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Advances in Dynamic Games pp 359–373Cite as

The Shapley Value in Cooperative Differential Games with Random Duration

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Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 11))

Abstract

The class of cooperative differential games with random duration is studied in this chapter. The problem of the Shapley Value calculation is examined. As a result, the Hamilton–Jacobi–Bellman equation for the problem with random duration is derived. The Shapley Value calculation method, which uses the obtained equation, is represented by an algorithm. An application of the theoretical results is illustrated with a model of nonrenewable resource extraction by n firms or countries.

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References

  1. Dockner, E.J., Jorgensen, S., van Long, N., Sorger, G.: Differential Games in Economics and Management Science. Cambridge University Press, Cambridge, U.K. (2000)

    MATH  Google Scholar 

  2. Henley, E.J., Kumamoto, H.: Reliability Engineering and Risk Assessment. Prentice Hall (1981)

    Google Scholar 

  3. Petrosjan, L.A., Zaccour, G.: Time-consistent Shapley Value Allocation of Pollution Cost Reduction. Journal of Economic Dynamics and Control 27, 381–398 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Petrosjan, L.A., Shevkoplyas, E.V.: Cooperative Solutions for Games with Random Duration. Game Theory and Applications IX, Nova Science Publishers, 125–139 (2003)

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  5. Weibull, W.: A statistical distribution function of wide applicability. Journal of Applied Mechanics 18, 293–297 (1951)

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Author information

Authors and Affiliations

  1. Faculty of Applied Mathematics, St. Petersburg State University, University pr., 35, Petrodvorets, 198 904, St. Petersburg, Russia

    Ekaterina Shevkoplyas

Authors
  1. Ekaterina Shevkoplyas
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Correspondence to Ekaterina Shevkoplyas .

Editor information

Editors and Affiliations

  1. , HEC Montréal, Department of Management Science, 3000 Chemin de la Côte-Sainte-Catherine, Montreal, H3T2A7, Canada

    Michèle Breton

  2. Wrocław University of Technology, Institute of Mathematics and Computer Sc, Wybrzeże Wyspiańskiego 27, Wrocław, PL-50-370, Poland

    Krzysztof Szajowski

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Shevkoplyas, E. (2011). The Shapley Value in Cooperative Differential Games with Random Duration. In: Breton, M., Szajowski, K. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 11. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8089-3_18

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