MATRIZ DE MARCO LÓGICO (MML)

Recall that von Neumann and Morgenstern talked about an equilibrium solution to some games.

They proved a famous theorem called the “minimax” theorem. To simplify things, the theorem states that for every zero-sum competitive game like Rock-Paper-Scissors, there is an optimal strategy for minimizing loss, which is the expected gain for the other player. Steve Heims, von Neumann’s biographer, wrote that this theorem “turned out to be so profound that it opened up new areas and manifested new connections within mathematics”.² First von Neumann and Morgenstern proved the minimax theorem for a situation where both players have total knowledge of the joint strategies of both players and their utilities (outcomes for each player). In their second minimax theorem they tackled games with incomplete information and proved that the theorem holds only on the average;

there is no best strategy for playing only one round. Von Neumann and Morgenstern also developed a rational game-theory strategy for a version of stud poker.

Because he distrusted human emotions so much, it was von Neumann’s dream that one day computers could eliminate emotion from decisions central to human survival, and pit alternative strategies of international conflict and military tactics against one another, simulate potential outcomes, and make the best automated, rational choice for our side.

As I have mentioned, the von Neumann-Morgenstern equilibrium point in game theory (when it exists) is a search for a combination of strategies between two opposing players that is “the best of the worst.” That means it minimizes each player’s potential losses. Even in its conceptualization, this equilibrium point can be considered a pessimistic viewpoint about human relationships. The point of this solution is to cut your losses.

It is very different from the equilibrium point of John Nash.³ The Nash equilibrium (when it exists) is that point at which neither player can do any better. Hence, it can be considered an equilibrium point that is more optimistic.

Von Neumann and Morgenstern’s book definitely put game theory on the map. It eventually led to a series of Nobel prizes in economics, including John Nash’s prize. Always connected with military applications, the new von Neumann game theory inspired a new generation of Cold War warriors, who contemplated using von Neumann’s computer to compute the advantages and disadvantages of nuances of diplomacy, brinksmanship, and fundamental nuclear strategy. The mathematical recommendations of game-theory analyses were not always apparent and did not always lead to obvious solutions to problems.

Game theory often comes up with surprises. For example in a “truel,” which is a duel fought by three people, suppose one of three is the best shot, another the second-best shot, and a third a terrible shot. In many situations of this sort the weakest shot will survive, because logically the other two would rather eliminate the better shots.

As mentioned, the design of the electronic computer was another of von Neumann’s great contributions. He built one of the world’s first computers, called “EDVAC.” He designed the

“architecture” of the modern computer with what he called four “organs,” the arithmetic logic unit, the control unit, the memory, and the input/output unit. Von Neumann’s enormous insight was to encode instructions in numerical form, with no distinction in memory between data and programs.

Von Neumann’s hope was that the logic and mathematics of game theory, using the electronic computer, could solve even the more complex games of nuclear, political, and military strategy.

Rapidly the real problems become too complex for ordinary computations. That computational need led to the development of faster and faster electronic computers. This development was supported by the U.S. military.

Why would game theory have been so appealing to the military and political thinking after

World War II? The games that any civilization plays usually tell us a lot about the values of the culture. For example, the ancient Chinese game of “Go” reflected a model of war, and chess was thought to have originated in India, where the pieces were originally the Elephant, Horse, and Chariot, instruments of war.

Even today the very language of a game tells us a great deal about the culture that loves the game. The late comedian George Carlin compared the language of baseball and football. He said that baseball is a 19th century pastoral game that played on a “diamond” in a “park,” whereas football is a 20th century technological struggle that is played on a “gridiron.” In football, he said, the players wear a helmet; in baseball they wear a cap. In football there are “downs”; in baseball “you’re up.” In football the specialist comes in to kick the ball; in baseball the specialist comes in to “relieve marches his troops into enemy territory balancing his aerial assault with a sustained ground attack as he punches holes in the enemy’s defensive wall.”⁴ In baseball the objective is to “come home and be safe.”

Games have a long and venerable history, and mathematics has been interested in games of chance for literally hundreds of years. In the 17th century, the French mathematician and philosopher Blaise Pascal developed the mathematics of probability to advise his friend, a gambler and philosopher named the Chevalier de Méré, about dice. Pascal was famous for his suggestion to weight the probability of an event with how much “utility” the outcome (the benefit, or the disaster) has for the player.⁵ In particular, he applied his advice in creating a famous argument about whether or not to believe in the existence of a personal God. His argument was that even though the probability that God existed might be low, the payoff of belief was potentially so high in the comfort it gave people—so the product of low probability and high benefit gave a high number for the payoff for belief—that it made sense to believe. Whether you agree or not, it was an interesting argument.

As rational as Pascal was, he was also, gratefully, a true Frenchman to the core. Pascal was famous for his saying that “the heart has its reason whereof reason knoweth not,” by which he meant that the emotions have their own logic.⁶ That important point of Pascal’s was lost on later game theorists, who assumed that all players of games must be totally logical and all players of the game must be operating with high levels of logical self-interest. Was it possible for von Neumann’s computer to eliminate emotion from decision making? Or do the correct representations of how humans deal with conflict of necessity follow Pascal’s famous saying?

A central part of early probability applied to games of chance was the assumption that the opponent was totally intelligent and rational. French mathematician Emil Borel was the first to begin developing the mathematics of game theory in the 1920s. Game theory, even from its inception, was closely tied to military strategy. In fact, it’s no accident that in 1925 Borel became minister of the Navy. The struggle for survival and the goal of winning were part of the development of game theory.

In the 18th and 19th centuries the idea of individuals in a species competing in the struggle to survive was in the air. It was critical in the formulation of Darwin’s “survival of the fittest”

competitions for food, mates, and territory. Competition and self-interest were also central to Adam Smith’s theory of free markets, which identified self-interest and economic again as the universal motive in civilized society, with the individual’s pursuit of his own ends providing maximum benefit

to society, the foundation of a capitalist system. Smith believed that self-interest and greed were good and an unregulated economy was enough to create a regulated market when people also had a strong moral responsibility.⁷ Marxist politics were instead presumably built on the alternative of only communist cooperation for the “common good” as a way of regulating human greed. Some writers preoccupation with cooperation. His father ran a grocery store. In his autobiography Rapoport wrote that all the grocery stores were open about 16 hours a day, 7 days a week, and his father was exhausted. So were the other grocers. Rapoport’s father got the grocers to agree collectively to close their stores at 7 P.M. on Mondays, Wednesdays, and Fridays, and also on Sundays from 1 P.M. to 5

P.M. However, the agreement lasted only a short time once one grocer defected. Rapoport wrote,

“Years later I read about Adam Smith’s ‘invisible hand’—the regulatory function of the free market—

which insures that pursuit of individual advantage by each participant results in the collective good.

Thinking back to the neighborhood grocers, I envisage ‘the invisible back of the hand’—situations in which pursuit of individual advantage by everyone results in a collective ‘bad.’ Much of my research in the psychology of decision making centered on this effect, illustrating the dichotomy between individual and collective rationality”.⁸ Rapoport never forgot that experience. His later social psychological research was designed to find strategies that maximized cooperation even in conditions of potential self-interest.