| Summary: | 博士 === 國立清華大學 === 數學系 === 92 === This thesis consists of two parts. One is to provide a noncooperative foundation for the kernel, another is to study f -just bankruptcy rules through a bargaining framework.
To be a solution concept of n-person cooperative game, the kernel has many nice properties and it is also philosophically unsound. Indeed, many interpretations of the kernel seem to rely on "interpersonal comparison of utility" which is still an obscure notion for us.
In this thesis, a noncooperative model is given and the kernel is implemented by this model in subgame perfect equilibrium. In other words, the kernel is justified from bargaining viewpoint.
It is known that the bilateral consistency and converse consistency are two properties to characterize some of the most important solution concepts in cooperative game theory. As for the bankruptcy problem, there are some important bankruptcy rules, like the proportional rule, the constrained equal award rule, the contested garment consistent rule, etc., also satisfy these two properties. In general, they are called f-just, f is a bilateral principle.
Two characterizations of f-just rule are proposed.
The first one is axiomatic approach. A f-just rule can be characterized by the bilateral consistency, the converse consistency and the bilateral principle f which is induced by the f-just rule.
The second one is from noncooperative viewpoint. A game form Γ which is designed by the guidance of the bilateral consistency and the converse consistency is proposed.
A necessary and sufficient condition for a bilateral principle f which has f-just extension is given in terms of Γ. The role that the game form Γ plays is the combination of the bilateral consistency and the converse consistency which are used to characterize the f-just rule in axiomatic approach.
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