All of these explanations are judged to be either incomplete or deficient in some way. As game theory has evolved, so have the explanations fashioned by its practitioners. An additional purpose of this chapter is to trace these explanatory refinements, using the Cuban crisis as a mooring. Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content. To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us. All Rights Reserved. OSO version 0. University Press Scholarship Online.
It applies to situations games where there are two or more people called players each attempting to choose between two more more ways of acting called strategies. The possible outcomes of a game depend on the choices made by all players, and can be ranked in order of preference by each player. In some two-person, two-strategy games, there are combinations of strategies for the players that are in a certain sense "stable".
This will be true when neither player, by departing from its strategy, can do better. Two such strategies are together known as a Nash equilibrium, named after John Nash , a mathematician who received the Nobel prize in economics in for his work on game theory.
Nash equilibria do not necessarily lead to the best outcomes for one, or even both, players. Moreover, for the games that will be analyzed - in which players can only rank outcomes "ordinal games" but not attach numerical values to them "cardinal games" - they may not always exist.
While they always exist, as Nash showed, in cardinal games, Nash equilibria in such games may involve "mixed strategies," which will be described later.
The Cuban missile crisis was precipitated by a Soviet attempt in October to install medium-range and intermediate-range nuclear-armed ballistic missiles in Cuba that were capable of hitting a large portion of the United States. The goal of the United States was immediate removal of the Soviet missiles, and U.
These strategies can be thought of as alternative courses of action that the two sides, or "players" in the parlance of game theory, can choose. Thus, the higher the number, the greater the payoff; but the payoffs are only ordinal, that is, they indicate an ordering of outcomes from best to worst, not the degree to which a player prefers one outcome over another.
The first number in the ordered pairs for each outcome is the payoff to the row player United States , the second number the payoff to the column player Soviet Union. Needless to say, the strategy choices, probable outcomes, and associated payoffs shown in Figure 1 provide only a skeletal picture of the crisis as it developed over a period of thirteen days.
Both sides considered more than the two alternatives listed, as well as several variations on each. The Soviets, for example, demanded withdrawal of American missiles from Turkey as a quid pro quo for withdrawal of their own missiles from Cuba, a demand publicly ignored by the United States. Nevertheless, most observers of this crisis believe that the two superpowers were on a collision course, which is actually the title of one book describing this nuclear confrontation. They also agree that neither side was eager to take any irreversible step, such as one of the drivers in Chicken might do by defiantly ripping off the steering wheel in full view of the other driver, thereby foreclosing the option of swerving.
Although in one sense the United States "won" by getting the Soviets to withdraw their missiles, Premier Nikita Khrushchev of the Soviet Union at the same time extracted from President Kennedy a promise not to invade Cuba, which seems to indicate that the eventual outcome was a compromise of sorts.
But this is not game theory's prediction for Chicken, because the strategies associated with compromise do not constitute a Nash equilibrium. To see this, assume play is at the compromise position 3,3 , that is, the U. This strategy is not stable, because both players would have an incentive to defect to their more belligerent strategy.
If the U. This classic game theory setup gives us no information about which outcome would be chosen, because the table of payoffs is symmetric for the two players. This is a frequent problem in interpreting the results of a game theoretic analysis, where more than one equilibrium position can arise. Finally, should the players be at the mutually worst outcome of 1,1 , that is, nuclear war, both would obviously desire to move away from it, making the strategies associated with it, like those with 3,3 , unstable.
As a consequence, this game is better modelled as one of sequential bargaining, in which neither side made an all-or-nothing choice but rather both considered alternatives, especially should the other side fail to respond in a manner deemed appropriate.
In the most serious breakdown in the nuclear deterrence relationship between the superpowers that had persisted from World War II until that point, each side was gingerly feeling its way, step by ominous step. Before the crisis, the Soviets, fearing an invasion of Cuba by the United States and also the need to bolster their international strategic position, concluded that installing the missiles was worth the risk. They thought that the United States, confronted by a fait accompli, would be deterred from invading Cuba and would not attempt any other severe reprisals.
There are good reasons to believe that U. I offer an alternative representation of the Cuban missile crisis in the form of a game I will call Alternative, retaining the same strategies for both players as given in Chicken but presuming a different ranking and interpretation of outcomes by the United States [ see Figure 2 ].
These rankings and interpretations fit the historical record better than those of "Chicken", as far as can be told by examining the statements made at the time by President Kennedy and the U. Air Force, and the type and number of nuclear weapons maintained by the S. Even though an air strike thwarts the Soviets at both outcomes 2,2 and 4,1 , I interpret 2,2 to be less damaging for the Soviet Union. This is because world opinion, it may be surmised, would severely condemn the air strike as a flagrant overreaction - and hence a "dishonourable" action of the United States - if there were clear evidence that the Soviets were in the process of withdrawing their missiles anyway.
On the other hand, given no such evidence, a U. The statements of U. In responding to a letter from Khrushchev, Kennedy said,. If the Soviets maintained their missiles, the United States preferred an air strike to the blockade. As Robert Kennedy, a close adviser to his brother during the crisis, said,. Finally, it is well known that several of President Kennedy's advisers felt very reluctant about initiating an attack against Cuba without exhausting less belligerent courses of action that might bring about the removal of the missiles with less risk and greater sensitivity to American ideals and values.
Pointedly, Robert Kennedy claimed that an immediate attack would be looked upon as "a Pearl Harbor in reverse, and it would blacken the name of the United States in the pages of history," which is again consistent with the Alternative since the United States ranks AW next worst 2 - a "dishonourable" U. If Alternative provides a more realistic representation of the participants' perceptions than Chicken does, standard game theory offers little help in explaining how the 3,3 compromise was achieved and rendered stable.
As in Chicken, the strategies associated with this outcome are not a Nash equilibrium, because the Soviets have an immediate incentive to move from 3,3 to 1,4. However, unlike Chicken, Alternative has no outcome at all that is a Nash equilibrium, except in "mixed strategies". These are strategies in which players randomize their choices, choosing each of their two so-called pure strategies with specified probabilities.
But mixed strategies cannot be used to analyse Alternative, because to carry out such an analysis, there would need to be numerical payoffs assigned to each of the outcomes, not the rankings I have assumed.
The instability of outcomes in Alternative can most easily be seen by examining the cycle of preferences, indicated by the arrows going in a clockwise direction in this game. Following these arrows shows that this game is cyclic , with one player always having an immediate incentive to depart from every state: the Soviets from 3,3 to 1,4 ; the United States from 1,4 to 4,1 ; the Soviets from 4,1 to 2,2 ; and the United States from 2,2 to 3,3.
Again we have indeterminacy, but not because of multiple Nash equilibria, as in Chicken, but rather because there are no equilibria in pure strategies in Alternative. Mail will not be published required. Third Action: The Soviets withdraw their missiles from Cuba.
Google Search. Entries Comments. Hosted by CampusPress. Skip to toolbar Log In Search.
0コメント