Pareto-efficient situations in infinite and finite pure-strategy staircase-function games

[1] S. Adlakha, R. Johari, and G.Y. Weintraub, Equilibria of dynamic games with many players: Existence, approximation, and market structure, J. Econ. Theory 156 (2015), 269–316.

[2] J.P. Benoit and V. Krishna, Finitely repeated games, Econometrica 53 (1985), no. 4, 905–922.

[3] S.P. Coraluppi and S.I. Marcus, Risk-sensitive and minimax control of discrete-time, finite-state Markov decision processes, Automatica 35 (1999), no. 2, 301–309.

[4] R.E. Edwards, Functional Analysis: Theory and Applications, Holt, Rinehart and Winston, New York City, New York, USA, 1965.

[5] D. G，asior and M. Drwal, Pareto-optimal Nash equilibrium in capacity allocation game for self-managed networks, Comput. Networks 57 (2013), no. 16, 2817–2832.

[6] J.C. Harsanyi and R. Selten, A General Theory of Equilibrium Selection in Games, The MIT Press, Cambridge, Massachusetts, USA, 1988.

[7] D. Hirshleifer, D. Jiang, and Y.M. DiGiovanni, Mood beta and seasonalities in stock returns, J. Financ. Econ. 137 (2020), no. 1, 272–295.

[8] H. Khaloie, A. Abdollahi, M. Shafie-khah, A. Anvari-Moghaddam, S. Nojavan, P. Siano, and J.P.S. Catalao, Coordinated wind-thermal-energy storage offering strategy in energy and spinning reserve markets using a multistage model, Appl. Energy 259 (2020), 114168.

[9] S. Kim, Y.R. Lee, and M.K. Kim, Flexible risk control strategy based on multi-stage corrective action with energy storage system, Int. J. Electric. Power Energy Syst. 110 (2019), 679–695.

[10] S.C. Kontogiannis, P.N. Panagopoulou, and P.G. Spirakis, Polynomial algorithms for approximating Nash equilibria of bimatrix games, Theor. Comput. Sci. 410 (2009), no. 17, 1599–1606.

[11] C.E. Lemke and J.T. Howson, Equilibrium points of bimatrix games, SIAM J. Appl. Math. 12 (1964), no. 2, 413–423.

[12] K. Leyton-Brown and Y. Shoham, Essentials of Game Theory: A Concise, Multidisciplinary Introduction, Morgan & Claypool Publishers, 2008.

[13] Y. Li, K. Li, Y. Xie, J. Liu, C. Fu, and B. Liu, Optimized charging of lithium-ion battery for electric vehicles: Adaptive multistage constant current–constant voltage charging strategy, Renew. Energy 146 (2020), 2688–2699.

[14] Q. Liu, Y. He, and J. Wang, Optimal control for probabilistic Boolean networks using discrete-time Markov decision processes, Phys. A: Statist. Mech. Appl. 503 (2018), 1297–1307.

[15] G.J. Mailath and L. Samuelson, Repeated Games and Reputations: Long-Run Relationships, Oxford University Press, 2006.

[16] H. Moulin, Theorie des jeux pour l’economie et la politique, Hermann, Paris, 1981.

[17] R.B. Myerson, Game Theory: Analysis of Conflict, Harvard University Press, 1997.

[18] N. Nisan, T. Roughgarden, E. Tardos, and V.V. Vazirani, Algorithmic Game Theory, Cambridge University Press, Cambridge, UK, 2007.

[19] S. Rahal, D.J. Papageorgiou, and Z. Li, Hybrid strategies using linear and piecewise-linear decision rules for multistage adaptive linear optimization, Eur. J. Oper. Res. 290 (2021), no. 3, 1014–1030.

[20] V.V. Romanuke and V.G. Kamburg, Approximation of isomorphic infinite two-person noncooperative games via variously sampling the players’ payoff functions and reshaping payoff matrices into bimatrix game, Appl. Comput. Syst. 20 (2016), 5–14.

[21] V.V. Romanuke, Finite approximation of continuous noncooperative two-person games on a product of linear strategy functional spaces, J. Math. Appl. 43 (2020), 123–138.

[22] T.C. Schelling, The Strategy of Conflict, Harvard University, 1980.

[23] Y. Teraoka, A two-person game of timing with random arrival time of the object, Math. Japon. 24 (1979), 427–438.

[24] N.N. Vorob’yov, Game theory fundamentals. Noncooperative games, Nauka, Moscow, 1984.

[25] N.N. Vorob’yov, Game theory for economists-cyberneticists, Nauka, Moscow, 1985.

[26] K.E. Wee and A. Iyer, Consolidating or non-consolidating queues: A game theoretic queueing model with holding costs, Oper. Res. Lett. 39 (2011), no. 1, 4–10.

[27] J. Yang, Y.-S. Chen, Y. Sun, H.-X. Yang, and Y. Liu, Group formation in the spatial public goods game with continuous strategies, Phys. A: Statist. Mech. Appl. 505 (2018), 737–743.

[28] E.B. Yanovskaya, Minimax theorems for games on the unit square, Probability Theory and Its Applications 9 (1964), no. 3, 554–555.

[29] E.B. Yanovskaya, Antagonistic games played in function spaces, Lithuan. Math. Bull. 3 (1967), 547–557.

[30] D. Ye and J. Chen, Non-cooperative games on multidimensional resource allocation, Future Gen. Comput. Syst. 29 (2013), no. 7, 1345–1352.

[31] Z. Zhou and Z. Jin, Optimal equilibrium barrier strategies for time-inconsistent dividend problems in discrete time, Insurance: Math. Econ. 94 (2020), 100–108.