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.
Throughout his career, Nash often treated his interactions with others as “games,” applying the same game strategies he studied to his social life—just as he “tested” von Neumann, engaging him in a non-cooperative game. Though this “testing” may have helped Nash to model his own research, by continually reducing relationships to games of strategy, Nash often had difficulty empathizing with others, a quality that would later wreak havoc on his relationships.
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.
Nash’s equilibrium theorem demonstrates his characteristically unusual yet effective brand of mathematical thinking. Determined to find meaning in chaotic situations, Nash discovered simple but powerful solutions to complicated questions with which generations of mathematicians had struggled. Though at the time, Nash’s achievements in game theory were not thought of as highly significant, later, they would have a sizeable impact on the field of economics; the brilliance of Nash’s thinking was to explore connections between math and other fields, refusing the limitations of “pure mathematics.”