메뉴 건너뛰기




Volumn 42, Issue 5, 2003, Pages 1876-1894

Zero-sum average semi-Markov games: Fixed-point solutions of the Shapley equation

Author keywords

Average payoff criterion; Fixed point approach; Lyapunov conditions; Zero sum semi Markov games

Indexed keywords

AVERAGE PAYOFF CRITERION; LYAPUNOV CONDITIONS; ZERO-SUM SEMI-MARKOV GAMES;

EID: 1642380053     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012902408423     Document Type: Article
Times cited : (31)

References (32)
  • 1
    • 0031210649 scopus 로고    scopus 로고
    • Contraction conditions for average and α-discount optimality in countable state Markov games with unbounded rewards
    • E. ALTMAN, A. HORDIJK, AND F. M. SPIEKSMA, Contraction conditions for average and α-discount optimality in countable state Markov games with unbounded rewards, Math. Oper. Res., 22 (1997), pp. 588-618.
    • (1997) Math. Oper. Res. , vol.22 , pp. 588-618
    • Altman, E.1    Hordijk, A.2    Spieksma, F.M.3
  • 2
    • 0029405524 scopus 로고
    • A convex analytic framework for ergodic control of semi-Markov processes
    • S. BHATNAGAR AND V. S. BORKAR, A convex analytic framework for ergodic control of semi-Markov processes, Math. Oper. Res., 20 (1995), pp. 923-936.
    • (1995) Math. Oper. Res. , vol.20 , pp. 923-936
    • Bhatnagar, S.1    Borkar, V.S.2
  • 3
    • 0027555501 scopus 로고
    • Denumerable stochastic games with limiting average payoff
    • V. S. BORKAR AND M. K. GHOSH, Denumerable stochastic games with limiting average payoff, J. Optim. Theory Appl., 76 (1993), pp. 539-560.
    • (1993) J. Optim. Theory Appl. , vol.76 , pp. 539-560
    • Borkar, V.S.1    Ghosh, M.K.2
  • 5
    • 0020749516 scopus 로고
    • Denumerable undiscounted semi-Markov decision processes with unbounded rewards
    • A. FERDEGRUEN, P. J. SCHWEITZER, AND H. C. TIJMS, Denumerable undiscounted semi-Markov decision processes with unbounded rewards, Math. Oper. Res., 8 (1983), pp. 298-313.
    • (1983) Math. Oper. Res. , vol.8 , pp. 298-313
    • Ferdegruen, A.1    Schweitzer, P.J.2    Tijms, H.C.3
  • 7
    • 0032209978 scopus 로고    scopus 로고
    • Stochastic games with average payoff criterion
    • M. K. GHOSH AND A. BAGCHI, Stochastic games with average payoff criterion, Appl. Math. Optim., 38 (1998), pp. 283-301.
    • (1998) Appl. Math. Optim. , vol.38 , pp. 283-301
    • Ghosh, M.K.1    Bagchi, A.2
  • 9
    • 0001259333 scopus 로고
    • Average cost Markov control processes with weighted norms: Existence of canonical policies
    • E. GORDIENKO AND O. HERNÁNDEZ-LERMA, Average cost Markov control processes with weighted norms: Existence of canonical policies, Appl. Math. (Warsaw), 23 (1995), pp. 199-218.
    • (1995) Appl. Math. (Warsaw) , vol.23 , pp. 199-218
    • Gordienko, E.1    Hernández-Lerma, O.2
  • 11
    • 0034769555 scopus 로고    scopus 로고
    • Zero-sum stochastic games in Borel spaces: Average payoff criteria
    • O. HERNÁNDEZ-LERMA AND J. B. LASSERRE, Zero-sum stochastic games in Borel spaces: Average payoff criteria, SIAM J. Control Optim., 39 (2001), pp. 1520-1539.
    • (2001) SIAM J. Control Optim. , vol.39 , pp. 1520-1539
    • Hernández-Lerma, O.1    Lasserre, J.B.2
  • 13
    • 0000563004 scopus 로고    scopus 로고
    • Infinite-horizon Markov control processes with undiscounted cost criteria: Prom average to overtaking optimality
    • O. HERNÁNDEZ-LERMA AND O. VEGA-AMAYA, Infinite-horizon Markov control processes with undiscounted cost criteria: Prom average to overtaking optimality, Appl. Math. (Warsaw), 25 (1998), pp. 153-178.
    • (1998) Appl. Math. (Warsaw) , vol.25 , pp. 153-178
    • Hernández-Lerma, O.1    Vega-Amaya, O.2
  • 14
    • 18544392871 scopus 로고    scopus 로고
    • Sample-path optimality and variance-minimization of average cost Markov control processes
    • O. HERNÁNDEZ-LERMA, O. VEGA-AMAYA, AND G. CARRASCO, Sample-path optimality and variance-minimization of average cost Markov control processes, SIAM J. Control Optim., 38 (1999), pp. 79-93.
    • (1999) SIAM J. Control Optim. , vol.38 , pp. 79-93
    • Hernández-Lerma, O.1    Vega-Amaya, O.2    Carrasco, G.3
  • 15
    • 0034774716 scopus 로고    scopus 로고
    • An approximation approach to ergodic semi-Markov control processes
    • A. JAŚKIEWICZ, An approximation approach to ergodic semi-Markov control processes, Math. Methods Oper. Res., 54 (2001), pp. 1-19.
    • (2001) Math. Methods Oper. Res. , vol.54 , pp. 1-19
    • Jaśkiewicz, A.1
  • 16
    • 0035658472 scopus 로고    scopus 로고
    • On the optimality equation for zero-sum ergodic stochastic games
    • A. JAŚKIEWICZ AND A. S. NOWAK, On the optimality equation for zero-sum ergodic stochastic games, Math. Methods Oper. Res., 54 (2001), pp. 291-301.
    • (2001) Math. Methods Oper. Res. , vol.54 , pp. 291-301
    • Jaśkiewicz, A.1    Nowak, A.S.2
  • 17
    • 0038803854 scopus 로고    scopus 로고
    • Zero-sum semi-Markov games
    • A. JAŚKIEWICZ, Zero-sum semi-Markov games, SIAM J. Control Optim., 41 (2002), pp. 723-739.
    • (2002) SIAM J. Control Optim. , vol.41 , pp. 723-739
    • Jaśkiewicz, A.1
  • 18
    • 0036461543 scopus 로고    scopus 로고
    • The optimality equation and e-optimal strategies in Markov games with average reward criterion
    • H.-U. KÜENLE AND R. SCHURAT, The optimality equation and e-optimal strategies in Markov games with average reward criterion, Math. Methods Oper. Res., 56 (2003), pp. 439-449.
    • (2003) Math. Methods Oper. Res. , vol.56 , pp. 439-449
    • Küenle, H.-U.1    Schurat, R.2
  • 19
    • 4944235782 scopus 로고
    • Average optimal adaptive policies in semi-Markov decision processes including an unknown parameter
    • M. KURANO, Average optimal adaptive policies in semi-Markov decision processes including an unknown parameter, J. Oper. Res. Soc. Japan, 28 (1985), pp. 252-266.
    • (1985) J. Oper. Res. Soc. Japan , vol.28 , pp. 252-266
    • Kurano, M.1
  • 20
    • 0038094624 scopus 로고
    • Zero-sum two-person semi-Markov games
    • A. K. LAL AND S. SINHA, Zero-sum two-person semi-Markov games, J. Appl. Probab., 29 (1992), pp. 56-72.
    • (1992) J. Appl. Probab. , vol.29 , pp. 56-72
    • Lal, A.K.1    Sinha, S.2
  • 21
    • 17744412522 scopus 로고    scopus 로고
    • Zero-sum semi-Markov games in Borel spaces: Discounted and average payoff
    • F. LUQUE-VÁSQUEZ, Zero-sum semi-Markov games in Borel spaces: Discounted and average payoff, Bol. Soc. Mat. Mexicana (3), 8 (2002), pp. 227-241.
    • (2002) Bol. Soc. Mat. Mexicana (3) , vol.8 , pp. 227-241
    • Luque-Vásquez, F.1
  • 24
    • 0022062295 scopus 로고
    • Measurable selection theorems for minimax stochastic optimization problems
    • A. S. NOWAK, Measurable selection theorems for minimax stochastic optimization problems, SIAM J. Control Optim., 23 (1985), pp. 466-476.
    • (1985) SIAM J. Control Optim. , vol.23 , pp. 466-476
    • Nowak, A.S.1
  • 25
    • 0001386709 scopus 로고    scopus 로고
    • Optimal strategies in a class of zero-sum ergodic stochastic games
    • A. S. NOWAK, Optimal strategies in a class of zero-sum ergodic stochastic games, Math. Methods Oper. Res., 50 (1999), pp. 399-419.
    • (1999) Math. Methods Oper. Res. , vol.50 , pp. 399-419
    • Nowak, A.S.1
  • 29
    • 0015080430 scopus 로고
    • Iterative solution of functional equations of undiscounted Markov renewal programming
    • P. J. SCHWEITZER, Iterative solution of functional equations of undiscounted Markov renewal programming, J. Math. Anal. Appl., 34 (1971), pp. 495-501.
    • (1971) J. Math. Anal. Appl. , vol.34 , pp. 495-501
    • Schweitzer, P.J.1
  • 30
    • 0042326540 scopus 로고    scopus 로고
    • The average cost optimality equation: A fixed point approach
    • O. VEGA-AMAYA, The average cost optimality equation: A fixed point approach, Bol. Soc. Mat. Mexicana (3), 9 (2003), pp. 185-195.
    • (2003) Bol. Soc. Mat. Mexicana (3) , vol.9 , pp. 185-195
    • Vega-Amaya, O.1
  • 31
    • 84864114548 scopus 로고    scopus 로고
    • A note on the regularity property of semi-Markov processes with borel stat space
    • Departamento de Matemáticas, Universidad de Sonora, México, Statist. Probab. Lett., to appear
    • O. VEGA-AMAYA, A Note on the Regularity Property of Semi-Markov Processes with Borel Stat Space, Reporte de Investigación 18, Departamento de Matemáticas, Universidad de Sonora, México, 2002, http://fractus.mat.uson.mx/~tedi/reportes. Statist. Probab. Lett., to appear.
    • (2002) Reporte De Investigación , vol.18
    • Vega-Amaya, O.1
  • 32
    • 0242441902 scopus 로고    scopus 로고
    • Sample-path average cost optimality for semi-Markov control processes on Borel spaces: Unbounded costs and mean holding times
    • O. VEGA-AMAYA AND F. LUQUE-VÁSQUEZ, Sample-path average cost optimality for semi-Markov control processes on Borel spaces: Unbounded costs and mean holding times, Appl. Math. (Warsaw), 27 (2000), pp. 343-367.
    • (2000) Appl. Math. (Warsaw) , vol.27 , pp. 343-367
    • Vega-Amaya, O.1    Luque-Vásquez, F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.