Flows and Decompositions of Games: Harmonic and Potential Games

Published Online:https://doi.org/10.1287/moor.1110.0500

References

  • Başar T., Ho Y. C. Informational properties of the Nash solutions of two stochastic nonzero-sum games. J. Econom. Theory (1974) 7(4):370–387CrossrefGoogle Scholar
  • Bertsimas D., Tsitsiklis J.Introduction to Linear Optimization (1997) (Athena Scientific, Belmont, MA) Google Scholar
  • Candogan O., Ozdaglar A., Parrilo P. A. A projection framework for near-potential games. Proc. 49th IEEE Conf. Decision and Control (CDC) (2010) (IEEE Computer Society, Washington, DC) 244-249Google Scholar
  • Candogan O., Ozdaglar A., Parrilo P. A. Learning in near-potential games. (2011) April). Technical report, Laboratory for Information and Decision Systems, MIT, Cambridge, MAGoogle Scholar
  • Candogan O., Menache I., Ozdaglar A., Parrilo P. A. Near-optimal power control in wireless networks: A potential game approach. Proc. 19th IEEE Internet. Conf. Comput. Comm. (INFOCOM) (2010) (IEEE Computer Society, Washington, DC) 1–9Google Scholar
  • Candogan O., Menache I., Ozdaglar A., Parrilo P. A. Flows and decompositions of games: Harmonic and potential games. (2010) . Arxiv preprint arXiv:1005.2405Google Scholar
  • Christodoulou G., Mirrokni V. S., Sidiropoulos A., Durand B., Thomas W. Convergence and approximation in potential games. STACS 2006 (2006) 3884(Springer-Verlag, Berlin/Heidelberg) 349–360Lecture Notes Comput. Sci.CrossrefGoogle Scholar
  • Chung F. R. K. Spectral graph theory. CBMS Regional Conference Series in Mathematics (1997) 92(AMS, Providence, RI) Google Scholar
  • Cressman R., Morrison W. G. On the evolutionary dynamics of crime. The Canadian J. Econom./Revue Canadienne d'Economique (1998) 31(5):1101–1117CrossrefGoogle Scholar
  • Facchini G., van Megen F., Borm P., Tijs S. Congestion models and weighted Bayesian potential games. Theory and Decision (1997) 42(2):193–206CrossrefGoogle Scholar
  • Friedman D. Evolutionary games in economics. Econometrica (1991) 59(3):637–666CrossrefGoogle Scholar
  • Fudenberg D., Levine D. K.The Theory of Learning in Games (1998) (MIT Press, Cambridge, MA) Google Scholar
  • Fudenberg D., Tirole J.Game Theory (1991) (MIT Press, Cambridge, MA) Google Scholar
  • Germano F. On some geometry and equivalence classes of normal form games. Internat. J. Game Theory (2006) 34(4):561–581CrossrefGoogle Scholar
  • Gilboa I., Schmeidler D. Canonical representation of set functions. Math. Oper. Res. (1995) 20(1):197–212LinkGoogle Scholar
  • Goemans M., Mirrokni V., Vetta A. Sink equilibria and convergence. Proc. 46th Annual IEEE Sympos. Foundations Comput. Sci. (FOCS '05) (2005) (IEEE Computer Society, Washington, DC) 142–154Google Scholar
  • Golub G. H., Van Loan C. F.Matrix Computations (1996) (Johns Hopkins University Press, Baltimore, MD) Google Scholar
  • Hammond P. J., Schmidt U., Traub S. Utility invariance in noncooperative games. Adv. Public Econom.: Utility, Choice Welfare (2005) 38(Springer, Dordecht, The Netherlands) 31–50Theory and Decision LibraryCrossrefGoogle Scholar
  • Hillas J., Kohlberg E., Aumann R. J., Hart S. Foundations of strategic equilibrium. Handbook of Game Theory with Economic Applications (2002) 3(Elsevier, North-Holland) 1597–1663Google Scholar
  • Hofbauer J., Hopkins E. Learning in perturbed asymmetric games. Games Econom. Behav. (2005) 52(1):133–152CrossrefGoogle Scholar
  • Hofbauer J., Sandholm W. H. On the global convergence of stochastic fictitious play. Econometrica (2002) 70(6):2265–2294CrossrefGoogle Scholar
  • Hofbauer J., Schlag K. H. Sophisticated imitation in cyclic games. J. Evolutionary Econom. (2000) 10(5):523–543CrossrefGoogle Scholar
  • Jiang X., Lim L. H., Yao Y., Ye Y. Statistical ranking and combinatorial Hodge theory. Math. Programming: Ser. A and B (2011) 127(1):203–244CrossrefGoogle Scholar
  • Jordan J. S. Three problems in learning mixed-strategy Nash equilibria. Games Econom. Behav. (1993) 5(3):368–386CrossrefGoogle Scholar
  • Kalai A. T., Kalai E. Engineering cooperation in two-player strategic games. (2010) . MimeoGoogle Scholar
  • Kannan R., Theobald T. Games of fixed rank: A hierarchy of bimatrix games. Econom. Theory (2010) 42(1):157–173CrossrefGoogle Scholar
  • Kleinberg N. L., Weiss J. H. Algebraic structure of games. Math. Soc. Sci. (1985) 9(1):35–44CrossrefGoogle Scholar
  • Kleinberg N. L., Weiss J. H. The orthogonal decomposition of games and an averaging formula for the Shapley value. Math. Oper. Res. (1986) 11(1):117–124LinkGoogle Scholar
  • Marden J. R., Shamma J. S. Revisiting log-linear learning: Asynchrony, completeness and a payoff-based implementation. Games Econom. Behav. (2008) . SubmittedGoogle Scholar
  • Marden J. R., Arslan G., Shamma J. S. Joint strategy fictitious play with inertia for potential games. IEEE Trans. Automatic Control (2009) 54(2):208–220CrossrefGoogle Scholar
  • Marinacci M. Decomposition and representation of coalitional games. Math. Oper. Res. (1996) 21(4):1000–1015LinkGoogle Scholar
  • Mertens J. F. Ordinality in noncooperative games. Internat. J. Game Theory (2004) 32(3):387–430CrossrefGoogle Scholar
  • Monderer D., Shapley L. S. Fictitious play property for games with identical interests. J. Econom. Theory (1996) 68(1):258–265CrossrefGoogle Scholar
  • Monderer D., Shapley L. S. Potential games. Games Econom. Behav. (1996) 14(1):124–143CrossrefGoogle Scholar
  • Morris S., Ui T. Best response equivalence. Games Econom. Behav. (2004) 49(2):260–287CrossrefGoogle Scholar
  • Moulin H., Vial J. P. Strategically zero-sum games: The class of games whose completely mixed equilibria cannot be improved upon. Internat. J. Game Theory (1978) 7(3):201–221CrossrefGoogle Scholar
  • Neyman A. Correlated equilibrium and potential games. Internat. J. Game Theory (1997) 26(2):223–227CrossrefGoogle Scholar
  • Polthier K., Preuß E. Identifying vector field singularities using a discrete Hodge decomposition. Visualization Math. III (2002) 5:113–134Google Scholar
  • Rosenthal R. Correlated equilibria in some classes of two-person games. Internat. J. Game Theory (1974) 3(3):119–128CrossrefGoogle Scholar
  • Sandholm W. H. Decompositions and potentials for normal form games. Games Econom. Behav. (2010) 70(2):446–456CrossrefGoogle Scholar
  • Shamma J. S., Arslan G. Unified convergence proofs of continuous-time fictitious play. IEEE Trans. Automatic Control (2004) 49(7):1137–1141CrossrefGoogle Scholar
  • Shapley L. S., Kuhn H. W., Tucker A. W. A value for n-person games. Contributions to the Theory of Games (1953) 2nd ed.(Princeton University Press, Princeton, NJ) 307–317Google Scholar
  • Smith J. M., Hofbauer J. The “battle of the sexes”: A genetic model with limit cycle behavior. Theoret. Population Biol. (1987) 32(1):1–14CrossrefGoogle Scholar
  • Tong Y., Lombeyda S., Hirani A. N., Desbrun M. Discrete multiscale vector field decomposition. ACM Trans. Graphics (2003) 22(3):445–452CrossrefGoogle Scholar
  • Topkis D. M.Supermodularity and Complementarity (1998) (Princeton University Press, Princeton, NJ) CrossrefGoogle Scholar
  • Ui T. Discrete concavity for potential games. Internat. Game Theory Rev. (2008) 10(1):137–143CrossrefGoogle Scholar
  • Von Neumann J., Morgenstern O.Theory of Games and Economic Behavior (1947) (Princeton University Press, Princeton, NJ) Google Scholar
  • Voorneveld M. Best-response potential games. Econom. Lett. (2000) 66(3):289–295CrossrefGoogle Scholar
  • Voorneveld M., Borm P., van Megen F., Tijs S., Facchini G. Congestion games and potentials reconsidered. Internat. Game Theory Rev. (1999) 1(3&4):283–299CrossrefGoogle Scholar
  • Young H. P.Strategic Learning and Its Limits (2004) (Oxford University Press, New York) CrossrefGoogle Scholar
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