Strategy thinking

Dr. Vidya Atal Strategic Thinking & Game Theory

Module 5 Assignment

Answer all the questions. Remember that every part of the question has points assigned; by just submitting an answer to each part you can get 50% submission credit, but if you do not submit an answer to a part, you get 0. So play strategically! Please upload the images of your answers on Canvas before the due date.

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(a) Suppose the game given above is repeated 5 times. What is the equilibrium strategy of the game? Explain how you got the answer. (10 points)

(b) Suppose the game is repeated infinitely many times.

i. How patient do the players have to be (i.e., how high does δ have to be) to sustain collusion under a grim strategy? Show your work. (10 points)

ii. How patient do the players have to be (i.e., how high does δ have to be) to sustain collusion under a tit-for-tat strategy? Show your work. (10 points)

iii. (1) Does there exist any value of the discount factor δ for which collusion can be sustained under a tit-for-tat strategy but not under a grim strategy? If yes, then provide a value for such δ; if no, then provide an explanation why. (2) Does there exist any value of the discount factor δ for which collusion can be sustained under a grim strategy but not under a tit-for-tat strategy? If yes, then provide a value for such δ; if no, then provide an explanation why. (10 points)

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