Game theory assignment:

For each scenario, draw the game tree, circle the preference branches, circle the Nash equilibria, and answer the questions. Before working on the problems, ask yourself: who are the players? What are their action spaces? What is the order of their actions? What are their payoffs? If there are no quantitatively defined payoffs, feel free to define qualitative ones, but be sure that they are consistent with the problem and among themselves. Do your work on paper and take pictures with your phone to submit on eLearning.

Divide & Choose

Kyle and Tony had jointly started a successful business around an Internet site for social networking. The business had grown into three service centers, one catering to aspiring actors ("Actors!"), one to jobless engineers ("Engineers!"), and a third consulting practice that specialized on improving employee morale.

After the initial growth period, Kyle and Tony felt their personalities were conflicting and decided to dissolve their partnership. They had an agreement when establishing the business that if they would ever dissolve their partnership, the "divide & choose" method should be used, where one partner divides the three service centers into two (non-empty) sets, and the other partner chooses which set to own (with the other set going to the divider). For example, Kyle may divide A, C and E into A/CE, and suppose Tony were to choose CE, Kyle would get A.

Kyle, having personally grown the consulting practice, was strongly attached to it. He definitely preferred to own the consulting practice regardless of anything else. He also preferred to own the "Actors!" center, although the preference was not as strong as for the consulting practice. He did not particularly enjoy interacting with the "Engineers!" users and was only slightly interested in it. On the other hand, Tony generally liked to own more assets than less, with one exception--he did not want to own both "Actors!" and "Engineers!" centers as he felt that their different cultures did not fit well together. Among the three centers, he likes consulting the best, and then "Actors!", and then "Engineers!". Kyle and Tony, having collaborated for years, knew each other's preference well.

First, suppose Kyle will be the divider. What is the predicted resolution outcome? Then, suppose Tony will be the divider. What is the predicted resolution outcome? Given these analyses, now consider Kyle and Tony deciding who should be the divider. Will they reach an agreement? What would you recommend as a practical solution?

Hint: usually in game-theory analyses you need to assign values to outcomes to facilitate comparisons, but in this case you should directly compare outcomes based on the stated preferences.