Answer the following questions. Each of your answers should be an essay of 250 to 350 words (with a typical font and spacing this will be about 1 to 1-1/2 pages).

1. A small time crook is being interrogated by a policeman. The crook committed a petty crime, but everyone knows that gathering sufficient evidence to prove it will be time consuming for the police. The policeman tells the crook that if she doesnâ€™t confess, heâ€™s going to spend all of his time making sure that she gets the harshest sentence possible. The crook, in light of the threat, confesses. Analyze these game strategies. Verify that this scenario represents a Nash equilibrium, provided that the policeman would actually follow through with his threat. Now verify that the subgame-perfect equilibrium is for the crook not to confess and for the policeman to go back on his threat. That is, explain why the policemanâ€™s threat is actually not credible.

2. Prisonerâ€™s dilemma situations arise frequently in life. Begin your answer to this question by providing a full explanation of what the prisonerâ€™s dilemma is. In your life, it is likely that you have played such games and in some cases, you found a way to cooperate with the other player. In other cases, both of you betrayed each other. Consider examples of each situation and ask yourself: What made the difference? When were your strategies effective, and when not?

3. You and a friend are selected as contestants on game show. You each must pick a whole number from 1 to 7. You will pick an odd number, and your friend will pick an even number. If the numbers you pick are consecutive, such as 5 and 6, then you each win \$1,000. If both you and your friend understand weakly dominated strategies, youâ€™re guaranteed to win the money. How? If you and your friend both understand IEDS for weakly-dominated strategies, you can win the money every time, even if the numbers are selected from 1 to 100, with you choosing odd and your friend choosing even. How?

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Lecture 5: Guessing Rightâ€”Simultaneous Move Games

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