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Dr. Lloyd Shapley passed away on March 12, 2016. He was called Mr. Game Theory, and won the 2012 Nobel Memorial Prize in Economic Sciences with Alvin Roth "for the theory of stable allocations and the practice of market design." He received the Bronze Star decoration, for breaking the Soviet weather code in Chengdu during the Chinese Resistance War against Japanese Invasion.
This study uses three little-known and yet still significant contributions of Lloyd Shapley to make three corrections in the literature. This presentation focuses on one of such corrections, which formalizes Shapley’s argument (1987) as a fundamental error or logical flaw in several areas of existing noncooperative game theory. The error centers on two assumptions:
A1: Players are able to take collective actions in choosing their choices; and
A2: Players are unable to take any coordinated or collective action in choosing their choices.
A2 characterizes the nature of Prisoner’s Dilemma game in which the two players have no access to any communication or coordination. If they could coordinate their choices by communicating with each other or make deals by using a joint counsel, the nature of the game will become that characterized by A1 and thus invalidate the Nash equilibrium predicted by A2. Although A1 and A2 determine a player’s rationality and are the foundations upon which game solutions are built, they have often been ignored or misunderstood in a large number of previous studies。 | 
