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Core Concepts For Dynamic Tu Games

Author

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  • LAURENCE KRANICH

    (Department of Economics, SUNY at Albany, Albany, NY 12222, USA)

  • ANDRÉS PEREA

    (Department of Quantitative Economics, University of Maastricht, P. O. Box 616, 6200 MD Maastricht, The Netherlands)

  • HANS PETERS

    (Department of Quantitative Economics, University of Maastricht, P. O. Box 616, 6200 MD Maastricht, The Netherlands)

Abstract

This paper is concerned with the question of how to define the core when cooperation takes place in a dynamic setting. The focus is on dynamic cooperative games in which the players face a finite sequence of exogenously specified TU-games. Three different core concepts are presented: the classical core, the strong sequential core and the weak sequential core. The differences between the concepts arise from different interpretations of profitable deviations by coalitions. Sufficient conditions are given for nonemptiness of the classical core in general and of the weak sequential core for the case of two players. Simplifying characterizations of the weak and strong sequential core are provided. Examples highlight the essential difference between these core concepts.

Suggested Citation

  • Laurence Kranich & Andrés Perea & Hans Peters, 2005. "Core Concepts For Dynamic Tu Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 43-61.
    • Handle: RePEc:wsi:igtrxx:v:07:y:2005:i:01:n:s0219198905000417
    DOI: 10.1142/S0219198905000417
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    1. Engwerda, J.C., 2012. "Prospects of Tools from Differential Games in the Study Of Macroeconomics of Climate Change," Discussion Paper 2012-045, Tilburg University, Center for Economic Research.
    2. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2015. "An allocation rule for dynamic random network formation processes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 283-313, October.
    3. Imma Curiel, 2015. "Compensation rules for multi-stage sequencing games," Annals of Operations Research, Springer, vol. 225(1), pages 65-82, February.
    4. Chander, Parkash & Wooders, Myrna, 2020. "Subgame-perfect cooperation in an extensive game," Journal of Economic Theory, Elsevier, vol. 187(C).
    5. Konstantin Avrachenkov & Laura Cottatellucci & Lorenzo Maggi, 2014. "Confidence Intervals for the Shapley–Shubik Power Index in Markovian Games," Dynamic Games and Applications, Springer, vol. 4(1), pages 10-31, March.
    6. Marc Germain & Philippe Toint & Henry Tulkens & Aart Zeeuw, 2006. "Transfers to Sustain Dynamic Core-Theoretic Cooperation in International Stock Pollutant Control," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 251-274, Springer.
    7. Habis, Helga & Herings, P. Jean-Jacques, 2011. "Transferable utility games with uncertainty," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2126-2139, September.
    8. Ketelaars, Martijn & Borm, Peter & Kort, Peter M., 2023. "Dynamic Stability of Cooperative Investment under Uncertainty," Other publications TiSEM 64e99402-3217-4efa-a759-0, Tilburg University, School of Economics and Management.
    9. Helga Habis & P. Herings, 2013. "Stochastic bankruptcy games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 973-988, November.
    10. 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.
    11. Berden, Caroline & Peters, Hans & Robles, Laura & Vermeulen, Dries, 2022. "Strategic transfers between cooperative games," Games and Economic Behavior, Elsevier, vol. 133(C), pages 77-84.
    12. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, July.
    13. Ehud Lehrer & Marco Scarsini, 2013. "On the Core of Dynamic Cooperative Games," Dynamic Games and Applications, Springer, vol. 3(3), pages 359-373, September.
    14. Helga Habis & P. Jean-Jacques Herings, 2010. "A Note On The Weak Sequential Core Of Dynamic Tu Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 407-416.
    15. D. Bauso & J. Timmer, 2009. "Robust dynamic cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 23-36, March.
    16. Besner, Manfred, 2022. "The grand surplus value and repeated cooperative cross-games with coalitional collaboration," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    17. Habis, H. & Herings, P.J.J., 2009. "Cooperation under incomplete contracting," Research Memorandum 026, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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    More about this item

    Keywords

    Cooperative games; dynamic games; core; differences; JEL classification: C71; JEL classification: C73;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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