Non-cooperative game

Theorem 11. The Shapley value, Tri for player i in an N—person non-cooperative game with transferable utility is ... 

Basar, T. Olsder, G.J. 1982. Dynamic non-cooperative game theory. New York Academic Press. 

Gahrszka, A. Swiemiak, A. 2005. Non-cooperative game approach to multi-robot planning. International Journal of Applied Mathematics and Comuter Science 15(3) 359-367,... 

Isil Bozma, H, Koditschek, D.E. 2001. Assembly as a non-cooperative game of its pieces Analysis of ID sphere assemblies, Robotica 19 93-108. 

Keywords Game theory, non-cooperative, cooperative, equilibrium concepts... 

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. 

In non-cooperative static games the players choose strategies simultaneously and are thereafter committed to their chosen strategies, i.e., these are simultaneous move, one-shot games. Non-cooperative GT seeks a rational... 

Taken together, the two best response functions form a best response mapping or in the more general case RP RP, Clearly, the best response is the best player i can hope for given the decisions of other players. Naturally, an outcome in which all players choose their best responses is a candidate for the non-cooperative solution. Such an outcome is called a Nash Equilibrium (hereafter NE) of the game. 

As has been noted in other reviews, Operations Management has been slow to adopt GT. But because SCM is an ideal candidate for GT applications, we have recently witnessed an explosion of GT papers in SCM. As our survey indicates, most of these papers utilize only a few GT concepts, in particular the concepts related to non-cooperative static games. Some attention has been given to stochastic games but several other important areas need additional work cooperative, repeated, differential, signaling, screening and Bayesian games. 

Algorithm mmg nc of multi-step non-cooperative matrix game... 

Goal function (13) for non-cooperative matrix game has the form (Basar Olsder 1982, Gahrszka Swiemiak 2005, Isil-Bozma Koditschek 2001) ... 

Algorithm mpg nc of multi-stage non-cooperative positional game... 

Goal function (16) for non-cooperative positional game has the form ... 

Fig. 12-15 shows the safe and optimal trajectory of the own ship in collision situation, which is determined using the algorithm of cooperative and non-cooperative matrix game. 

Figure 13. Computer simulation of multi-step non-cooperative matrix game algorithm mmg c for safe own ship control in situation of passing 34 encountered ships in restricted visibility at sea, D =3.0 nm, J(fi)=l. 88 nm (nautical mile).

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