When both players of a game have dominant strategies, the outcome which is the intersection of the dominant strategies is a Nash equilibrium. In the prisoners’ dilemma, since confessing is dominant strategy for each prisoner, the Nash equilibrium occurs when both confess.
Full Answer
In the prisoners’ dilemma, since confessing is dominant strategy for each prisoner, the Nash equilibrium occurs when both confess. It is Nash equilibrium because no prisoner is better off by unilaterally changing its strategy.
A prisoners’ dilemma refers to a type of economic game in which the Nash equilibrium is such that both players are worse off even though they both select their optimal strategies. The prisoners’ dilemma is a classic example of a game which involves two suspects, say P and Q, arrested by police and who must decide whether to confess or not.
It is Nash equilibrium because no prisoner is better off by unilaterally changing its strategy. For example, if Prisoner P decides to not confess while Prisoner Q does confess, Prisoner P would get 8 years instead of 4 years. Hence, Prisoner P is worse off if he moves away from the Nash equilibrium.
It is Nash equilibrium because no prisoner is better off by unilaterally changing its strategy.
A prisoners’ dilemma refers to a type of economic game in which the Nash equilibrium is such that both players are worse off even though they both select their optimal strategies.
He knows that confessing is the dominant strategy of Prisoner Q. He doesn’t want to not confess and get an 8-year term and confesses. But when he does so, both get 4-year prison terms each. Ultimately both are worse off because they get 4 years each instead of just 2 years each.
A Nash equilibrium is a combination of strategies such that player firm has any incentive to unilaterally change its strategy. When both players of a game have dominant strategies, the outcome which is the intersection of the dominant strategies is a Nash equilibrium. In the prisoners’ dilemma, since confessing is dominant strategy ...
If one confesses but the other doesn’t, the prisoner which confesses gets a lighter prison term, say 1 year, but the prisoner which doesn’t confess get a very harsh term, say 8 years. If neither confesses, they both get lighter terms, say 2 years each; but if both confess, both of them get a strict term, say 4 years each.
Firms in oligopoly are better off if they could both restrict their output and charge a monopoly price. But since collusion is illegal, both produce a higher output which reduces payoff to each firm. The Cournot model is an illustration of such a prisoners’ dilemma.
If Prisoner Q confesses, it is better for Prisoner P to confess too because otherwise he would get a term of 8 years instead of 4 years. Similarly, if Prisoner Q doesn’t confess, it is in the interest of Prisoner P to confess because by confessing he would get a 1-year term instead of 2 years.