Problem 4: [30 pts] Consider the following scenario. Three people A, B, C each decide simulta- neously on a cafe to study at. There are two choices of cafes, Cafe X and Cafe Y. The problem with this situation is that none of these people mutually like each other. A dislikes B, B dislikes C, and C dislikes A. On the other hand, A likes C, B likes A, and C likes B. After deciding on a cafe, each individual 2' obtains a utility. Everyone likes Cafe X better than Cafe Y and so being at Cafe X yields each player an additional 1 unit of utility. Each individual 2' also obtains an additional k: > 0 utils if the person they like decides to study at the same cafe and obtains E