Cooperative game

Vol. 556 R. Branzei, D. Dimitrov, S. Tijs, Models in Cooperative Game Theory. VIII, 135 pages. 2005. 

Now we can take the next st and establish the model that will characterize rdations within the firm repeated cooperative games. A two-person, two-choice matrix of payoffs for each stage of our cooperative game can be d icted as shown in figure 5.1. 

If both players cooperate they will do better than if they both defect (it is a cooperative game, after all) but if only one player cooperates, she will do worse than if she had defected, while the defector will do better than if he had cooperated. Thus there are ben ts to mutual cooperation, but at least temporary benefits from opportunism (taking advantage of the cooperation of others) and costs to unredprocated beneficence. Two important variations suggest themselves (1) The other conditions may hold, but there may be no benefit from opportunism... 

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 what follows, we will cover transferable utility cooperative games (players can share utility via side payments) and two solution concepts the core of the game and the Shapley value, and also biform games that have found several applications in SCM. Not covered are alternative concepts of value, e.g., nu-... 

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

From the SCM point of view, cooperative games are somewhat unsatisfactory in that they do not explicitly describe the equilibrium actions taken by the players that is often the key in SC models. Biform games, developed by Bran-denburger and Stuart (2003), compensate to some extent for this shortcoming. 

Stuart, H. W., Jr. 2001. Cooperative games and business strategy. In Game theory and business applications", K. Chatteijee and W.F. Samuelson, editors. Kluwer Academic Publishers. 

Kohli, R. and Park, H. (1989). A cooperative game theory model of quantity discounts. Management Science, 35(6) 693-707. 

Cooperative Game Game in which rational actors find a means to cooperate so as to enhance the utility of each. 

The common sense nature of game theory (in this case, a cooperative game) can be used to explain why soldiers in the trenches on both sides of the front in World War I refrained from firing at each other at certain times of the day such as mealtimes. 

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. 

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