Strong Time-Consistent Core for a Class of Linear-State Games

1. Petrosyan L A, Stability of solutions in differential games with many participants, Vestnik Leningradskogo Universiteta. Ser. 1. Matematika Mekhanika Astronomiya, 1977, 19: 46–52 (in Russian).

   Google Scholar 

2. Petrosjan L A, Cooperative differential games, Advances in Dynamic Games, Annals of the International Society of Dynamic Games, Eds. by Nowak A S and Szajowski K, Boston, 2005, 7: 183–200.

3. Petrosyan L A and Danilov N N, Stability of solutions in non-zero-sum differential games with transferable payoffs, Vestnik Leningradskogo Universiteta. Ser. 1. Matematika Mekhanika Astronomiya, 1979, 1: 52–59 (in Russian).

   MATH  Google Scholar 

4. Sedakov A A, The strong time-consistent core, Matematicheskaya Teoriya Igr I Ee Prilozheniya, 2015, 7(2): 69–84 (in Russian).

   MATH  Google Scholar 

5. Jørgensen S, A dynamic game of waste management, Journal of Economic Dynamics and Control, 2010, 34(2): 258–265.

   MathSciNet  MATH  Google Scholar 

6. Kimms A and Kozeletskyi I, Core-based cost allocation in the cooperative traveling salesman problem, European Journal of Operational Research, 2016, 248(3): 910–916.

   MathSciNet  MATH  Google Scholar 

7. Rosenthal E C, Shortest path games, European Journal of Operational Research, 2013, 224(1): 132–140.

   MathSciNet  MATH  Google Scholar 

8. Drechsel J and Kimms A, Computing core allocations in cooperative games with an application to cooperative procurement, International Journal of Production Economics, 2010, 128: 310–321.

   MATH  Google Scholar 

9. Van den Heuvel W, Borm P, and Hamers H, Economic lot-sizing games, European Journal of Operational Research, 2007, 176(2): 1117–1130.

   MathSciNet  MATH  Google Scholar 

10. Toriello A and Uhan N A, Dynamic cost allocation for economic lot sizing games, Operations Research Letters, 2014, 42(1): 82–84.

    MathSciNet  MATH  Google Scholar 

11. Toriello A and Uhan N A, Dynamic linear programming games with risk-averse players, Mathematical Programming, 2017, 163(1): 25–56.

    MathSciNet  MATH  Google Scholar 

12. Xu N and Veinott A F, Sequential stochastic core of a cooperative stochastic programming game, Operations Research Letters, 2013, 41(5): 430–435.

    MathSciNet  MATH  Google Scholar 

13. Parilina E and Zaccour G, Node-consistent core for games played over event trees, Automatica, 2015, 53: 304–311.

    MathSciNet  MATH  Google Scholar 

14. Germain M, Tulkens H, and Magnus A, Dynamic core-theoretic cooperation in a two-dimensional international environmental model, Mathematical Social Sciences, 2010, 59: 208–226.

    MathSciNet  MATH  Google Scholar 

15. Lehrer E and Scarsini M, On the core of dynamic cooperative games, Dynamic Games and Applications, 2013, 3(3): 359–373.

    MathSciNet  MATH  Google Scholar 

16. Kranich L, Perea A, and Peters H, Core concepts for dynamic TU games, International Game Theory Review, 2005, 7(1): 43–61.

    MathSciNet  MATH  Google Scholar 

17. Koutsougeras L C, A two-stage core with applications to asset market and differential information economies, Economic Theory, 1998, 11: 563–584.

    MathSciNet  MATH  Google Scholar 

18. Yeung D W K and Petrosyan L A, Subgame Consistent Economic Optimization: An Advanced Cooperative Dynamic Game Analysis, Birkhäuser, Boston, 2012.

    MATH  Google Scholar 

19. Gromova E, The Shapley value as a sustainable cooperative solution in differential games of three players, Recent Advances in Game Theory and Applications, Static & Dynamic Game Theory: Foundations & Applications, Eds. by Petrosyan L A and Mazalov V V, Basel, 2016, 67–89.

20. Gromova E V and Petrosyan L A, Strongly time-consistent cooperative solution for a differential game of pollution control, Upravlenie Bolshimi Sistemamy, 2015, 55: 140–159 (in Russian).

    MATH  Google Scholar 

21. Petrosyan L A and Pankratova Y B, Construction of strongly time-consistent subcores in differential games with prescribed duration, Trudy Instituta Matematiki I Mekhamiki UrO RAN, 2017, 23(1): 219–227 (in Russian).

    Google Scholar 

22. Petrosyan L, Sedakov A, Sun H, et al., Convergence of strong time-consistent payment schemes in dynamic games, Applied Mathematics and Computation, 2017, 315: 96–112.

    MathSciNet  MATH  Google Scholar 

23. Gao H, Petrosyan L, Qiao H, et al., Cooperation in two-stage games on undirected networks, Journal of Systems Science and Complexity, 2017, 30(3): 680–693.

    MathSciNet  MATH  Google Scholar 

24. Sedakov A A, On the strong time consistency of the core, Automation and Remote Control, 2018, 79(4): 757–767.

    MathSciNet  Google Scholar 

25. Parilina E M and Petrosyan L A, Strongly subgame consistent core in stochastic games, Matematicheskaya Teoriya Igr I Ee Prilozheniya, 2017, 9(2): 39–61 (in Russian).

    MATH  Google Scholar 

26. Calvo E and Rubio S J, Dynamic models of international environmental agreements: A differential game approach, International Review of Environmental and Resource Economics, 2012, 6(4): 289–339.

    Google Scholar 

27. Dockner E, Jørgensen S, Long N V, et al., Differential Games in Economics and Management Science, Cambridge University Press, Cambridge, 2000.

    MATH  Google Scholar 

28. Jørgensen S, Martín-Herrán G, and Zaccour G, Dynamic games in the economics and management of pollution, Environmental Modeling & Assessment, 2010, 15(6): 433–467.

    Google Scholar 

29. Long N V, Applications of dynamic games to global and transboundary environmental issues: A review of the literature, Strategic Behavior and the Environment, 2012, 2(1): 1–59.

    MathSciNet  Google Scholar 

30. Martín-Herrán G and Zaccour G, Credibility of incentive equilibrium strategies in linear-state differential games, Journal of Optimization Theory and Applications, 2005, 126(2): 367–389.

    MathSciNet  MATH  Google Scholar 

31. Petrosjan L and Zaccour G, Time-consistent Shapley value allocation of pollution cost reduction, Journal of Economic Dynamics and Control, 2003, 27(3): 381–398.

    MathSciNet  MATH  Google Scholar 

32. Aumann R, Acceptable points in general cooperative n-person games, Contributions to the theory of games IV. Annals of Mathematics Studies, No 40, Ed. by Tucker L, 1959, 287–324.

33. Chander P and Tulkens H, A core of an economy with multilateral environmental externalities, International Journal of Game Theory, 1997, 26: 379–401.

    MathSciNet  MATH  Google Scholar 

34. Von Neumann J and Morgenstern O, Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1944.

    MATH  Google Scholar 

35. Shapley L, Cores of convex games, International Journal of Game Theory, 1971, 1(1): 11–26.

    MathSciNet  MATH  Google Scholar 

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