not to confess it is in each ones individual interest to confess Prisoners

Not to confess it is in each ones individual interest

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not to confess; it is in each one’s individual interestto confess.Prisoners’ dilemmais a game based ontwo premises: (1) Each player has anincentive to choose an action that ben-efits itself at the other player’s expense.(2) When both players act in this way,both are worse off than if they had cho-sen different actions.
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C H A P T E R 1 5O L I G O P O LY373The answer is clear: both will confess. Look at it first from Thelma’spoint of view: she is better off confessing, regardless of what Louisedoes. If Louise doesn’t confess, Thelma’s confession reduces her ownsentence from 5 years to 2. If Louise doesconfess, Thelma’s confessionreduces her sentence from 20 to 15 years. Either way, it’s clearly inThelma’s interest to confess. And because she faces the same incen-tives, it’s clearly in Louise’s interest to confess, too. To confess in thissituation is a type of action that economists call a dominant strategy.An action is a dominant strategywhen it is the player’s best actionregardless of what action the other player takes. It’s important to notethat not all games have a dominant strategy—it depends on the struc-ture of payoffs in the game. But in the case of Thelma and Louise, it isclearly in the interest of the police to structure the payoffs so that con-fessing is a dominant strategy for each person. So as long as the twoprisoners have no way to make an enforceable agreement that neitherwill confess (something they can’t do if they can’t communicate, andthe police certainly won’t allow them to do because the police want tocompel each one to confess), Thelma and Louise will each act in a waythat hurts the other.So if each prisoner acts rationally in her own interests, both will con-fess. Yet if neither of them had confessed, both would have received amuch lighter sentence! In a prisoners’ dilemma, each player has a clear incentive toact in a way that hurts the other player—but when both make that choice, it leavesboth of them worse off.When Thelma and Louise both confess, they reach an equilibriumof the game. Wehave used the concept of equilibrium many times in this book; it is an outcome in whichno individual or firm has any incentive to change his or her action. In game theory, thiskind of equilibrium, in which each player takes the action that is best for her given theactions taken by other players, and vice versa, is known as a Nash equilibrium,afterthe mathematician John Nash. (Nash’s life was chronicled in the best-selling biographyA Beautiful Mind, which was made into a movie.) Because the players in a Nash equilib-rium do not take into account the effect of their actions on others, this is also known asa noncooperative equilibrium.Now look back at Figure 15-1; ADM and Ajinomoto are in the same situation asThelma and Louise. Each firm is better off producing the higher output, regardless ofwhat the other firm does; yet if both produce 40 million pounds, both are worse offthan if they had followed their agreement and produced only 30 million pounds.
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