Constrained average stochastic games with continuous-time independent state processes

References

• Shapley LS. Stochastic games. Natl Acad Sci. 1953;39(10):1095–1100.
   PubMed Web of Science ®Google Scholar
• Altman E, Avrachenkov K, Bonneau N, et al. Constrained cost-coupled stochastic games with independent state processes. Oper Res Lett. 2008;36:160–164.
   Web of Science ®Google Scholar
• Filar JA, Vrieze K. Competitive Markov decision processes. New York: Springer-Verlag; 1997.
   Google Scholar
• Liu QL, Huang XX. Discrete-time zero-sum Markov games with first passage criteria. Optimization. 2017;66:571–587.
   Web of Science ®Google Scholar
• Nowak AS. On stochastic games in economics. Math Methods Oper Res. 2007;66:513–530.
   Web of Science ®Google Scholar
• Sennott LI. Nonzero-sum stochastic games with unbounded costs: discounted and average cost cases. Z Oper Res. 1994;40:145–162.
   Google Scholar
• Federgruen A. On N-person stochastic games with denumerable state space. Adv Appl Probab. 1978;10:452–471.
   Web of Science ®Google Scholar
• Guo XP, Hernández-Lerma O. Nonzero-sum games for continuous-time Markov chains with unbounded discounted payoffs. J Appl Probab. 2005;42:303–320.
   Web of Science ®Google Scholar
• Nowak AS. Remarks on sensitive equilibria in stochastic games with additive reward and transition structure. Math Methods Oper Res. 2006;64:481–494.
   Web of Science ®Google Scholar
• Wei QD, Chen X. Stochastic games for continuous-time jump processes under finite-horizon payoff criterion. Appl Math Optim. 2016;74:273–301.
   Web of Science ®Google Scholar
• Altman E, Shwartz A. Constrained Markov games: Nash equilibria. In: JA Filar, et al., editors. Advances in dynamic games and applications; 1996 Kanagawa. Boston (MA): Birkh a¨user; 2000. p. 213–221.(Ann Int Soc Dynam Games. Vol 5).
   Google Scholar
• Wei QD, Chen X. Constrained stochastic games with the average payoff criteria. Oper Res Lett. 2015;43:83–88.
   Web of Science ®Google Scholar
• Alvarez-Mena J, Hernández-Lerma O. Existence of Nash equilibria for constrained stochastic games. Math Methods Oper Res. 2006;63:261–285.
   Web of Science ®Google Scholar
• Zhang WZ, Huang YH, Guo XP. Nonzero-sum constrained discrete-time Markov games: the case of unbounded costs. TOP. 2014;22:1074–1102.
   Web of Science ®Google Scholar
• Zhang WZ. Continuous-time constrained stochastic games under the discounted cost criteria. Appl Math Optim. 2018;77:275–296.
   Web of Science ®Google Scholar
• Zhang WZ, Wang BF, Chen DW. Continuous-time constrained stochastic games with average criteria. Oper Res Lett. 2018;46:109–115.
   Web of Science ®Google Scholar
• Wei QD. Constrained expected average stochastic games for continuous-time jump processes. Appl Math Optim. 2019. doi: 10.1007/s00245-019-09588-9.
   PubMed Web of Science ®Google Scholar
• Zhang WZ. Discrete-time constrained average stochastic games with independent state processes. Math. 2019;7:1089.
   Google Scholar
• Faraci F, Raciti F. On generalized Nash equilibrium in infinite dimension: the Lagrange multipliers approach. Optimization. 2015;64(2):321–338.
   Web of Science ®Google Scholar
• Mastroeni G, Pappalardo M, Raciti F. Generalized Nash equilibrium problems and variational inequalities in Lebesgue spaces. Minimax Theory Appl. 2020;5(1):47–64.
   Google Scholar
• Filar JA, Schultz TA, Thuijsman F, et al. Nonlinear programming and stationary equilibria in stochastic games. Math Programming. 1991;50:227–237.
   Web of Science ®Google Scholar
• Yaji VG, Bhatnagar S. Necessary and sufficient conditions for optimality in constrained general sum stochastic games. Syst Control Lett. 2015;85:8–15.
   Web of Science ®Google Scholar
• Singh VV, Hemachandra N. A characterization of stationary Nash equilibria of constrained stochastic games with independent state processes. Oper Res Lett. 2014;42:48–52.
   Web of Science ®Google Scholar
• Singh VV, Hemachandra N. A characterization of stationary Nash equilibria of single controller constrained stochastic games. Int Game Theory Rev. 2015;17:1–22.
   Web of Science ®Google Scholar
• Kitaev MY, Rykov VV. Controlled queueing systems. Boca Raton: CRC Press; 1995.
   Google Scholar
• Prieto-Rumeau T, Hernández-Lerma O. Selected topics on continuous-time controlled Markov chains and Markov games. London: Imperial College Press; 2012.
   Google Scholar
• Guo XP, Hernández-Lerma O. Continuous-time Markov decision processes. Berlin: Springer-Verlag; 2009.
   Google Scholar
• Föllmer H, Schied A. Stochastic finance: an introduction in discrete time. Berlin: Walter de Gruyter; 2004.
   Google Scholar
• Guo XP, Wei QD, Zhang JY. A constrained optimization problem with applications to constrained MDPs. In: D Hernández-Hernández, JA Minjárez-Sosa, editors. Optimization, control, and applications of stochastic systems; Boston: Birkhäuser; 2012. p. 125–150.
   Google Scholar
• Sennott LI. Stochastic dynamic programming and the control of queueing systems. New York: John Wiley & Sons; 1999.
   Google Scholar
• Fan K. Fixed-point and minimax theorems in locally convex topological linear spaces. Proc Nat Acad Sci USA. 1952;38:121–126.
   PubMed Web of Science ®Google Scholar
• Hernández-Lerma O, Lasserre JB. Discrete-time Markov control processes: basic optimality criteria. New York: Springer-Verlag; 1996.
   Google Scholar