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# ECON 601 - Microeconomics: Theory and Applications - Final Exam - Question 1: Games and game theory

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Economics 601 -Microeconomics: Theory and Applications

Final Exam

Please answer all questions below. Answers are due as a single document (pdf preferred) on Canvas. Feel free to scan / take photos of hand-drawn answers for math, figures, or diagrams, just make sure to embed them in your answers. Email me if you have any clarifying or similar questions, and good luck!

1.     Games and game theory (20 points)

1.1.  Suppose table A is the payoff matrix for the row player in a two-person symmetrical game. Indicate restrictions on the relative values of the payoffs in table A that would be sufficient to define the game as a Prisoner’s Dilemma, an Assurance Game, or a Hawk Dove Game where hawks fighting other hawks receive a negative payout (i.e., cost of fighting c > v, the value of the prize). Draw three versions of table A corresponding to the three different game types, circle all pure strategy Nash Equilibria and underline all Pareto optima, i.e, efficient outcomes.

1.2.  Suppose two students are working on a group project and can either expend costly effort to work on the project or shirk (i.e., neglect) their responsibilities and free ride on the final outcome, with payoffs given as in table B. Suppose each student believes that the probability their partner will shirk is 1⁄4. If students are risk neutral, will they generally decide to work on the project or shirk?

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