04 Jun Question Click the link above to submit the assignment.
Question
Click the link above to submit the assignment.
Week 3 Homework Problems:
Chapter 5: 5.1(a-b), 5.2(a-c), 5.3(a-c), 5.5(a-c), 5.10(a-c)
Chapter 6: 6.2(a-e), 6.4(a-e), 6.6(a-d), 6.7(a-e), 6.9 (a-d)
Note: Homework problems are worth 2 points for each part of the problem.
5.3
Return to the game given by the payoff matrix in Problem.
Two classmates A and B are assigned an extra credit group project. Each student can choose to Shirk or Work. If one or more players choose Work, the project is completed and provides each with extra 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 teacher can only tell whether the project is completed and not which students contributed to it.
a. Write down the extensive form for the simultaneous- move game.
b. Suppose the game is now sequential move, with A moving first and then B. Write down the extensive form for this sequential-move game.
c. Write down the normal form for the sequential-move game. Find all the Nash equilibria. Which Nash equilibrium is sub game-perfect?
5.5
Two classmates A and B are assigned an extra credit group project. Each student can choose to Shirk or Work. If one or more players choose Work, the project is completed and provides each with extra 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 teacher can only tell whether the project is completed and not which students contributed to it.
a. Write down the normal form for this game, assuming students choose to Shirk or Work simultaneously.
b. Find the Nash equilibrium or equilibria.
c. Does either player have a dominant strategy? What game from the chapter does this resemble?
5.10
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