Question

For their economic class, students are asked to form pairs to complete an assignment. The professor asks them to work together but to turn only one copy of the problem set. Johnny and Kristen, two students of the class, decide to work together. Both of the students value the assignment. However, because Kristen and Johnny received different grades at the exam, they do not value the assignment the same way: Kristen would receive a payoff of 10 if the assignment is completed, while Johnny would receive a payoff of 15. In case the assignment is not completed, they would both receive zero payoff. The students can choose to work or not on the assignment. If both students work, it will take them 5 hours each. If only one of them work, it will take this student 12 hours to complete the assignment by itself. If none of them work, the assignment will not be completed. We assume that each hour of work costs one unit of payoff to students. Moreover, students cannot change partners.

We consider first this game as a static game in which students decide simultaneously whether to work on the assignment.

1. Write down the normal form of the game. Make sure to include the players, actions and payoffs.

2. Do Kristen or Johnny have a dominant strategy? Explain. 3. What is the Nash equilibrium of the game

3. What is the Nash equilibrium of the game.

Answer 1

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