Yan-an Hwang Department of Applied Mathematics, National Dong Hwa University, Taiwan   No. 1, Sec. 2, Da Hsueh Rd. Shoufeng Hualien, Taiwann 97401 台灣   yahwang@gms.ndhu.edu.tw             JEL Areas: C7 : Game Theory and Bargaining Theory:General D5 : General Equilibrium and Disequilibrium: General