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Dynamic Consistency in Discrete-Time Cooperative Games

  • David W. K. Yeung
  • Leon A. Petrosyan
Part of the Static & Dynamic Game Theory: Foundations & Applications book series (SDGTFA)

Abstract

In some economic situations, the economic process is in discrete time rather than in continuous time. The discrete-time counterpart of differential games are known as dynamic games. Bylka et al (Ann. Oper. Res. 97:69–89, 2000) analyzed oligopolistic price competition in a dynamic game model. Wie and Choi (KSCE J. Civ. Eng. 4(4):239–248, 2000) examined discrete-time traffic network. Beard and McDonald (Ann. Int. Soc. Dyn. Games 9:393–410, 2007) investigated water sharing agreements and Amir and Nannerup (J. Bioecon. 8:147–165, 2006) considered resource extraction problems in a discrete-time dynamic framework. Yeung (Ann. Oper. Res. doi: 10.1007/s10479-011-0844-0, 2011) examined dynamically consistent collaborative environmental management with technology selection in a discrete-time dynamic game framework. The properties of Nash equilibria in dynamic games are examined in Basar (J. Optim. Theory Appl. 14:425–430, 1974; Int. J. Game Theory 5:65–90, 1976). The solution algorithm for solving dynamic games can be found in Basar (IEEE Trans. Autom. Control AC-22:124–126, 1977; In: Differential Games and Control Theory II, pp. 201–228, 1977). Petrosyan and Zenkevich (Game theory. World Scientific, Singapore, 1996) presented an analysis on cooperative dynamic games in a discrete time framework. The SIAM Classics on Dynamic Noncooperative Game Theory by Basar and Olsder (Dynamic noncooperative game theory, 2nd edn. Academic Press, London, 1995) gave a comprehensive treatment of discrete-time noncooperative dynamic games.

Keywords

Nash Equilibrium Differential Game Dynamic Game Optimality Principle Resource Stock 
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.

References

  1. Amir, R., Nannerup, N.: Information structure and the tragedy of the commons in resource extraction. J. Bioecon. 8, 147–165 (2006) CrossRefGoogle Scholar
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.SRS Consortium for Advanced Study in Cooperative Dynamic GamesHong Kong Shue Yan UniversityHong KongPeople’s Republic of China
  2. 2.Center of Game TheorySt. Petersburg State UniversitySaint PetersburgRussia
  3. 3.Faculty of Applied Mathematics and Control ProcessesSt. Petersburg State UniversitySaint PetersburgRussia

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