Advertisement

Dynamically Consistent Cooperative Solutions in Differential Games with Asynchronous Players’ Horizons

  • David W. K. Yeung
Chapter
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 11)

Abstract

This paper considers cooperative differential games in which players enter the game at different times and have diverse horizons. Moreover, the types of future players are not known with certainty. Dynamically consistent cooperative solutions and analytically tractable payoff distribution mechanisms leading to the realization of these solutions are derived. This analysis widens the application of cooperative differential game theory to problems where the players’ game horizons are asynchronous and the types of future players are uncertain. It represents the first attempt to seek dynamically consistent solution for cooperative games with asynchronous players’ horizons and uncertain types of future players.

Keywords

Differential Game Joint Payoff Stochastic Differential Game Game Interval Generation Player 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Basar, T., Olsder, G.J.: Dynamic Noncooperative Game Theory. SIAM Edition, SIAM’s Classics in Applied mathematics, Society for Industrial and Applied Mathematics, Philadelphia (1999)MATHGoogle Scholar
  2. 2.
    Bellman, R.: Dynamic Programming. Princeton University Press, Princeton, NJ (1957)MATHGoogle Scholar
  3. 3.
    Haurie, A.: A Note on Nonzero-Sum Differential Games with Bargaining Solutions. Journal of Optimization Theory and Applications 18, 31–39 (1976)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Jørgensen, S., Yeung, D.W.K.: Overlapping Generations Stochastic Differential Games. Automatica 41, 69–74 (2005)CrossRefGoogle Scholar
  5. 5.
    Petrosyan, L.A.: Agreeable Solutions in Differential Games. International Journal of Mathematics, Game Theory and Algebra 7, 165–177 (1997)MATHMathSciNetGoogle Scholar
  6. 6.
    Petrosyan, L.A., Danilov, N.N.: Cooperative Differential Games and Their Applications. Izd. Tomskogo University, Tomsk (1982)Google Scholar
  7. 7.
    Petrosyan, L.A., Yeung, D.W.K.: Subgame-consistent Cooperative Solutions in Randomly-furcating Stochastic Differential Games. International Journal of Mathematical and Computer Modelling (Special Issue on Lyapunov’s Methods in Stability and Control) 45, 1294–1307 (2007)Google Scholar
  8. 8.
    Yeung, D.W.K., Petrosyan, L.A.: Subgame Consistent Cooperative Solutions in Stochastic Differential Games. Journal of Optimization Theory and Applications 120, 651–666 (2004)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Yeung, D.W.K., Petrosyan, L.A.: Subgame Consistent Solution of A Cooperative Stochastic Differential Game with Nontransferable Payoffs. Journal of Optimization Theory and Applications 124, 701–724 (2005)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Yeung, D.W.K., Petrosyan, L.A.: Cooperative Stochastic Differential Games. Springer, New York (2006)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Business AdministrationHong Kong Shue Yan UniversityHong KongChina
  2. 2.Center of Game TheorySt. Petersburg State UniversitySt. PetersburgRussia

Personalised recommendations