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The Owen value for differential cooperative games with a coalition structure

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper researches differential cooperative games with a coalition structure. To show the payoffs of players, the Owen value for traditional case is extended to the new cooperative model, and its existence and uniqueness are discussed. Furthermore, the relationship between the core and the Owen value is shown. In addition, the sub-game consistency of the Owen value is analyzed that maintains the efficiency of the payoff throughout the game. With the defined characteristic function, it is proved that the Owen value is sub-game consistent. Finally, theoretical results of this paper are applied to solve the problem of cost allocation of environmental governance.
Rocznik
Strony
251--273
Opis fizyczny
Bibliogr. 32 poz., rys.
Twórcy
autor
  • Department of Basic Education, Zhengzhou Technology and Business University, Zhengzhou 450000, China
autor
  • School of Management and Economics, North China University of Water Resources and Electric Power, Zhengzhou 450000, China
Bibliografia
  • [1] Albizuri, M. J. Axiomatizations of the Owen value without efficiency. Mathematical Social Sciences 55, 1 (2008), 78–89.
  • [2] Alonso-Meijide, J. M., and Fiestras-Janeiro, M. G. Modification of the Banzhaf value for games with a coalition structure. Annals of Operations Research 109, 1-4 (2002), 213–227.
  • [3] Amer, R., Carreras, F., an, Giménez J. M. The modified Banzhaf value for games with coalition structure: an axiomatic characterization. Mathematical Social Sciences 43, 1 (2002), 45–54.
  • [4] Aumann, R. J., and Dreze, J. H. Cooperative games with coalition structures. International Journal of Game Theory 3, 4 (1974), 217–237.
  • [5] Bellman, R. Dynamic programming. Princeton University Press, 1957.
  • [6] Filar, J. A., and Petrosjan, L. A. Dynamic cooperative games. International Game Theory Review 2, 1 (2000), 47–65.
  • [7] Gromova, E. V., and Petrosyan, L. A. On an approach to constructing a characteristic function in cooperative differentia games. Automation and Remote Control 78, 9 (2017), 1680–1692.
  • [8] Hamiache, G. A new axiomatization of the Owen value for games with coalition structures. Mathematical Social Sciences 37, 1 (1999), 281–305.
  • [9] Huang, X., He, P., and Zhang, W. A cooperative differential game of transboundary industrial pollution between two regions. Journal of Cleaner Production 120 (2016), 43–52.
  • [10] Isaacs, R. Differential games. Wiley, New York, 1965.
  • [11] Jørgensen, S., and Zaccour, G. Time consistency in cooperative differential games. In Decision and Control in Management Science (New York, 2002), G. Zaccour, Ed., Springer, pp. 349–366.
  • [12] Kamijo, Y. A two-step Shapley value for cooperative games with coalition structures. International Game Theory Review 11, 2 (2009), 207–214.
  • [13] Khmelnitskaya, A. B., and Yanovskaya, E. B. Owen coalitional value without additivity axiom. Mathematical Methods of Operations Research 66, 2 (2007), 255–261.
  • [14] Li, S. A differential game of transboundary industrial pollution with emission permits trading. Journal of Optimization Theory and Applications 163, 2 (2014), 642–659.
  • [15] Lorenzo-Freire, S. New characterizations of the Owen and Banzhaf–Owen values using the intracoalitional balanced contributions property. Top 25, 3 (2017), 579–600.
  • [16] Lorenzo-Freire, S. On the Owen value and the property of balanced contributions within unions. Journal of Optimization Theory and Applications 183, 2 (2019), 757–762.
  • [17] Owen, G. Values of games with a priori unions. In Mathematical Economy and Game Theory (Berlin, 1977), R. Henn and O. Moeschlin, Eds., Springer, pp. 76–88.
  • [18] Petrosyan, L. A. Differential Games of Pursuit. World Scientific, 1993.
  • [19] Petrosyan, L. A. The Shapley value for differential games. In New Trends in Dynamic Games and Applications. Boston, MA 1995, G. J. Olsder, Ed., Birkhäuser, pp. 409–417.
  • [20] Petrosyan, L. A. Agreeable solutions in differential games. Nova Journal of Mathematics Game Theory and Algebra 7, 2-3 (1998), 165–177.
  • [21] Petrosyan, L. A., and Danilov, N. L. Stability of solutions in non-zero sum differential games with transferable payoffs. Viestnik of Leningrad Universtiy 1 (1979), 52–59.
  • [22] Petrosyan, L., and Mamkina, S. Dynamic games with coalitional structures. International Game Theory Review 8, 2 (2006), 295–307.
  • [23] Petrosyan, L., and Zaccour, G. Time-consistent shapley value allocation of pollution cost reduction. Journal of Economic Dynamics and Control 27, 3 (2003), 381–398.
  • [24] Pontryagin, L. S. On the theory of differential games. Russian Mathematical Surveys 21, 4 (1966), 193.
  • [25] Reddy, P. V., and Engwerda, J. C. Necessary and sufficient conditions for Pareto optimality in infinite horizon cooperative differential games. IEEE Transactions on Automatic Control 59, 9 (2014), 2536–2543.
  • [26] Shapley, L. S. A value for n-person games. In Contributions to the Theory of Games II, Annals of Mathematics Studies, vol. 28 (Princeton, NJ, 1953), H. W. Kuhn and A. W. Tucker, Eds., Princeton University Press, pp. 307-317.
  • [27] Stalford, H. L. Criteria for Pareto-optimality in cooperative differential games. Journal of Optimization Theory and Applications 9 (1972), 391–398.
  • [28] van den Brink, R., Khmelnitskaya, A., and van der Laan, G. An Owen-type value for games with two-level communication structure. Annals of Operations Research 243, 1-2 (2016), 179–198.
  • [29] Von Neumann, J., and Morgenstern, O. Theory of Games and Economic Behavior. Princeton University Press, 1944.
  • [30] Wang, L., Gao, H., Petrosyan, L., Qiao, H., and Sedakov, A. Strategically supported cooperation in dynamic games with coalition structures. Science China Mathematics 59, 5 (2016), 1015–1028.
  • [31] Yeung, D. W. K., and Petrosyan, L. A. Cooperative dynamic games with control lags. Dynamic Games and Applications 9, 2 (2019), 550–567.
  • [32] Yeung, D. W. K., Petrosyan, L., and Yeung, P. M. Subgame consistent solutions for a class of cooperative stochastic differential games with nontransferable payoff. In Advances in Dynamic Game Theory. Numerical Methods, Algorithms, and Applications to Ecology and Economics (Boston, MA, 2007), S. Jørgensen, M. Quincampoix and T. L. Vincent, Eds., Birkhäuser, pp. 153–170.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).
Typ dokumentu
Bibliografia
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