Satoru Takahashi Department of Economics, National University of Singapore   Department of Economics National University of Singapore Singapore, 117570 Singapore   ecsst@nus.edu.sg   http://www.fas.nus.edu.sg/ecs/people/profile/ecsst.html           JEL Areas: C7 : Game Theory and Bargaining Theory:General D8 : Information, Knowledge, and Uncertainty: General