Dynamic consistency in discrete-time cooperative games

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.