Chihiro Morooka Faculty of Economics, the University of Tokyo   206-1 Futto Inashiki-shi, Ibaraki 300-0638 Japan   morooka.chihiro@mail.u-tokyo.ac.jp   https://orcid.org/0000-0001-5811-9133           JEL Areas: C7 : Game Theory and Bargaining Theory:General C6 : Mathematical Methods and Programming: General