IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v84y2018i4d10.1007_s11238-017-9619-7.html
   My bibliography  Save this article

Stability and cooperative solution in stochastic games

Author

Listed:
  • Elena M. Parilina

    (Saint Petersburg State University)

  • Alessandro Tampieri

    (University of Bologna and CREA
    CREA, University of Luxembourg)

Abstract

This paper analyses the principles of stable cooperation for stochastic games. Starting from the non-cooperative version of a discounted, non zero-sum stochastic game, we build its cooperative form and find the cooperative solution. We then analyse the conditions under which this solution is stable. Principles of stability include subgame consistency, strategic stability and irrational behaviour proof of the cooperative solution. We finally discuss the existence of a stable cooperative solution, and consider a type of stochastic games for which the cooperative solution is found and the principles of stable cooperation are checked.

Suggested Citation

  • Elena M. Parilina & Alessandro Tampieri, 2018. "Stability and cooperative solution in stochastic games," Theory and Decision, Springer, vol. 84(4), pages 601-625, June.
    • Handle: RePEc:kap:theord:v:84:y:2018:i:4:d:10.1007_s11238-017-9619-7
    DOI: 10.1007/s11238-017-9619-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11238-017-9619-7
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11238-017-9619-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Elon Kohlberg & Abraham Neyman, 2015. "The Cooperative Solution of Stochastic Games," Discussion Paper Series dp679, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    2. Chen, Xi & Kanbur, Ravi & Zhang, Xiaobo, 2011. "Peer effects, risk pooling, and status seeking: What explains gift spending escalation in rural China?," IFPRI discussion papers 1151, International Food Policy Research Institute (IFPRI).
    3. Herings, P. Jean-Jacques & Peeters, Ronald J. A. P., 2004. "Stationary equilibria in stochastic games: structure, selection, and computation," Journal of Economic Theory, Elsevier, vol. 118(1), pages 32-60, September.
    4. Kirman, Alan P & Sobel, Matthew J, 1974. "Dynamic Oligopoly with Inventories," Econometrica, Econometric Society, vol. 42(2), pages 279-287, March.
    5. Anne Case & Anu Garrib & Alicia Menendez & Analia Olgiati, 2013. "Paying the Piper: The High Cost of Funerals in South Africa," Economic Development and Cultural Change, University of Chicago Press, vol. 62(1), pages 1-20.
    6. Leon A Petrosyan & Nikolay A Zenkevich, 2016. "Game Theory," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9824, September.
    7. Solan, Eilon & Vieille, Nicolas, 2002. "Correlated Equilibrium in Stochastic Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 362-399, February.
    8. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    9. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    10. Arthur Charpentier & Stéphane Mussard, 2011. "Income inequality games," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(4), pages 529-554, December.
    11. Jaśkiewicz, Anna & Nowak, Andrzej S., 2014. "Stationary Markov perfect equilibria in risk sensitive stochastic overlapping generations models," Journal of Economic Theory, Elsevier, vol. 151(C), pages 411-447.
    12. Abhijit V. Banerjee & Esther Duflo, 2007. "The Economic Lives of the Poor," Journal of Economic Perspectives, American Economic Association, vol. 21(1), pages 141-168, Winter.
    13. Anastasia Litina & Theodore Palivos, 2015. "Corruption and Tax Evasion: Reflections on Greek Tragedy," Working Papers 193, Bank of Greece.
    14. Messner, Matthias & Polborn, Mattias K., 2003. "Cooperation in Stochastic OLG games," Journal of Economic Theory, Elsevier, vol. 108(1), pages 152-168, January.
    15. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    16. AMIR, Rabah, 2001. "Stochastic games in economics and related fields: an overview," LIDAM Discussion Papers CORE 2001060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. AMIR, Rabah, 2001. "Stochastic games in economics: the lattice-theoretic approach," LIDAM Discussion Papers CORE 2001059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    20. Lenter, David & Slemrod, Joel & Shackelford, Douglas A., 2003. "Public Disclosure of Corporate Tax Return Information: Accounting, Economics, and Legal Perspectives," National Tax Journal, National Tax Association;National Tax Journal, vol. 56(4), pages 803-830, December.
    21. repec:dau:papers:123456789/6019 is not listed on IDEAS
    22. Benno Torgler, 2004. "Moral suasion: An alternative tax policy strategy? Evidence from a controlled field experiment in Switzerland," Economics of Governance, Springer, vol. 5(3), pages 235-253, November.
    23. McCain, Roger A., 2008. "Cooperative games and cooperative organizations," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 37(6), pages 2155-2167, December.
    24. Benno Torgler, 2004. "Moral Suasion: An alternative tax policy strategy? Evidence from a controlled field experiment in Switzerland," CREMA Working Paper Series 2004-01, Center for Research in Economics, Management and the Arts (CREMA).
    25. Paola Giuliano & Antonio Spilimbergo, 2014. "Growing up in a Recession," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(2), pages 787-817.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Elena Parilina & Stepan Akimochkin, 2021. "Cooperative Stochastic Games with Mean-Variance Preferences," Mathematics, MDPI, vol. 9(3), pages 1-15, January.
    2. Elena M. Parilina & Georges Zaccour, 2022. "Sustainable Cooperation in Dynamic Games on Event Trees with Players’ Asymmetric Beliefs," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 92-120, July.
    3. Al-Jarhi, Mabid Ali M. M., 2016. "An Economic Theory of Islamic Finance Regulation," Islamic Economic Studies, The Islamic Research and Training Institute (IRTI), vol. 24, pages 1-44.
    4. Troncoso-Valverde, Cristián & Chávez-Bustamante, Felipe, 2024. "Do you want to know a secret? Strategic alliances and competition in product markets," European Journal of Operational Research, Elsevier, vol. 313(3), pages 1180-1190.
    5. 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.
    6. Parilina, Elena M. & Zaccour, Georges, 2022. "Payment schemes for sustaining cooperation in dynamic games," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).

    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. Litina, Anastasia & Palivos, Theodore, 2016. "Corruption, tax evasion and social values," Journal of Economic Behavior & Organization, Elsevier, vol. 124(C), pages 164-177.
    2. Xi Chen & Xiaobo Zhang, 2012. "Costly Posturing: Relative Status, Ceremonies and Early Child Development in China," WIDER Working Paper Series wp-2012-070, World Institute for Development Economic Research (UNU-WIDER).
    3. Ayala Mashiah-Yaakovi, 2015. "Correlated Equilibria in Stochastic Games with Borel Measurable Payoffs," Dynamic Games and Applications, Springer, vol. 5(1), pages 120-135, March.
    4. Roger A McCain, 2013. "Value Solutions in Cooperative Games," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8528, September.
    5. Chen, Xi & Zhang, Xiaobo, 2017. "Costly Posturing: Ceremonies and Early Child Development in China," IZA Discussion Papers 10662, Institute of Labor Economics (IZA).
    6. Chen, Xi, 2014. "Fetus, Fasting, and Festival: The Persistent Effects of in Utero Social Shocks," IZA Discussion Papers 8494, Institute of Labor Economics (IZA).
    7. Eilon Solan & Rakesh V. Vohra, 1999. "Correlated Equilibrium, Public Signaling and Absorbing Games," Discussion Papers 1272, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Anastasia Litina & Theodore Palivos, 2015. "Corruption and Tax Evasion: Reflections on Greek Tragedy," Working Papers 193, Bank of Greece.
    9. Alisher Aldashev, 2024. "Ceremonial expenditures, informal networks and economic consequences: Evidence from Kyrgyzstan," Economics of Transition and Institutional Change, John Wiley & Sons, vol. 32(2), pages 571-582, April.
    10. Forges, Françoise & Ray, Indrajit, 2024. "“Subjectivity and correlation in randomized strategies”: Back to the roots," Journal of Mathematical Economics, Elsevier, vol. 114(C).
    11. Ramsey, David M. & Szajowski, Krzysztof, 2008. "Selection of a correlated equilibrium in Markov stopping games," European Journal of Operational Research, Elsevier, vol. 184(1), pages 185-206, January.
    12. Chen, Xi & Zhang, Xiaobo, 2012. "Costly posturing: relative status, ceremonies and early child development in China:," IFPRI discussion papers 1206, International Food Policy Research Institute (IFPRI).
    13. repec:unu:wpaper:wp2012-70 is not listed on IDEAS
    14. Christoph Engel & Luigi Mittone & Azzurra Morreale, 2024. "Outcomes or participation? Experimentally testing competing sources of legitimacy for taxation," Economic Inquiry, Western Economic Association International, vol. 62(2), pages 563-583, April.
    15. Konstantinos Georgalos & Indrajit Ray & Sonali SenGupta, 2020. "Nash versus coarse correlation," Experimental Economics, Springer;Economic Science Association, vol. 23(4), pages 1178-1204, December.
    16. Richard Kwabena Nkrumah & Samuel Kobina Annim & Benedict Afful, 2021. "Household Social Expenditure in Ghana: Examining the Ex-Post Effects and Vulnerability to Poverty," Social Sciences, MDPI, vol. 10(2), pages 1-15, January.
    17. Antonio Cabrales & Michalis Drouvelis & Zeynep Gurguy & Indrajit Ray, 2017. "Transparency is Overrated: Communicating in a Coordination Game with Private Information," CESifo Working Paper Series 6781, CESifo.
    18. Ehud Lehrer & Eilon Solan, 2007. "Learning to play partially-specified equilibrium," Levine's Working Paper Archive 122247000000001436, David K. Levine.
    19. Sergiu Hart & Andreu Mas-Colell, 2013. "A Simple Adaptive Procedure Leading To Correlated Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 2, pages 17-46, World Scientific Publishing Co. Pte. Ltd..
    20. Montero, M.P., 2002. "Two-Stage Bargaining with Reversible Coalitions : The Case of Apex Games," Other publications TiSEM 7dba0283-bc13-4f2c-8f5e-5, Tilburg University, School of Economics and Management.
    21. Tommaso Denti & Doron Ravid, 2023. "Robust Predictions in Games with Rational Inattention," Papers 2306.09964, arXiv.org.

    More about this item

    Keywords

    Cooperative stochastic game; Subgame perfect equilibrium; Subgame consistency; Strategic stability; Irrational behaviour proof;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    Statistics

    Access and download statistics

    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:kap:theord:v:84:y:2018:i:4:d:10.1007_s11238-017-9619-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.