메뉴 건너뛰기




Volumn 50, Issue 3, 2005, Pages 312-327

Dynamic fictitious play, dynamic gradient play, and distributed convergence to nash equilibria

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; GAME THEORY; MATHEMATICAL MODELS; MATRIX ALGEBRA; ORDINARY DIFFERENTIAL EQUATIONS; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; VECTORS;

EID: 16244381482     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2005.843878     Document Type: Article
Times cited : (337)

References (44)
  • 1
    • 0022045622 scopus 로고
    • "A new general routh-like algorithm to determine the number of rhp roots of a real or complex polynomial"
    • Apr
    • S. D. Agashe, "A new general routh-like algorithm to determine the number of rhp roots of a real or complex polynomial," IEEE Trans. Autom. Control, vol. 30, no. 4, pp. 406-409, Apr. 1985.
    • (1985) IEEE Trans. Autom. Control , vol.30 , Issue.4 , pp. 406-409
    • Agashe, S.D.1
  • 2
    • 14344254789 scopus 로고    scopus 로고
    • "Distributed convergence to Nash equilibria with local utility measurements"
    • G. Arslan and J. S. Shamma, "Distributed convergence to Nash equilibria with local utility measurements," in 43rd IEEE Conf. Decision and Control, 2004, pp. 1538-1543.
    • (2004) 43rd IEEE Conf. Decision and Control , pp. 1538-1543
    • Arslan, G.1    Shamma, J.S.2
  • 4
    • 38249035395 scopus 로고
    • "Relaxation techniques and asynchronous algorithms for online computation of noncooperative equilibria"
    • T. Basar, "Relaxation techniques and asynchronous algorithms for online computation of noncooperative equilibria," J. Econ. Dyna. Control vol. 11, pp. 531-549, 1987.
    • (1987) J. Econ. Dyna. Control , vol.11 , pp. 531-549
    • Basar, T.1
  • 5
    • 0030104967 scopus 로고    scopus 로고
    • "A dynamical systems approach to stochastic approximation"
    • M. Benaim and M. W. Hirsch, "A dynamical systems approach to stochastic approximation," SIAM J. Control Optim., vol. 34, pp. 437-472, 1996.
    • (1996) SIAM J. Control Optim. , vol.34 , pp. 437-472
    • Benaim, M.1    Hirsch, M.W.2
  • 6
    • 0002277539 scopus 로고    scopus 로고
    • "Mixed equilibria and dynamical systems arising from fictitious play in perturbed games"
    • M. Benaim and M. W. Hirsch,"Mixed equilibria and dynamical systems arising from fictitious play in perturbed games," Games Econ. Behav. vol. 29, pp. 36-72, 1999.
    • (1999) Games Econ. Behav. , vol.29 , pp. 36-72
    • Benaim, M.1    Hirsch, M.W.2
  • 7
    • 34147148387 scopus 로고    scopus 로고
    • Stochastic approximations and differential inclusions
    • [Online]
    • M. Benaim, J. Hofbauer, and S. Sorin. (2003) Stochastic approximations and differential inclusions. [Online] http://ceco.polytechnique.fr/ CAHIERS/pdf/2003-029.pdf
    • (2003)
    • Benaim, M.1    Hofbauer, J.2    Sorin, S.3
  • 8
    • 0141820167 scopus 로고    scopus 로고
    • "Fictitious play in 2 × n games"
    • WUSTL, Economics Working Paper Archive
    • U. Berger, "Fictitious play in 2 × n games," WUSTL, Economics Working Paper Archive, 2003.
    • (2003)
    • Berger, U.1
  • 9
    • 0002672918 scopus 로고
    • "Iterative solutions of games by fictitious play"
    • T C. Koopmans, Ed. New York: Wiley
    • G. W. Brown, "Iterative solutions of games by fictitious play," in Activity Analysis of Production and Allocation, T C. Koopmans, Ed. New York: Wiley, 1951, pp. 374-376.
    • (1951) Activity Analysis of Production and Allocation , pp. 374-376
    • Brown, G.W.1
  • 10
    • 38248998837 scopus 로고
    • "Adaptation in games: Two solutions to the Crawford puzzle"
    • J. Conlisk, "Adaptation in games: two solutions to the Crawford puzzle" J. Econ. Behav. Organ., vol. 22, pp. 25-50, 1993.
    • (1993) J. Econ. Behav. Organ. , vol.22 , pp. 25-50
    • Conlisk, J.1
  • 11
    • 0002070953 scopus 로고
    • "Learning behavior and mixed strategy Nash equilibria"
    • V. P. Crawford, "Learning behavior and mixed strategy Nash equilibria," J. Econ. Behav. Organ., vol. 6, pp. 69-78, 1985.
    • (1985) J. Econ. Behav. Organ. , vol.6 , pp. 69-78
    • Crawford, V.P.1
  • 12
    • 0002345370 scopus 로고    scopus 로고
    • "Learning purified mixed equilibria"
    • G. Ellison and D. Fudenberg, "Learning purified mixed equilibria," J. Econ. Theory, vol. 90, pp. 83-115, 2000.
    • (2000) J. Econ. Theory , vol.90 , pp. 83-115
    • Ellison, G.1    Fudenberg, D.2
  • 13
    • 13844280666 scopus 로고    scopus 로고
    • "Equilibrium, evolutionary stability and gradient dynamics"
    • S. D. Flam, "Equilibrium, evolutionary stability and gradient dynamics," Int. Game Theory Rev., vol. 4, no. 4, pp. 357-370, 2002.
    • (2002) Int. Game Theory Rev. , vol.4 , Issue.4 , pp. 357-370
    • Flam, S.D.1
  • 14
    • 0013501521 scopus 로고    scopus 로고
    • "Newtonian mechanics and Nash play"
    • Dip. di Matematica e Applicazioni, Univ. di Napoli, Naples, Italy, Tech. Rep. 5-2001
    • S. D. Flam and J. Morgan, "Newtonian mechanics and Nash play" Dip. di Matematica e Applicazioni, Univ. di Napoli, Naples, Italy, Tech. Rep. 5-2001, 2001.
    • (2001)
    • Flam, S.D.1    Morgan, J.2
  • 16
    • 0031256578 scopus 로고    scopus 로고
    • "Calibrated learning and correlated equilibrium"
    • D. P. Foster and R. V. Vohra, "Calibrated learning and correlated equilibrium," Games Econ. Behav., vol. 21, pp. 40-55, 1997.
    • (1997) Games Econ. Behav. , vol.21 , pp. 40-55
    • Foster, D.P.1    Vohra, R.V.2
  • 17
    • 0141838158 scopus 로고    scopus 로고
    • "Learning, hypothesis testing, and Nash equilibrium"
    • D. P. Foster and H. P. Young, "Learning, hypothesis testing, and Nash equilibrium," Games Econ. Behav., vol. 45, pp. 73-96, 2003.
    • (2003) Games Econ. Behav. , vol.45 , pp. 73-96
    • Foster, D.P.1    Young, H.P.2
  • 18
    • 27744474653 scopus 로고    scopus 로고
    • Regret testing: A simple payoff-based procedure for learning Nash equilibrium
    • [Online]
    • D. P. Foster and H. P. Young, (2003) Regret testing: A simple payoff-based procedure for learning Nash equilibrium. [Online] http://www.econ.jhu.edu/people/young/RegretTesting.pdf
    • (2003)
    • Foster, D.P.1    Young, H.P.2
  • 19
    • 0141708883 scopus 로고    scopus 로고
    • "On the nonconvergence of fictitious play in coordination games"
    • D. P. Foster and H. P. Young, "On the nonconvergence of fictitious play in coordination games" Games Econ. Behav., vol. 25, pp. 79-96.
    • Games Econ. Behav. , vol.25 , pp. 79-96
    • Foster, D.P.1    Young, H.P.2
  • 20
    • 0000466473 scopus 로고
    • "Learning mixed equilibria"
    • D. Fudenberg and D. Kreps, "Learning mixed equilibria," Games Econ. Behav., vol. 5, pp. 320-367, 1993.
    • (1993) Games Econ. Behav. , vol.5 , pp. 320-367
    • Fudenberg, D.1    Kreps, D.2
  • 22
    • 0008547696 scopus 로고    scopus 로고
    • "Conditional universal consistency"
    • D. Fudenberg and D. K. Levine, "Conditional universal consistency," Games Econ. Behav., vol. 29, pp. 104-130, 1999.
    • (1999) Games Econ. Behav. , vol.29 , pp. 104-130
    • Fudenberg, D.1    Levine, D.K.2
  • 24
    • 16244398351 scopus 로고    scopus 로고
    • Adaptive heuristics
    • [Online]
    • S. Hart. (2004) Adaptive heuristics. [Online] http://www.ma.huji.ac,il/ ~hart/abs/heurist.html
    • (2004)
    • Hart, S.1
  • 25
    • 0000908510 scopus 로고    scopus 로고
    • "A simple adaptive procedure leading to correlated equilibrium"
    • S. Hart and A. Mas-Colell, "A simple adaptive procedure leading to correlated equilibrium" Econometrica, vol. 68, pp. 1127-1150, 2000.
    • (2000) Econometrica , vol.68 , pp. 1127-1150
    • Hart, S.1    Mas-Colell, A.2
  • 26
    • 2942744741 scopus 로고    scopus 로고
    • "Uncoupled dynamics do not lead to Nash equilibrium"
    • S. Hart and A. Mas-Colell, "Uncoupled dynamics do not lead to Nash equilibrium," Amer. Econ. Rev., vol. 93, no. 5, pp. 1830-1836, 2003.
    • (2003) Amer. Econ. Rev. , vol.93 , Issue.5 , pp. 1830-1836
    • Hart, S.1    Mas-Colell, A.2
  • 27
    • 16244405242 scopus 로고    scopus 로고
    • Stochastic uncoupled dynamics and Nash equilibrium
    • [Online]
    • S. Hart and A. Mas-Colell, (2004) Stochastic uncoupled dynamics and Nash equilibrium. [Online] http://www.ma.huji.ac.il/~hart/abs/ uncoupl-st.html
    • (2004)
    • Hart, S.1    Mas-Colell, A.2
  • 28
    • 0000415605 scopus 로고
    • "Three problems in game theory"
    • J. Jordan, "Three problems in game theory," Games Econ. Behav., vol. 5, pp. 368-386, 1993.
    • (1993) Games Econ. Behav. , vol.5 , pp. 368-386
    • Jordan, J.1
  • 29
    • 32144463947 scopus 로고    scopus 로고
    • Deterministic calibration and Nash equilibrium
    • [Online]
    • S. M. Kakade and D. P. Foster. (2004) Deterministic calibration and Nash equilibrium. [Online] http://www.cis.upenn.edu/~skakade/papers/gt/ calibration.pdf
    • (2004)
    • Kakade, S.M.1    Foster, D.P.2
  • 31
    • 0032075278 scopus 로고    scopus 로고
    • "On the convergence of fictitious play"
    • V. Krishna and T. Sjöström, "On the convergence of fictitious play," Math. Oper. Res., vol. 23, no. 2, pp. 479-511, 1998.
    • (1998) Math. Oper. Res. , vol.23 , Issue.2 , pp. 479-511
    • Krishna, V.1    Sjöström, T.2
  • 33
    • 0346913265 scopus 로고    scopus 로고
    • "Convergent multiple-timescales reinforcement learning algorithms in normal form games"
    • D. S. Leslie and E. J. Collins, "Convergent multiple-timescales reinforcement learning algorithms in normal form games," Ann. Appl. Probab., vol. 4, no. 4, pp. 1231-1251, 2003.
    • (2003) Ann. Appl. Probab. , vol.4 , Issue.4 , pp. 1231-1251
    • Leslie, D.S.1    Collins, E.J.2
  • 34
    • 4243770097 scopus 로고    scopus 로고
    • "Modeling the function of the cerebellum in scheduled linear servo control of simple horizontal planar arm movements"
    • Ph.D. dissertation, MIT, Cambridge, MA
    • S. G. Massaquoi, "Modeling the function of the cerebellum in scheduled linear servo control of simple horizontal planar arm movements," Ph.D. dissertation, MIT, Cambridge, MA, 1999.
    • (1999)
    • Massaquoi, S.G.1
  • 35
    • 0003646168 scopus 로고
    • "On the convergence of learning processes in a 2 × 2 non-zero-sum two person game"
    • Princeton Univ., Economic Research Program, Princeton, NJ, Tech. Rep. 33
    • K. Miyasawa, "On the convergence of learning processes in a 2 × 2 non-zero-sum two person game," Princeton Univ., Economic Research Program, Princeton, NJ, Tech. Rep. 33, 1961.
    • (1961)
    • Miyasawa, K.1
  • 36
    • 0029690246 scopus 로고    scopus 로고
    • "Fictitious play property for games with identical interests"
    • D. Monderer and L. S. Shapley, "Fictitious play property for games with identical interests," J. Econ. Theory, vol. 68, pp. 258-265, 1996.
    • (1996) J. Econ. Theory , vol.68 , pp. 258-265
    • Monderer, D.1    Shapley, L.S.2
  • 37
    • 0001402950 scopus 로고
    • "An iterative method of solving a game"
    • J. Robinson, "An iterative method of solving a game," Ann. Math. vol. 54, pp. 296-301, 1951.
    • (1951) Ann. Math. , vol.54 , pp. 296-301
    • Robinson, J.1
  • 38
    • 0000989514 scopus 로고
    • "Comments on the interpretation of game theory"
    • A. Rubinstein, "Comments on the interpretation of game theory," Econometrica, vol. 59, no. 4, pp. 909-924, 1991.
    • (1991) Econometrica , vol.59 , Issue.4 , pp. 909-924
    • Rubinstein, A.1
  • 40
    • 0002623794 scopus 로고
    • "Some topics in two-person games"
    • L. S. Shapley, M. Dresher, and A. W. Tucker, Eds. Princeton, NJ: Princeton Univ. Press
    • L. S. Shapley, " Some topics in two-person games," in Advances in Game Theory, L. S. Shapley, M. Dresher, and A. W. Tucker, Eds. Princeton, NJ: Princeton Univ. Press, 1964, pp. 1-29.
    • (1964) Advances in Game Theory , pp. 1-29
    • Shapley, L.S.1
  • 41
    • 0027306535 scopus 로고
    • "The necessary conditions for a complex polynomial to be strictly Hurwitz and their applications in robust stability analysis"
    • Jan
    • Y. Q. Shi, K. K. Yen, and C. M. Chen, "The necessary conditions for a complex polynomial to be strictly Hurwitz and their applications in robust stability analysis," IEEE Trans. Autom. Control, vol. 38, no. 1, pp. 125-128, Jan. 1993.
    • (1993) IEEE Trans. Autom. Control , vol.38 , Issue.1 , pp. 125-128
    • Shi, Y.Q.1    Yen, K.K.2    Chen, C.M.3
  • 42
    • 0033284396 scopus 로고    scopus 로고
    • "On stability of mixed equilibria"
    • A. Vasin, "On stability of mixed equilibria," Nonlinear Anal., vol. 38, pp. 793-802, 1999.
    • (1999) Nonlinear Anal. , vol.38 , pp. 793-802
    • Vasin, A.1
  • 44
    • 14344265932 scopus 로고    scopus 로고
    • Information theory - The bridge connecting bounded rational game theory and statistical physics
    • [Online]
    • D. H. Wolpert. (2004) Information theory - The bridge connecting bounded rational game theory and statistical physics. [Online] http://arxiv.org/ PSc_cache/cond-mat/pdf/0402/0402508.pdf
    • (2004)
    • Wolpert, D.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.