GAME THEORY:

For each scenario, draw the game tree, circle the preference branches, circle the Nash equilibria, and answer the questions. If payoffs are not quantitatively specified, you can assign appropriate values. Do so on paper and take pictures with your phone to submit.

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 assets into two sets, and the other partner chooses which set to own (with the rest going to the divider).

Kyle, having personally managed the consulting practice, was strongly attached to it. He definitely wanted to own the consulting practice. He also wanted to own the "Actors!" center, although the preference was not as strong as for the consulting practice. He did not enjoy interacting with the "Engineers!" users and was only slightly interested in it. On the other hand, Tony generally liked to own more asset, 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?