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# A Beautiful Mind: Chapter 13 Summary & Analysis

Summary
Analysis
Even before Nash arrives at RAND, mathematicians there have been working on game theory, though they had focused mainly on two-person zero-sum games—"games of total conflict,” which produce a “fixed payoff.” Yet these models are beginning to prove inadequate for investigating military strategy during the Cold War. As nuclear weapons become more dangerous and potentially destructive, strategists realize that the idea of “mutual dependence” has merit, since it is not always in the United States’ best interest to make decisions that inflict the greatest amount of damage on an opponent: strategy has to focus on cooperation as well as conflict.
Ironically, though Nash often sought to “inflict damage” on his mathematical rivals, the research he conducted at RAND focused on cooperation rather than “total conflict,” underscoring the tension between his own behavior and the mathematical work that afforded him success.
Themes
At RAND, game theory is used to model tactics, particularly in air battles between fighters and bombers. RAND’s mathematicians are “cold” to the idea of applying cooperative game theory—for which stable, straight-forward solutions have already been generated—to military strategy, since they believe that true cooperation between opponents in war would be impossible to come by. By proving that noncooperative games had stable solutions, too, Nash’s equilibrium provides a “framework” for RAND research.
Nash’s equilibrium proves invaluable to RAND’s military research objectives, once again proving Nash’s incredible ability to think beyond the boundaries of his field.
Themes
Shortly after Nash formulates his famous equilibrium, Albert Tucker formulates a similar theorem, the “Prisoner’s Dilemma,” to describe a situation in which two individuals acting in their own best interests do not necessarily “promote the best interest of the collective”—using a hypothetical story of two prisoners who given the choice of confessing, implicating the other, or keeping silent. Since neither prisoner is aware of the other’s actions, the best choice for each of them—considered without the other—is confessing. Ironically, both prisoners, considered together, would be better off not confessing. Though RAND scientists do not use the “Prisoner’s Dilemma” as a basis for their research, Nash’s own ideas prove useful. Nash solves a problem that two RAND scientists set up—designed to test whether the Nash equilibrium would occur as an option in a real game between two individuals—by proving a case in which his equilibrium would function stably.
Though Tucker is a more established mathematician, it is Nash’s ideas, not Tucker’s, that prove most useful to RAND, demonstrating that Nash’s mathematical thinking is unusually advanced and widely applicable. Moreover, Nash is able solve the difficult challenge that the RAND scientists pose to his equilibrium idea: Nash is determined never to “lose” to any rival, applying the competitive strategies he studies as a mathematician to his own behavior.
Themes
The most important application of game theory to a military problem involves RAND’s “most influential” strategic study, on the SAC operational project: a plan to fly bombers from the United States to bases overseas, where an attack could be mounted against the Soviet Union. The RAND study allows the Air Force to understand the potential vulnerabilities of this plan, viewing America’s best tactics through the lens of the Soviet Union’s best tactics. However, by the 1950s, the “golden age” of RAND is drawing to a close, and game theory falls out favor, as “mathematicians got bored and frustrated,” becoming “disillusioned” with their own game theorems.
Though game theory was incredibly useful to RAND’s military research, the field lost traction in the 1950s, as scientists moved onto other fields as a basis for conducting high-level research. Nash’s ideas, too, would fall out of the favor in the 1950s and 1960s, though game theory experienced a resurgence in the 1980s and 1990s—leading to the rediscovery of Nash’s important work.
Themes