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Dynamic Cooperative Games

Author

Listed:
  • JERZY A. FILAR

    (School of Mathematics, University of South Australia, The Levels SA 5095, Australia)

  • LEON A. PETROSJAN

    (Faculty of Applied Mathematics, St. Petersburg State University, Bibliotechnaya pl. 2, Petrodvorets, 198904, St. Petersburg, Russia)

Abstract

We consider dynamic cooperative games in characteristic function form in the sense that the characteristic function evolves over time in accordance with a difference or differential equation that is influenced not only by the current ("instantaneous") characteristic function but also by the solution concept used to allocate the benefits of cooperation among the players. The latter solution concept can be any one of a number of now standard solution concepts of cooperative game theory but, for demonstration purposes, we focus on the core and the Shapley value.In the process, we introduce some new mechanisms by which players may regard the evolution of cooperative game over time and analyse them with respect to the goal of attaining time consistency either in discrete or in continuous time setting. In discrete time, we illustrate the phenomena that can arise when an allocation according to a given solution concept is used to adapt the values of coalitions at successive time points. In continuous time, we introduce the notion of an "instantaneous" game and its integration over time.

Suggested Citation

  • Jerzy A. Filar & Leon A. Petrosjan, 2000. "Dynamic Cooperative Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 2(01), pages 47-65.
    • Handle: RePEc:wsi:igtrxx:v:02:y:2000:i:01:n:s0219198900000044
    DOI: 10.1142/S0219198900000044
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    Citations

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    Cited by:

    1. Imma Curiel, 2015. "Compensation rules for multi-stage sequencing games," Annals of Operations Research, Springer, vol. 225(1), pages 65-82, February.
    2. 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.
    3. Predtetchinski, Arkadi, 2007. "The strong sequential core for stationary cooperative games," Games and Economic Behavior, Elsevier, vol. 61(1), pages 50-66, October.
    4. Casas, Omar J. & Romera, Rosario, 2009. "Controlling the international stock pollutant with policies depending on target values," DES - Working Papers. Statistics and Econometrics. WS ws096019, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Casajus, André & Kramm, Michael & Wiese, Harald, 2020. "Asymptotic stability in the Lovász-Shapley replicator dynamic for cooperative games," Journal of Economic Theory, Elsevier, vol. 186(C).
    6. Hennlock, Magnus, 2006. "Coasean Bargaining Games with Stochastic Stock Externalities," Working Papers in Economics 229, University of Gothenburg, Department of Economics.
    7. 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.
    8. B. D. Bernheim & S. N. Slavov, 2009. "A Solution Concept for Majority Rule in Dynamic Settings," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(1), pages 33-62.
    9. Beard, Rodney & McDonald, Stuart, 2005. "Dynamic Recontracting of Water Rights," 2005 Conference (49th), February 9-11, 2005, Coff's Harbour, Australia 137781, Australian Agricultural and Resource Economics Society.
    10. 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.
    11. Mohammad Keyhani & Moren Lévesque & Anoop Madhok, 2015. "Toward a theory of entrepreneurial rents: A simulation of the market process," Strategic Management Journal, Wiley Blackwell, vol. 36(1), pages 76-96, January.
    12. 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.
    13. 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.
    14. Berden, C., 2007. "The role of individual intertemporal transfers in dynamic TU-Games," Research Memorandum 030, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

    More about this item

    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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