monma,et al.  Sequencing with Series-Parallel Precedence Constraints , 1979, Math. Oper. Res..

[4]  Ashish Goel,et al.  Truthful auctions for pricing search keywords , 2006, EC '06.

[5]  Glenn Ellison,et al.  Position Auctions with Consumer Search , 2007 .

[6]  Anna R. Karlin,et al.  On the Equilibria and Efficiency of the GSP Mechanism in Keyword Auctions with Externalities , 2008, WINE.

[7]  Luca Trevisan,et al.  A PCP characterization of NP with optimal amortized query complexity , 2000, STOC '00.

[8]  Satoru Iwata,et al.  A combinatorial, strongly polynomial-time algorithm for minimizing submodular functions , 2000, STOC '00.

[9]  David H. Reiley,et al.  Northern exposure: a field experiment measuring externalities between search advertisements , 2010, EC '10.

[10]  Roger B. Myerson,et al.  Optimal Auction Design , 1981, Math. Oper. Res..

[11]  Nicole Immorlica,et al.  Externalities in Keyword Auctions: An Empirical and Theoretical Assessment , 2009, WINE.

[12]  Tomasz P. Michalak,et al.  Combinatorial auctions with externalities , 2010, AAMAS.

[13]  E. Lawler.  Sequencing Jobs to Minimize Total Weighted Completion Time Subject to Precedence Constraints , 1978 .

[14]  Arpita Ghosh,et al.  Expressive auctions for externalities in online advertising , 2010, WWW '10.

[15]  Nick Craswell,et al.  An experimental comparison of click position-bias models , 2008, WSDM '08.

[16]  Fanica Gavril,et al.  Some NP-complete problems on graphs , 2011, CISS 2011.

[17]  Jon Feldman,et al.  Sponsored Search Auctions with Markovian Users , 2008, WINE.

[18]  R. Vohra,et al.  Algorithmic Game Theory: Sponsored Search Auctions , 2007 .

[19]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[20]  Riccardo Colini-Baldeschi,et al.  Sponsored search auctions , 2013, WSDM.

[21]  Mohammad Mahdian,et al.  A Cascade Model for Externalities in Sponsored Search , 2008, WINE.

[22]  Mohammad Mahdian,et al.  Externalities in online advertising , 2008, WWW.

[23]  Jon Feldman,et al.  Bidding to the Top: VCG and Equilibria of Position-Based Auctions , 2006, WAOA.

[24]  Subhash Khot,et al.  On the power of unique 2-prover 1-round games , 2002, Proceedings 17th IEEE Annual Conference on Computational Complexity.

[25]  B. Moldovanu,et al.  Efficient Design with Interdependent Valuations , 2001 .

[26]  Kevin D. Glazebrook,et al.  On Single-Machine Scheduling with Precedence Relations and Linear or Discounted Costs , 1981, Oper. Res..

[27]  I. Segal,et al.  What Makes Them Click: Empirical Analysis of Consumer Demand for Search Advertising , 2012 .

[28]  Satoru Iwata,et al.  A combinatorial strongly polynomial algorithm for minimizing submodular functions , 2001, JACM.

[29]  E. Stacchetti,et al.  Multidimensional Mechanism Design for Auctions with Externalities , 1999 .

[30]  N. Meyers,et al.  H = W. , 1964, Proceedings of the National Academy of Sciences of the United States of America.

[31]  Subhash Khot,et al.  Inapproximability of Vertex Cover and Independent Set in Bounded Degree Graphs , 2009, 2009 24th Annual IEEE Conference on Computational Complexity.

[32]  Jon Feldman,et al.  Position Auctions with Bidder-Specific Minimum Prices , 2008, WINE.

[33]  M. R. Garey,et al.  Optimal task sequencing with precedence constraints , 1973, Discrete Mathematics.

[34]  Monaldo Mastrolilli,et al.  Single Machine Precedence Constrained Scheduling Is a Vertex Cover Problem , 2009, Algorithmica.

[35]  S. Muthukrishnan,et al.  Bidding on Configurations in Internet Ad Auctions , 2009, COCOON.

[36]  D. Parkes,et al.  Optimize-and-Dispatch Architecture for Expressive Ad Auctions , 2005 .