Game Theory, Complexity And Simplicity II: Problems and Applications

this paper. The reader interested in this novel approach to social stability should consult either von Neumann and Morgenstern (1944) directly or Lucas (1992) 6 counterexamples to apparently reasonable conjectures, which can be established only in high dimensions. The stable set solution generated considerable mathematical investigation (as is indicated by the Lucas 1992 survey). However, to some extent due to its lack of universal existence, it has not been utilized much in applied game theory. Other cooperative solutions The most utilized cooperative solutions in the development of cooperative game theory have been the core and the value. They have been described in Part I; lesser known, but with a substantial literature are the bargaining set, the kernel and the nucleolus of a game. Intuitively the core reflects the imputations protected from the direct bargaining power of subgroups in a society (it reflects the limitations of countervailing power), the nucleolus is an imputation that has the property that the largest complaint against it by any group is minimized and the bargaining set and kernel reflect plausible requirements for an acceptable bargaining outcome. All of these solutions have lead to considerable mathematical investigation. A survey of the literatures on the bargaining set, kernel and nucleolus which covers, not only the mathematics, but indicates applications and gaming experiments has been provided by Maschler (1992) Noncooperative solutions The noncooperative equilibrium The ruling solution concept for games in strategic form is the noncooperative equilibrium of Nash (1950). A fixed point argument was utilized to show that for a finite matrix game there was an outcome which satisfied mutually consistent expectations. Unfortunately there may be m..