메뉴 건너뛰기




Volumn 48, Issue 4, 2009, Pages 2461-2479

Repeated games and qualitative differential games: Approachability and comparison of strategies

Author keywords

Differential games; Repeated games; Viability

Indexed keywords

DIFFERENTIAL GAMES; REPEATED GAMES; VIABILITY;

EID: 79955838045     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/090749098     Document Type: Article
Times cited : (21)

References (32)
  • 1
    • 4243184510 scopus 로고
    • Contingent isaacs equation of a differential game
    • T. Basar and P. Bernhard, eds., Lecture Notes in Control and Inform. Sci. Springer, Berlin
    • J.-P. AUBIN, Contingent Isaacs equation of a differential game, in Differential Games and Applications, T. Basar and P. Bernhard, eds., Lecture Notes in Control and Inform. Sci. 119, Springer, Berlin, 1989, pp. 51-61.
    • (1989) Differential Games and Applications , vol.119 , pp. 51-61
    • Aubin, J.-P.1
  • 5
    • 33244474665 scopus 로고    scopus 로고
    • Stochastic approximations and differential inclusions
    • M. BENAÏM, J. HOFBAUER, and S. SORIN, Stochastic approximations and differential inclusions, SIAM J. Control Optim., 44 (2005), pp. 328-348.
    • (2005) SIAM J. Control Optim. , vol.44 , pp. 328-348
    • Benaïm, M.1    Hofbauer, J.2    Sorin, S.3
  • 6
    • 33847230190 scopus 로고    scopus 로고
    • Stochastic approximations and differential inclusions. Part II: Applications
    • M. BENAIM, J. HOFBAUER, and S. SORIN, Stochastic approximations and differential inclusions. Part II: Applications, Math. Oper. Res., 31 (2006), pp. 673-695.
    • (2006) Math. Oper. Res. , vol.31 , pp. 673-695
    • Benaim, M.1    Hofbauer, J.2    Sorin, S.3
  • 7
    • 84972545864 scopus 로고
    • An analog of the minmax theorem for vector payoffs
    • D. BLACKWELL, An analog of the minmax theorem for vector payoffs, Pacific J. Math., 6 (1956), pp. 1-8.
    • (1956) Pacific J. Math. , vol.6 , pp. 1-8
    • Blackwell, D.1
  • 8
    • 33750626526 scopus 로고    scopus 로고
    • Computing the viability kernel in large state dimension
    • N. BONNEUIL, Computing the viability kernel in large state dimension, J. Math. Anal. Appl., 323 (2006), pp. 1444-1454.
    • (2006) J. Math. Anal. Appl. , vol.323 , pp. 1444-1454
    • Bonneuil, N.1
  • 9
    • 0000376647 scopus 로고
    • Principe du maximum, inégalité de harnack et unicité du probléme de cauchy pou r le s opérateurs elliptiques dégénérés
    • J. M. BONY, Principe du maximum, inégalité de Harnack et unicité du probléme de Cauchy pou r le s opérateurs elliptiques dégénérés, Ann. Inst. Fourier (Grenoble), 19 (1969), pp. 277-304.
    • (1969) Ann. Inst. Fourier (Grenoble) , vol.19 , pp. 277-304
    • Bony, J.M.1
  • 11
    • 0030196316 scopus 로고    scopus 로고
    • A differential game with two players and one target
    • P. CARDALIAGUET, A differential game with two players and one target, SIAM J. Control Optim., 34 (1996), pp. 1441-1460.
    • (1996) SIAM J. Control Optim. , vol.34 , pp. 1441-1460
    • Cardaliaguet, P.1
  • 12
    • 0031234221 scopus 로고    scopus 로고
    • Nonsmooth semi-permeable barriers, isaacs equation, and application to a differential game with one target and two players
    • P. CARDALIAGUET, Nonsmooth semi-permeable barriers, Isaacs equation, and application to a differential game with one target and two players, Appl. Math. Optim., 36 (1997), pp. 125-146.
    • (1997) Appl. Math. Optim. , vol.36 , pp. 125-146
    • Cardaliaguet, P.1
  • 15
    • 84155164780 scopus 로고    scopus 로고
    • Differential games throug hviability theory: Old and recent results
    • S. Jorgensen, M. Quincampoix, and T. Vincent, eds., Birkhäuser, Boston
    • P. CARDALIAGUET, M. QUINCAMPOIX, and P. SAINT-PIERRE, Differential games throug hviability theory: Old and recent results, in Advances in Dynamic Games Theory, Ann. Internat. Soc. Dynam. Games, S. Jorgensen, M. Quincampoix, and T. Vincent, eds., Birkhäuser, Boston, 2007, pp. 3-36.
    • (2007) Advances in Dynamic Games Theory, Ann. Internat. Soc. Dynam. Games , pp. 3-36
    • Cardaliaguet, P.1    Quincampoix, M.2    Saint-Pierre, P.3
  • 17
    • 0002961583 scopus 로고
    • The existence of value in differential games of pursuit and evasion
    • N. J. ELLIOT and N. J. KALTON, The existence of value in differential games of pursuit and evasion, J. Differential Equations, 12 (1972), pp. 504-523.
    • (1972) J. Differential Equations , vol.12 , pp. 504-523
    • Elliot, N.J.1    Kalton, N.J.2
  • 18
    • 0002476325 scopus 로고    scopus 로고
    • Regret in the on-line decision problem
    • D. FOSTER and R. VOHRA, Regret in the on-line decision problem, Games Econom. Behav., 29 (1999), pp. 7-35.
    • (1999) Games Econom. Behav. , vol.29 , pp. 7-35
    • Foster, D.1    Vohra, R.2
  • 19
    • 27744533227 scopus 로고    scopus 로고
    • Adaptive heuristics
    • S. HART, Adaptive heuristics, Econometrica, 73 (2005), pp. 1401-1430.
    • (2005) Econometrica , vol.73 , pp. 1401-1430
    • Hart, S.1
  • 20
    • 33748432530 scopus 로고
    • Approachability in a two-person game
    • T.-F. HOU, Approachability in a two-person game, Ann. Math. Statist., 42 (1971), pp. 735-744.
    • (1971) Ann. Math. Statist. , vol.42 , pp. 735-744
    • Hou, T.-F.1
  • 22
    • 0037000740 scopus 로고    scopus 로고
    • Approachability in infinite dimensional spaces
    • E. LEHRER, Approachability in infinite dimensional spaces, Internat. J. Game Theory, 31 (2002), pp. 253-268.
    • (2002) Internat. J. Game Theory , vol.31 , pp. 253-268
    • Lehrer, E.1
  • 24
    • 33748438402 scopus 로고    scopus 로고
    • Excludability and bounded computational capacity
    • E. LEHRER and E. SOLAN, Excludability and bounded computational capacity, Math. Oper. Res., 31 (2006), pp. 637-648.
    • (2006) Math. Oper. Res. , vol.31 , pp. 637-648
    • Lehrer, E.1    Solan, E.2
  • 25
    • 0000899238 scopus 로고
    • Über die lage der integralkurven gewühnlicher differentialgleichungen
    • M. NAGUMO, Über die Lage der Integralkurven gewühnlicher Differentialgleichungen, Proc. Phys.-Math. Soc. Japan (3), 24 (1942), pp. 551-559.
    • (1942) Proc. Phys.-Math. Soc. Japan (3) , vol.24 , pp. 551-559
    • Nagumo, M.1
  • 27
    • 0001749783 scopus 로고
    • The axiomatic approach in differential games
    • E. ROXIN, The axiomatic approach in differential games, J. Optim. Theory Appl., 3 (1969), pp. 153-163.
    • (1969) J. Optim. Theory Appl. , vol.3 , pp. 153-163
    • Roxin, E.1
  • 28
    • 14244264927 scopus 로고    scopus 로고
    • A first course on zero-sum repeated games
    • Springer, Berlin
    • S. SORIN, A First Course on Zero-Sum Repeated Games, Math. Appl. (Berlin) 37, Springer, Berlin, 2002.
    • (2002) Math. Appl. (Berlin) , vol.37
    • Sorin, S.1
  • 30
    • 0036474456 scopus 로고    scopus 로고
    • A necessary and sufficient condition for approachability
    • X. SPINAT, A necessary and sufficient condition for approachability, Math. Oper. Res., 27 (2002), pp. 31-44.
    • (2002) Math. Oper. Res. , vol.27 , pp. 31-44
    • Spinat, X.1
  • 31
    • 0000223358 scopus 로고
    • On the existence of solutions to a differential game
    • P. P. VARAIYA, On the existence of solutions to a differential game, SIAM J. Control, 5 (1967), pp. 153-162.
    • (1967) SIAM J. Control , vol.5 , pp. 153-162
    • Varaiya, P.P.1
  • 32
    • 0000720418 scopus 로고
    • Weak approachability
    • N. VIEILLE, Weak approachability, Math. Oper. Res., 17 (1992), pp. 781-791.
    • (1992) Math. Oper. Res. , vol.17 , pp. 781-791
    • Vieille, N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.