Four colleagues, A, B,C, and D, want to decide how to commute to work. The company they work for offers a shuttle service, for a total cost of 12 pounds, that would be evenly split among the people who chose to use it. For example, if two people use the shuttle service, each of them would pay 6 pounds. Each person also has the option to drive with their own car to work. The cost for using their own car is fixed but different for each person: A's cost for driving is 2; B's cost for driving is 3, C's cost for driving is 5; D's cost for driving is 11 . Your tasks: a. [6\% ] Give a formal definition of the game described above. Who are the players, what are their strategies and how are their utilities defined for each state (strategy combination). b. [9\% ] Are there any strictly dominated strategies in this game? If so, reduce the game as much as possible by eliminating them. c. [5\% ] Identify all pure Nash equilibria of the game and their social cost (sum of costs). d. [5\% ] What is the price of stability of the game