A Beautiful Mind: Chapter 10 Summary & Analysis

In summer 1949, Nash asks Albert Tucker to supervise his thesis, surprising Tucker, who had had little direct contact with Nash. After a summer of preparing for his general examinations, Nash is prepared to dive back into his own research; he also decides to visit von Neumann to discuss his ideas for an “equilibrium” in games of more than two players. Von Neumann quickly rejects Nash’s idea, though Nash would later claim that the meeting had still been useful. He had actually tested out his theories by meeting with von Neumann: “I was playing a non-cooperative game in relation to von Neumann rather than simply seeking to join his coalition.” David Gale realizes that Nash’s equilibrium idea might apply to a “far broader class of real-world situations” than von Neumann’s own ideas on zero-sum games.

Later, Tucker would claim that he wasn’t sure if Nash’s equilibrium, the basis of his thesis, would be useful to economists. Nonetheless, Tucker manages to convince Nash to stick with his research topic, with the addition of a few changes. Importantly, Nash’s theorem is the first to draw a clear distinction between cooperative and noncooperative games: whereas cooperative games involve agreements among players, there are no agreements to be made in noncooperative games. Nash defines his equilibrium as the event in which players in a game are unable to improve their own positions, since no better game strategy exists: the player picks a “dominant strategy,” their best choice for a move, based on the best choices made by other players. Nash’s theory is elegant and deceptively simple. Though it attracted some criticism at first, it would later become a fundamental paradigm in economics.