(10 points) There is a famous game which is called “Prisoners’ Dilemma”. In this game, two people are arrested for a severe crime. The district attorney doesn’t have enough evidence and would need a confession to get a conviction. She separates the two individuals and offers them the same deal as follows:
If you confess and your partner doesn’t, I can give you a reduced sentence of 1 year, while your partner will receive 10 years.
If you both confess you will each get 3 years.
They both also know that if neither confesses they will still end up being convicted to a two year sentence for other crimes they have committed.
Note that here the numbers are the number of years in jail, so smaller is better for this particular case.
Payoff matrix (Row player, Column player)
Confess
Not Confess
Confess
3, 3
1, 10
Not Confess
10, 1
2, 2
(a) Does each player in the game have a dominant strategy? If so, what are they?
(b) Solve for the Nash Equilibrium
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