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On a Simplified Method of Defining Characteristic Function in Stochastic Games

Author

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  • Elena Parilina

    (Department of Mathematical Game Theory and Statistical Decisions, Saint Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russia
    These authors contributed equally to this work.)

  • Leon Petrosyan

    (Department of Mathematical Game Theory and Statistical Decisions, Saint Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russia
    These authors contributed equally to this work.)

Abstract

In the paper, we propose a new method of constructing cooperative stochastic game in the form of characteristic function when initially non-cooperative stochastic game is given. The set of states and the set of actions for any player is finite. The construction of the characteristic function is based on a calculation of the maximin values of zero-sum games between a coalition and its anti-coalition for each state of the game. The proposed characteristic function has some advantages in comparison with previously defined characteristic functions for stochastic games. In particular, the advantages include computation simplicity and strong subgame consistency of the core calculated with the values of the new characteristic function.

Suggested Citation

  • Elena Parilina & Leon Petrosyan, 2020. "On a Simplified Method of Defining Characteristic Function in Stochastic Games," Mathematics, MDPI, vol. 8(7), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1135-:d:383218
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    References listed on IDEAS

    as
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    2. Parkash Chander & Henry Tulkens, 2006. "The Core of an Economy with Multilateral Environmental Externalities," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 153-175, Springer.
    3. Elena M. Parilina & Alessandro Tampieri, 2018. "Stability and cooperative solution in stochastic games," Theory and Decision, Springer, vol. 84(4), pages 601-625, June.
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    5. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
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