kf011 - 1 Ka-fu Wong University of Hong Kong Strategic...

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Unformatted text preview: 1 Ka-fu Wong University of Hong Kong Strategic Choice in Oligopoly, Monopolistic Competition, and Everyday Life 2 Games and Strategic Behavior Thus far, we have viewed economic decision makers as confronting an environment that is essentially passive. But there exist many cases in which relevant costs and benefits depend not only on the behavior of the decision makers themselves but also on the behavior of others. 3 Example 11.1. Should the prisoners confess? 4 Example 11.1. Should the prisoners confess? Two prisoners, X and Y, are held in separate cells for a serious crime that they did, in fact, commit. The prosecutor, however, has only enough hard evidence to convict them of a minor offense, for which the penalty is, say, a year in jail. Each prisoner is told that if one confesses while the other remains silent, the confessor will go free while the other spends 20 years in prison. If both confess, they will get an intermediate sentence, say five years. 5 Example 11.1. Should the prisoners confess? It is often convenient to summarize the elements of a game in the form of a payoff matrix. Three elements: 1. Players (2 prisoners) 2. Strategies (confess, remain silent) 3. Payoffs (jail sentences) 6 Example 11.1. Should the prisoners confess? Prisoner X Prisoner Y Confess Remain Silent 5 years for each 1 year for each 20 years for X 0 years for Y 0 years for X 20 years for Y Confess Remain Silent The two prisoners are not allowed to communicate with one another. If the prisoners are rational and narrowly self-interested, what will they do? 7 Example 11.1. Should the prisoners confess? Prisoner X Prisoner Y Confess Remain Silent 5 years for each 1 year for each 20 years for X 0 years for Y 0 years for X 20 years for Y Confess Remain Silent Their dominant strategy is to confess. No matter what Y does, X gets a lighter sentence by speaking out. 1. If Y too confesses, X gets five years instead of 20. 2. And if Y remains silent, X goes free instead of spending a year in jail. The payoffs are perfectly symmetric, so Y also does better to confess, no matter what X does. Dominant Strategy : One that yields a higher payoff no matter what the other players in a game choose. 8 Example 11.1. Should the prisoners confess? The difficulty is that when each behaves in a self- interested way, both do worse than if each had shown restraint. Thus, when both confess, they get five years, instead of the one year they could have gotten by remaining silent. And hence the name of this game, prisoner's dilemma . 9 Example 11.2....
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kf011 - 1 Ka-fu Wong University of Hong Kong Strategic...

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