IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i7p1135-d383218.html
   My bibliography  Save this article

On a Simplified Method of Defining Characteristic Function in Stochastic Games

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/7/1135/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/7/1135/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Parkash Chander, 2007. "The gamma-core and coalition formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 539-556, April.
    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. Konstantin Avrachenkov & Laura Cottatellucci & Lorenzo Maggi, 2013. "Cooperative Markov decision processes: time consistency, greedy players satisfaction, and cooperation maintenance," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 239-262, February.
    4. Elena M. Parilina & Alessandro Tampieri, 2018. "Stability and cooperative solution in stochastic games," Theory and Decision, Springer, vol. 84(4), pages 601-625, June.
    5. Petrosjan, Leon & Zaccour, Georges, 2003. "Time-consistent Shapley value allocation of pollution cost reduction," Journal of Economic Dynamics and Control, Elsevier, vol. 27(3), pages 381-398, January.
    6. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    7. G. Zaccour, 2003. "Computation of Characteristic Function Values for Linear-State Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 183-194, April.
    8. Bezalel Peleg & Peter Sudhölter, 2007. "Introduction to the Theory of Cooperative Games," Theory and Decision Library C, Springer, edition 0, number 978-3-540-72945-7, December.
    9. Reddy, Puduru V. & Zaccour, Georges, 2016. "A friendly computable characteristic function," Mathematical Social Sciences, Elsevier, vol. 82(C), pages 18-25.
    10. Leon Petrosyan, 2019. "Strong Strategic Support of Cooperation in Multistage Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-12, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chander, Parkash & Wooders, Myrna, 2020. "Subgame-perfect cooperation in an extensive game," Journal of Economic Theory, Elsevier, vol. 187(C).
    2. Parilina, Elena M. & Zaccour, Georges, 2022. "Payment schemes for sustaining cooperation in dynamic games," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).
    3. Reddy, Puduru V. & Zaccour, Georges, 2016. "A friendly computable characteristic function," Mathematical Social Sciences, Elsevier, vol. 82(C), pages 18-25.
    4. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, December.
    5. Giorgos Stamatopoulos, 2020. "On the $$\gamma $$γ-core of asymmetric aggregative games," Theory and Decision, Springer, vol. 88(4), pages 493-504, May.
    6. Elena Parilina & Stepan Akimochkin, 2021. "Cooperative Stochastic Games with Mean-Variance Preferences," Mathematics, MDPI, vol. 9(3), pages 1-15, January.
    7. Dritan Osmani & Richard S.J. Tol, 2008. "Evolution in time of Farsightedly Stable Coalitions: An Application of FUND," Working Papers FNU-162, Research unit Sustainability and Global Change, Hamburg University, revised May 2008.
    8. Casas, Omar J. & Romera, Rosario, 2011. "The international stock pollutant control: a stochastic formulation with transfers," DES - Working Papers. Statistics and Econometrics. WS ws112217, Universidad Carlos III de Madrid. Departamento de Estadística.
    9. Gonzalez, Stéphane & Rostom, Fatma Zahra, 2022. "Sharing the global outcomes of finite natural resource exploitation: A dynamic coalitional stability perspective," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 1-10.
    10. Hassan Benchekroun & Farnaz Taherkhani, 2014. "Adaptation and the Allocation of Pollution Reduction Costs," Dynamic Games and Applications, Springer, vol. 4(1), pages 32-57, March.
    11. Aymeric Lardon, 2019. "On the coalitional stability of monopoly power in differentiated Bertrand and Cournot oligopolies," Theory and Decision, Springer, vol. 87(4), pages 421-449, November.
    12. Calvo, Emilio & Rubio, Santiago J., 2013. "Dynamic Models of International Environmental Agreements: A Differential Game Approach," International Review of Environmental and Resource Economics, now publishers, vol. 6(4), pages 289-339, April.
    13. Michel Grabisch & Peter Sudhölter, 2012. "The bounded core for games with precedence constraints," Annals of Operations Research, Springer, vol. 201(1), pages 251-264, December.
    14. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications,, Elsevier.
    15. Effrosyni Diamantoudi & Eftichios S. Sartzetakis, 2018. "International Environmental Agreements—The Role of Foresight," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 71(1), pages 241-257, September.
    16. BRECHET, Thierry & GERARD, François & TULKENS, Henry, 2007. "Climate coalitions: a theoretical and computational appraisal," LIDAM Discussion Papers CORE 2007003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. Pisciella, Paolo & Gaivoronski, Alexei A., 2024. "Modeling collaborative data service provision around an open source platform under uncertainty with stochastic provision games," Omega, Elsevier, vol. 129(C).
    18. Bloch, Francis & de Clippel, Geoffroy, 2010. "Cores of combined games," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2424-2434, November.
    19. Fuentes-Albero, Cristina & Rubio, Santiago J., 2010. "Can international environmental cooperation be bought?," European Journal of Operational Research, Elsevier, vol. 202(1), pages 255-264, April.
    20. Dritan Osmani, "undated". "A note on optimal transfer schemes, stable coalition for environmental protection and joint maximization assumption," Working Papers FNU-176, Research unit Sustainability and Global Change, Hamburg University.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1135-:d:383218. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.