Bargaining and Cooperation in Strategic Form Games with Suspended Realizations of Threats

The Hart-and-Mas-Colell bargaining model [Hart and Mas-Colell (2010). “Bargaining and Cooperation in Strategic Form Games.” Journal of the European Economics Association, 8, 7-33], which is based on strategic form games, is a very promising model possessing many beautiful features. Nevertheless, it is not flawless: threats used in this model may behave quite counter-intuitive, and the expected payoffs may not be consistent with the min-max solution in two-person-zero-sum games. If we postpone realizations of all threats to the end of the game, the two problems can be solved simultaneously. This is exactly the 2(a) model suggested by Hart and Mas-Colell in the last section of their paper. I prove that the new model can guarantee the existence of an SP equilibrium in the two player case. For the three-or-more-player case, unfortunately, it is shown through a counter-example that SP equilibrium may not exist