Please answer all 5 questions regarding game theory . Consider the following Pay

Question

Please answer all 5 questions regarding game theory.

Consider the following Payoff Matrix for the Prisoner's Dilemma Problem. Two prisoners A and B are kept in separate cells and not allowed to talk to each other. If they both confess that they committed a big crime, they get 7 years in prison each. If one confesses, that one is set free, while the other who refuses gets 14 years in prison. If they both refuse, they both get 2 years in prison for a petty offence. With reference to this example and the Payoff Matrix below, answer the questions next. [2 points each, total 10 pointsl A confesses A refuses B confesses A:-7, B:-7 A: -14, B:0 B refuses A: 0, B: -14 A: -2, B: -2 16. If n is number of years in prison (per player per action), the payoff function f for this matrix is: a) f n b)f--n c) f 2n d) f n/2 17. Which state constitutes an example of Nash equilibrium here? a) Both confess b) Both refuse c) A confesses, B refuses d) B confesses, A refuses 18. Does the Nash equilibrium provide the best cumulative payoff and/or best individual gain here? a) Cumulative payoff b) Individual gain c)Both d) Neither 19. Is this an example of a constant sum game? a) Yes b) No c) Maybe d) Impossible to tell 20. It is found that a Repeated Game in this problem is most likely to give a) Freedom to A or Bb) Maximum n c) Nash equilibrium d) Best cumulative payoff

Explanation / Answer

Nash Equilibrium for this type of Prisoner s dilemma is (confess,confess) players A and B can improve upon by changing from (confess,confess) to (refuse,refuse)

Ans 17

Option A is correct response as each player try to maximise self benefit and hence the best response for confess is confess

Ans 18

No Both players can improve cumulatively by switching fromm confess to refuse

Ans 19)

No it is not zero sum game as payoff sum for each pair isnt zero

Ans 20)

If they repeat this game then they will learn that players can improve their payoff by switching from refuse to confess

Hence option D is correct response

Ans 16)

I am kind of doubtful about the completeness of question still f=-n would be coorrect answer

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