Algorithmic game theory

A new era of theoretical computer science addresses fundamental problems about auctions, networks, and human behavior.

[1]  N. Vorob’ev Equilibrium Points in Bimatrix Games , 1958 .

[2]  Bala Kalyanasundaram,et al.  An optimal deterministic algorithm for online b-matching , 1996, Theor. Comput. Sci..

[3]  B. Hajek,et al.  Optimal allocation of a divisible good to strategic buyers , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[4]  J. Harsanyi Games with Incomplete Information Played by “Bayesian” Players Part II. Bayesian Equilibrium Points , 1968 .

[5]  Yossi Azar,et al.  Fast convergence to nearly optimal solutions in potential games , 2008, EC '08.

[6]  Vahab S. Mirrokni,et al.  Sink equilibria and convergence , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[7]  Ramesh Johari,et al.  Efficiency loss in market mechanisms for resource allocation , 2004 .

[8]  E. Maskin The Theory of Implementation in Nash Equilibrium: A Survey , 1983 .

[9]  Moshe Babaioff,et al.  Truthful Mechanisms for One-Parameter Agents , 2008, Encyclopedia of Algorithms.

[10]  M. Satterthwaite Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions , 1975 .

[11]  Bernhard von Stengel,et al.  Computing Normal Form Perfect Equilibria for Extensive Two-Person Games , 2002 .

[12]  S. Bikhchandani,et al.  Incentive Compatibility in Multi-unit Auctions , 2003 .

[13]  Tim Roughgarden,et al.  Truthful Approximation Schemes for Single-Parameter Agents , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[14]  Vijay Kumar,et al.  Online learning in online auctions , 2003, SODA '03.

[15]  D. Koller,et al.  Efficient Computation of Equilibria for Extensive Two-Person Games , 1996 .

[16]  Noam Nisany,et al.  The Communication Requirements of E¢cient Allocations and Supporting Lindahl Prices¤ , 2003 .

[17]  Ilya Segal,et al.  An Efficient Dynamic Mechanism , 2013 .

[18]  Tim Roughgarden,et al.  How bad is selfish routing? , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[19]  N. Nisan,et al.  On the Computational Power of Iterative Auctions I: Demand Queries , 2005 .

[20]  J. Rochet A necessary and sufficient condition for rationalizability in a quasi-linear context , 1987 .

[21]  Jerry R. Green,et al.  Characterization of Satisfactory Mechanisms for the Revelation of Preferences for Public Goods , 1977 .

[22]  N. Nisan The Communication Complexity of Approximate Set Packing and Covering , 2002, ICALP.

[23]  John. Moore,et al.  Subgame Perfect Implementation , 1988 .

[24]  Xiaotie Deng,et al.  Settling the Complexity of Two-Player Nash Equilibrium , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[25]  L. A. Goodman,et al.  Social Choice and Individual Values , 1951 .

[26]  Ronald M. Harstad,et al.  Computationally Manageable Combinational Auctions , 1998 .

[27]  David C. Parkes,et al.  The sequential auction problem on eBay: an empirical analysis and a solution , 2006, EC '06.

[28]  B. Stengel,et al.  Efficient Computation of Behavior Strategies , 1996 .

[29]  Avrim Blum,et al.  Online algorithms for market clearing , 2002, SODA '02.

[30]  Noam Nisan,et al.  Bidding and allocation in combinatorial auctions , 2000, EC '00.

[31]  Tim Roughgarden,et al.  The price of anarchy is independent of the network topology , 2002, STOC '02.

[32]  Charles A. Holt,et al.  Competitive Bidding for Contracts under Alternative Auction Procedures , 1980, Journal of Political Economy.

[33]  Mohammad Taghi Hajiaghayi,et al.  Regret minimization and the price of total anarchy , 2008, STOC.

[34]  Noam Nisan,et al.  Towards a characterization of truthful combinatorial auctions , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[35]  Paul W. Goldberg,et al.  The complexity of computing a Nash equilibrium , 2006, STOC '06.

[36]  Jérémie Gallien,et al.  Sloan School of Management Working Paper 4268-02 December 2002 Dynamic Mechanism Design for Online Commerce , 2002 .

[37]  E. Damme Stability and perfection of Nash equilibria , 1987 .

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

[39]  T. Sandholm,et al.  Chapter 12 The Winner Determination Problem , 2004 .

[40]  Joel E. Cohen,et al.  Paradoxical behaviour of mechanical and electrical networks , 1991, Nature.

[41]  Yoav Shoham,et al.  Computer science and game theory , 2008, CACM.

[42]  Margo I. Seltzer,et al.  Virtual worlds: fast and strategyproof auctions for dynamic resource allocation , 2003, EC '03.

[43]  John N. Tsitsiklis,et al.  Communication Requirements of VCG-Like Mechanisms in Convex Environments , 2006 .

[44]  Bruce Hajek,et al.  Do Greedy Autonomous Systems Make for a Sensible Internet , 2003 .

[45]  László Lovász,et al.  On the ratio of optimal integral and fractional covers , 1975, Discret. Math..

[46]  Jean François Pique,et al.  A revised simplex method with integer Q-matrices , 2001, TOMS.

[47]  Noam Nisan,et al.  Approximations by Computationally-Efficient VCG-Based Mechanisms , 2006, Electron. Colloquium Comput. Complex..

[48]  Mohammad Taghi Hajiaghayi,et al.  Adaptive limited-supply online auctions , 2004, EC '04.

[49]  Russell Bent,et al.  Online stochastic combinatorial optimization , 2006 .

[50]  D. Hoffman,et al.  How to acquire customers on the Web. , 2000, Harvard business review.

[51]  R.T. Maheswaran,et al.  Social welfare of selfish agents: motivating efficiency for divisible resources , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[52]  Ron Lavi,et al.  Algorithmic Mechanism Design , 2008, Encyclopedia of Algorithms.

[53]  David C. Parkes,et al.  Approximately Efficient Online Mechanism Design , 2004, NIPS.

[54]  Christos H. Papadimitriou,et al.  Worst-case Equilibria , 1999, STACS.

[55]  E. Vandamme Stability and perfection of nash equilibria , 1987 .

[56]  J. Harsanyi Games with Incomplete Information Played by 'Bayesian' Players, Part III. The Basic Probability Distribution of the Game , 1968 .

[57]  Pierre Hansen,et al.  Enumeration of All Extreme Equilibria of Bimatrix Games , 1996, SIAM J. Sci. Comput..

[58]  Noam Nisan,et al.  Online ascending auctions for gradually expiring items , 2005, SODA '05.

[59]  Noam Nisan,et al.  Competitive analysis of incentive compatible on-line auctions , 2000, EC '00.

[60]  Uriel Feige,et al.  Approximation algorithms for allocation problems: Improving the factor of 1 - 1/e , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[61]  Kursad Asdemir BIDDING PATTERNS IN SEARCH ENGINE AUCTIONS , 2006 .

[62]  Xiaotie Deng,et al.  Settling the complexity of computing two-player Nash equilibria , 2007, JACM.

[63]  T. Roughgarden Intrinsic robustness of the price of anarchy , 2012, Commun. ACM.

[64]  Avrim Blum,et al.  Preference Elicitation and Query Learning , 2004, J. Mach. Learn. Res..

[65]  D. Gale,et al.  Multi-Item Auctions , 1986, Journal of Political Economy.

[66]  M. Satterthwaite,et al.  Efficient Mechanisms for Bilateral Trading , 1983 .

[67]  Yu Jeffrey Hu Performance-Based Pricing Models in Online Advertising , 2004 .

[68]  Moshe Babaioff,et al.  Single-value combinatorial auctions and implementation in undominated strategies , 2006, SODA '06.

[69]  C. Papadimitriou,et al.  The complexity of computing a Nash equilibrium , 2009, CACM.

[70]  B. Stengel,et al.  COMPUTING EQUILIBRIA FOR TWO-PERSON GAMES , 1996 .

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

[72]  Mallesh M. Pai,et al.  Optimal Dynamic Auctions , 2008 .

[73]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[74]  Berthold Vöcking,et al.  Approximation techniques for utilitarian mechanism design , 2005, STOC '05.

[75]  Rahul Savani,et al.  Hard‐to‐Solve Bimatrix Games , 2006 .

[76]  Paul R. Milgrom,et al.  A theory of auctions and competitive bidding , 1982 .

[77]  Annamária Kovács,et al.  Fast Monotone 3-Approximation Algorithm for Scheduling Related Machines , 2005, ESA.

[78]  Anshul Kothar,et al.  Approximately-strategyproof and tractable multi-unit auctions , 2003 .

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

[80]  Chaitanya Swamy,et al.  Truthful and near-optimal mechanism design via linear programming , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[81]  Paul R. Milgrom,et al.  Rational Expectations, Information Acquisition, and Competitive Bidding , 1981 .

[82]  Avrim Blum,et al.  Near-optimal online auctions , 2005, SODA '05.

[83]  Matthew O. Jackson,et al.  A crash course in implementation theory , 2001, Soc. Choice Welf..

[84]  Oriol Carbonell-Nicolau Games and Economic Behavior , 2011 .

[85]  Noam Nisan,et al.  Incentive compatible multi unit combinatorial auctions , 2003, TARK '03.

[86]  F. Kelly,et al.  A Combinatorial Auction with Multiple Winners for Universal Service , 2000 .

[87]  Eyal Kushilevitz,et al.  Communication Complexity , 1997, Adv. Comput..

[88]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[89]  David C. Parkes,et al.  Models for Truthful Online Double Auctions , 2005, UAI.

[90]  Yunhong Zhou,et al.  Vindictive bidding in keyword auctions , 2007, ICEC.

[91]  Noam Nisan,et al.  Approximation algorithms for combinatorial auctions with complement-free bidders , 2005, STOC '05.

[92]  David C. Parkes,et al.  Iterative combinatorial auctions: achieving economic and computational efficiency , 2001 .

[93]  Richard J. La,et al.  Charge-sensitive TCP and rate control in the Internet , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[94]  Tuomas Sandholm Chapter 14: Optimal Winner Determination Algorithms , 2004 .

[95]  Aranyak Mehta,et al.  AdWords and generalized on-line matching , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[96]  M. D. Wilkinson,et al.  Management science , 1989, British Dental Journal.

[97]  Christos H. Papadimitriou,et al.  The complexity of pure Nash equilibria , 2004, STOC '04.

[98]  Eric J. Friedman,et al.  Pricing WiFi at Starbucks: issues in online mechanism design , 2003, EC '03.

[99]  Christos H. Papadimitriou,et al.  On the Complexity of the Parity Argument and Other Inefficient Proofs of Existence , 1994, J. Comput. Syst. Sci..

[100]  Mihalis Yannakakis,et al.  How easy is local search? , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[101]  S. Bikhchandani,et al.  Weak Monotonicity Characterizes Deterministic Dominant-Strategy Implementation , 2006 .

[102]  L. Shapley A note on the Lemke-Howson algorithm , 1974 .

[103]  Uriel Feige,et al.  On maximizing welfare when utility functions are subadditive , 2006, STOC '06.

[104]  T. Koopmans,et al.  Studies in the Economics of Transportation. , 1956 .

[105]  Shahar Dobzinski,et al.  An improved approximation algorithm for combinatorial auctions with submodular bidders , 2006, SODA '06.

[106]  Theodore Groves,et al.  Incentives in Teams , 1973 .

[107]  Michel Gendreau,et al.  Combinatorial auctions , 2007, Ann. Oper. Res..

[108]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[109]  Sushil Bikhchandani,et al.  The Package Assignment Model , 2002, J. Econ. Theory.

[110]  E. H. Clarke Multipart pricing of public goods , 1971 .

[111]  Tim Roughgarden,et al.  Algorithmic Game Theory: Some Greatest Hits and Future Directions , 2008, IFIP TCS.

[112]  Subhash Suri,et al.  Approximately-strategyproof and tractable multi-unit auctions , 2003, EC '03.

[113]  Lawrence M. Ausubel,et al.  The Clock-Proxy Auction: A Practical Combinatorial Auction Design , 2004 .

[114]  Dirk Bergemann,et al.  Dynamic Price Competition , 2003, J. Econ. Theory.

[115]  John C. Harsanyi,et al.  Games with Incomplete Information Played by "Bayesian" Players, I-III: Part I. The Basic Model& , 2004, Manag. Sci..

[116]  J. Nash Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[117]  M. Jansen Maximal nash subsets for bimatrix games , 1981 .

[118]  H. Keiding On the Maximal Number of Nash Equilibria in ann × nBimatrix Game , 1997 .

[119]  Christos H. Papadimitriou,et al.  On the Hardness of Being Truthful , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[120]  Amin Saberi,et al.  Multi-unit auctions with unknown supply , 2006, EC '06.

[121]  S. Reiter,et al.  Game forms with minimal message spaces , 1988 .

[122]  Roberto Burguet The condominium problem; auctions for substitutes , 2005 .

[123]  G. Rosenberg Enumeration of All Extreme Equilibria of Bimatrix Games with Integer Pivoting and Improved Degeneracy Check , 2005 .

[124]  Ennio Stacchetti,et al.  The English Auction with Differentiated Commodities , 2000, J. Econ. Theory.

[125]  Bruce E. Hajek,et al.  An efficient mechanism for allocation of a divisible good , 2004 .

[126]  K. Steiglitz Snipers, Shills, and Sharks: eBay and Human Behavior , 2007 .

[127]  Christos H. Papadimitriou,et al.  On Total Functions, Existence Theorems and Computational Complexity , 1991, Theor. Comput. Sci..

[128]  J. Geanakoplos Three brief proofs of Arrow’s Impossibility Theorem , 2001 .

[129]  Yoav Shoham,et al.  Multiagent Systems - Algorithmic, Game-Theoretic, and Logical Foundations , 2009 .

[130]  Maria-Florina Balcan,et al.  Mechanism design via machine learning , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[131]  Kousha Etessami,et al.  On the Complexity of Nash Equilibria and Other Fixed Points , 2010, SIAM J. Comput..

[132]  M. Trick,et al.  The computational difficulty of manipulating an election , 1989 .

[133]  Yishay Mansour,et al.  A Sparse Sampling Algorithm for Near-Optimal Planning in Large Markov Decision Processes , 1999, Machine Learning.

[134]  R. Pieters,et al.  Working Paper , 1994 .

[135]  Daniel Lehmann,et al.  Combinatorial auctions with decreasing marginal utilities , 2001, EC '01.

[136]  A. Gibbard Manipulation of Voting Schemes: A General Result , 1973 .

[137]  Aranyak Mehta,et al.  AdWords and Generalized On-line Matching , 2005, FOCS.

[138]  Noam Nisan,et al.  The communication requirements of efficient allocations and supporting prices , 2006, J. Econ. Theory.

[139]  T. Başar,et al.  Nash Equilibrium and Decentralized Negotiation in Auctioning Divisible Resources , 2003 .

[140]  Felix Wu,et al.  Incentive-compatible online auctions for digital goods , 2002, SODA '02.

[141]  V. Crawford,et al.  Job Matching with Heterogeneous Firms and Workers , 1981 .

[142]  Nicole Immorlica,et al.  Multi-unit auctions with budget-constrained bidders , 2005, EC '05.

[143]  Juan Feng Optimal mechanism for selling a set of commonly ranked objects , 2005 .

[144]  G. Ziegler Lectures on Polytopes , 1994 .

[145]  J. Walrand,et al.  Mechanisms for Efficient Allocation in Divisible Capacity Networks , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[146]  Garud Iyengar,et al.  Characterizing Optimal Adword Auctions , 2006, ArXiv.

[147]  C. E. Lemke,et al.  Bimatrix Equilibrium Points and Mathematical Programming , 1965 .

[148]  D. Bergemann,et al.  Efficient Dynamic Auctions , 2006 .

[149]  Paul Klemperer,et al.  Auctions: Theory and Practice , 2004 .

[150]  Christos H. Papadimitriou,et al.  The complexity of game dynamics: BGP oscillations, sink equilibria, and beyond , 2008, SODA '08.

[151]  Noam Nisan,et al.  Truthful randomized mechanisms for combinatorial auctions , 2006, STOC '06.

[152]  Sébastien Lahaie,et al.  An analysis of alternative slot auction designs for sponsored search , 2006, EC '06.

[153]  P. McMullen The maximum numbers of faces of a convex polytope , 1970 .

[154]  David Avis,et al.  A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra , 1991, SCG '91.

[155]  Nils J. Nilsson,et al.  Artificial Intelligence , 1974, IFIP Congress.

[156]  Tuomas Sandholm,et al.  Expressive Commerce and Its Application to Sourcing , 2006, AAAI.

[157]  Todd R. Kaplan,et al.  A Program for Finding Nash Equilibria , 1993 .

[158]  Coenraad Bron,et al.  Finding all cliques of an undirected graph , 1973 .

[159]  Dietrich Braess,et al.  Über ein Paradoxon aus der Verkehrsplanung , 1968, Unternehmensforschung.

[160]  Steve Chien,et al.  Convergence to approximate Nash equilibria in congestion games , 2007, SODA '07.

[161]  R. Rosenthal A class of games possessing pure-strategy Nash equilibria , 1973 .

[162]  Joan Feigenbaum,et al.  Computational challenges in e-commerce , 2009, CACM.

[163]  Aranyak Mehta,et al.  Inapproximability Results for Combinatorial Auctions with Submodular Utility Functions , 2005, Algorithmica.

[164]  Tuomas Sandholm,et al.  Algorithm for optimal winner determination in combinatorial auctions , 2002, Artif. Intell..

[165]  Bernhard von Stengel,et al.  New Maximal Numbers of Equilibria in Bimatrix Games , 1999, Discret. Comput. Geom..

[166]  Takayuki Ito,et al.  Online auctions for bidders with interdependent values , 2007, AAMAS '07.

[167]  Joseph Naor,et al.  Online Primal-Dual Algorithms for Maximizing Ad-Auctions Revenue , 2007, ESA.

[168]  David C. Parkes,et al.  An MDP-Based Approach to Online Mechanism Design , 2003, NIPS.

[169]  Dirk Bergemann,et al.  Dynamic Common Agency , 1998, J. Econ. Theory.

[170]  David C. Parkes,et al.  Iterative Combinatorial Auctions: Theory and Practice , 2000, AAAI/IAAI.

[171]  H W Kuhn,et al.  AN ALGORITHM FOR EQUILIBRIUM POINTS IN BIMATRIX GAMES. , 1961, Proceedings of the National Academy of Sciences of the United States of America.

[172]  Lawrence M. Ausubel,et al.  Ascending Auctions with Package Bidding , 2002 .

[173]  Moshe Babaioff,et al.  Single-value combinatorial auctions and algorithmic implementation in undominated strategies , 2009, JACM.

[174]  Moshe Tennenholtz,et al.  Bundling equilibrium in combinatorial auctions , 2002, Games Econ. Behav..

[175]  David Zuckerman,et al.  Electronic Colloquium on Computational Complexity, Report No. 100 (2005) Linear Degree Extractors and the Inapproximability of MAX CLIQUE and CHROMATIC NUMBER , 2005 .

[176]  Lawrence M. Ausubel An efficient dynamic auction for heterogeneous commodities , 2006 .

[177]  N. Nisan,et al.  On the Computational Power of Iterative Auctions II: Ascending Auctions , 2005 .

[178]  Gagan Ghosh Multi-unit auctions with budget-constrained bidders , 2012 .

[179]  John N. Tsitsiklis,et al.  Efficiency loss in a network resource allocation game: the case of elastic supply , 2004, IEEE Transactions on Automatic Control.

[180]  D. Koller,et al.  The complexity of two-person zero-sum games in extensive form , 1992 .

[181]  Nicole Immorlica,et al.  Matroids, secretary problems, and online mechanisms , 2007, SODA '07.

[182]  Frank Kelly,et al.  Charging and rate control for elastic traffic , 1997, Eur. Trans. Telecommun..

[183]  Ryan Porter,et al.  Mechanism design for online real-time scheduling , 2004, EC '04.

[184]  I. Vogelsang,et al.  Handbook of telecommunications economics, volume I. structure, regulation & competition. Cave, M., Majumdar , 2010 .

[185]  L. Shapley,et al.  Potential Games , 1994 .

[186]  Zoë Abrams,et al.  Revenue maximization when bidders have budgets , 2006, SODA '06.

[187]  Ilya Segal,et al.  The Communication Requirements of Combinatorial Allocation Problems , 2005 .

[188]  Michael E. Saks,et al.  Weak monotonicity suffices for truthfulness on convex domains , 2005, EC '05.

[189]  Andrew McLennan,et al.  Gambit: Software Tools for Game Theory , 2006 .

[190]  Rudolf Müller,et al.  Tractable cases of the winner determination problem , 2006 .

[191]  V. Crawford,et al.  Job Matching, Coalition Formation, and Gross Substitutes , 1982 .

[192]  Y. Shoham,et al.  Truth revelation in approximately efficient combinatorial auctions , 2002, EC '99.

[193]  Paul R. Milgrom,et al.  Putting Auction Theory to Work: The Simultaneous Ascending Auction , 1999, Journal of Political Economy.

[194]  Yoav Shoham,et al.  Taming the Computational Complexity of Combinatorial Auctions: Optimal and Approximate Approaches , 1999, IJCAI.

[195]  William Vickrey,et al.  Counterspeculation, Auctions, And Competitive Sealed Tenders , 1961 .

[196]  Aurel A. Lazar,et al.  Market mechanisms for network resource sharing , 1999 .

[197]  Amin Saberi,et al.  Allocating online advertisement space with unreliable estimates , 2007, EC '07.

[198]  G. Iyengar Characterizing Optimal Keyword Auctions ∗ , 2006 .

[199]  Maria Serna,et al.  Algorithmic Game Theory , 2012, Lecture Notes in Computer Science.

[200]  Thomas A. Weber,et al.  Efficient Dynamic Allocation with Uncertain Valuations , 2005 .

[201]  L. Shapley,et al.  REGULAR ARTICLEPotential Games , 1996 .

[202]  Robert B. Wilson A Bidding Model of Perfect Competition , 1977 .

[203]  Faruk Gul,et al.  WALRASIAN EQUILIBRIUM WITH GROSS SUBSTITUTES , 1999 .

[204]  A. Mas-Colell,et al.  Microeconomic Theory , 1995 .

[205]  Mohammad Taghi Hajiaghayi,et al.  Online auctions with re-usable goods , 2005, EC '05.

[206]  Noam Nisan,et al.  Two simplified proofs for Roberts’ theorem , 2009, Soc. Choice Welf..

[207]  A. Roth,et al.  Games and Economic Behavior , 1995 .

[208]  Yossi Azar,et al.  Reducing truth-telling online mechanisms to online optimization , 2003, STOC '03.

[209]  Paul Milgrom,et al.  Putting Auction Theory to Work , 2004 .

[210]  T. Roughgarden Potential functions and the inefficiency of equilibria , 2006 .

[211]  O. Mangasarian Equilibrium Points of Bimatrix Games , 1964 .

[212]  F. Mosteller,et al.  Recognizing the Maximum of a Sequence , 1966 .

[213]  H. Kuk On equilibrium points in bimatrix games , 1996 .

[214]  H. Arndt Von Schemde,et al.  Index and Stability in Bimatrix Games , 2008 .

[215]  G. Myles Journal of Economic Theory: J.-M. Grandmont, 1992, Transformations of the commodity space, behavioural heterogeneity, and the aggregation problem 57, 1-35 , 1993 .

[216]  S. Bikhchandani,et al.  Competitive Equilibrium in an Exchange Economy with Indivisibilities , 1997 .