The following game is a zero-sum game (up to renormalization of utility). Fill in the missing entries: Y Z

Exercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 R O player pay 000 2 1 M 3 b 010 O player 3's payoff 1 2 221 2 000 0 0 (a) Find all the pure-strategy Nash equilibria. Which ones are also subgame perfect? (b) [This is a more challenging question] Prove that there is no mixed-strategy Nash equilibrium where Player 1 plays Mwith probability strictly between 0 and 1.

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Please no written by hand and no emage Two classmates A and B are assigned a group project. Each student can choose to Shirk or Work. If one or more students chooses Work, the project is completed and provides each with credit valued at 4 payoff units each. The cost of completing the project is that 6 total units of effort (measured in payoff units) is divided equally among all players who choose to Work and this is subtracted from their payoff. If both Shirk, they do not have to expend any effort but the project is not completed, giving each a payoff of 0. The instructor can only tell whether the project is completed and cannot determine which students contributed to the project. A. Write down (draw) the normal form game, with payoff in the format of (player A payoff, player B payoff). Note that we assume students choose to Shirk or Work simultaneously. B. Does either player have a dominant strategy? C. Find the Nash equilibrium or equilibria. D. Explain ‘Prisoners’ dilemma’ using the…

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