Positively homogeneous quasidifferentiable functions and their applications in cooperative game theory

Abstract

PREFACE I n t h i s p a p e r , t h e a u t h o r s t u d i e s t h e p r o p e r t i e s of p o s i t i ve l y homogeneous f u n c t i o n s , which r e p r e s e n t a subc l a s s of t h e set of q u a s i d i f f e r e n t i a b l e f u n c t i o n s . I t i s shown t h a t t h e s e f u n c t i o n s c a n be used t o d e r i v e some new r e s u l t s i n t h e t h e o r y of c o o p e r a t i v e games. T h i s p a p e r i s a c o n t r i b u t i o n t o r e s e a r c h on nondiff e r e n t i a b l e o p t i m i z a t i o n c u r r e n t l y underway w i t h i n t h e System and D e c i s i o n S c i e n c e s program. One interesting class of quasidifferentiable functions is that formed by the family of positively homogeneous functions. In this paper, the author studies the properties of these functions and uses them to derive some new results in the theory of cooperative games.