Question

pls Answer Question ASAP.

Short answer questions: (write no more than a paragraph for each question)

1. (5 points) Tell me a story from your personal experience where you were involved in a
situation that could be described as a prisoner’s dilemma game. (I am certain that you
were in that type of situation at least once.) First briefly describe the situation and then
explain how the incentives could be interpreted as a prisoner’s dilemma game. Discuss a
potential difficulty in identifying a real-life situation as a prisoner’s dilemma game.

2. (5 points) Can the iterative elimination of dominated strategies (IEDS) procedure
eliminate Nash equilibrium strategy? Explain why yes or why no.

3. (5 points) In the Matching pennies game there is a Nash equilibrium in which both
players play “Heads” and “Tails” with probability ½. Would it still be an equilibrium if say
the row player switched to playing “Heads” with probability 1/3? Explain

Answer 1

prisoner’s dilemma game

To illustrate the kinds of difficulties that arise in two-person non cooperative variable-sum games, consider the celebrated prisoner’s dilemma (PD), originally formulated by the American mathematician Albert W. Tucker. Two prisoners, A and B, suspected of committing a robbery together, are isolated and urged to confess. Each is concerned only with getting the shortest possible prison sentence for himself; each must decide whether to confess without knowing his partner’s decision. Both prisoners, however, know the consequences of their decisions: (1) if both confess, both go to jail for five years; (2) if neither confesses, both go to jail for one year (for carrying concealed weapons); and (3) if one confesses while the other does not, the confessor goes free (for turning state’s evidence) and the silent one goes to jail for 20 years.

Superficially, the analysis of PD is very simple. Although A cannot be sure what B will do, he knows that he does best to confess when B confesses (he gets five years rather than 20) and also when B remains silent (he serves no time rather than a year); analogously, B will reach the same conclusion. So the solution would seem to be that each prisoner does best to confess and go to jail for five years. Paradoxically, however, the two robbers would do better if they both adopted the apparently irrational strategy of remaining silent; each would then serve only one year in jail. The irony of PD is that when each of two (or more) parties acts selfishly and does not cooperate with the other (that is, when he confesses), they do worse than when they act unselfishly and cooperate together (that is, when they remain silent).