Differential games

There are many GT concepts, but this chapter focuses on concepts that are particularly relevant to SCM and, perhaps, already found their applications in the literature. We dedicate a considerable amount of space to the discussion of static non-cooperative, non-zero sum games, the typQ of game which has received the most attention in the recent SCM literature. We also discuss cooperative games, dynamic/differential games and games with asym-metric/incomplete information. We omit discussion of important GT concepts covered in other chapters in this book auctions in Chapters 5 and 7 and principal-agent models in Chapter 4. 

The following is a simple example of a differential game taken from Kamien and Schwartz (2000). Suppose two players indexed by 2 = 1,2 are engaged into production and sales of the same product. Firms choose production levels Ui t) at any moment of time and incur total cost Ci ui) = cui + The price in the market is determined as per Cournot competition. Typically, this would mean that p t) = a—Ui t)-U2 t), However, the twist in this problem is that if the production level is changed, price adjustments are not instantaneous. Namely, there is a parameter 5, referred to as the speed of price adjustment, so... 

Feichtinger, G. and S. Jorgensen. 1983. Differential game models in management science. European Journal of Operational Research, Vol.l4, 137-155. 

Mukhopadhyay, S.K. and P. Kouvelis. 1997. A differential game theoretic model for duopolistic competition on design quality. Operations Research, Vol.45, 886-893. 

Simaan, M. and J. B. Cruz, Jr. 1976. On the Stackelberg strategy in nonzero-sum games. In Multicriteria decision making and differential games , G. Leitmann, editor. Plenum Press, NY. 

Miloh T., Sharma S. D. 1977 Maritime collision avoidance as a differential game, Schiffstechnik, Vol. 24, p. 69-88. 

Olsder G. J., Walter J. L. 1977 A differential game approach to collision avoidance of ships. Proceedings of the 8th IFIP Conference on Optimization Techniques, Wilrzburg. 

The most general description of the own ship passing j other encountered ships is the model of a differential game dg of j moving control objects (Fig. 4), (Baba Jain 2001, Mesterton-Gibbons 2001). 

Figure 4. Block diagram of die basic model of differential game.

Engwerda, J.C. 2005. LQ dynamic optimization and differential games. West Sussex John Wiley Sons. 

Isaacs, R, 1965, Differential games. New York John Wiley Sons. 

In mathematics, Laplace s name is most often associated with the Laplace transform, a technique for solving differential equations. Laplace transforms are an often-used mathematical tool of engineers and scientists. In probability theory he invented many techniques for calculating the probabilities of events, and he applied them not only to the usual problems of games but also to problems of civic interest such as population statistics, mortality, and annuities, as well as testimony and verdicts. 

In Figure 4.12 the analysis of some game meat species after restriction with Mho I and Hinf I is shown. The combination of only two restriction patterns is sufficient to differentiate nine game meat and two farm animal species (pig, cattle). Restriction... 

WaihUnger HU, Weher W (1998). [Differentiation of game meat samples hy means of DNA-and protein-analysis]. Lebensmittelchemie 52 97-99. 

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