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Game Theory For Students: Work vs Shirk

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You and a classmate are assigned a project on which you will receive one combined grade. You each want to receive a good grade, but you also want to avoid hard work. In particular, here is the situation:

If both of you work hard, you both get an A, which gives each of you 40 units of happiness.
If only one of you works hard, you both get a B, which gives each of you 30 units of happiness.
If neither of you works hard, you both get a D, which gives each of you 10 units of happiness.
Working hard costs 25 units of happiness.

a. Construct a payoff table, where you and your classmate both have Work and Shirk as possible actions you could take.
b. What is the likely outcome?
c. If you get this classmate as your partner on a series of projects throughout the year, rather than only once, how might that change the outcome you predicted in part (b)?
d. Another one of your classmate cares more about good grades. He gets 50 units of happiness from a B and 80 units of happiness from an A. If this other classmate were your partner (but your preferences were unchanged), how would your answers to part (a) and (b) change? Which of the two classmates would you prefer as a partner? Would he also want you as a partner?

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Solution Summary

This solution examines a payoff matrix of possible outcomes if my partner and I work together on a project and have to decide whether to work hard or not.

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a) See the attached file. Our payoff from working is the happiness we get for each grade minus the 25 points we lose if we choose to work.
b) Each of us gets a higher payoff by shirking no matter what ...

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