Consider a group of 10 friends who are considering going on a road trip (is that still a thing you kids do these days, or do you just sit around and look computers?). In determining whether or not to go, each friend considers both how much they would enjoy the trip and how much it will cost them. The cost of the trip will be $500 total, and will be split equally between those who decide to go. Each friend values the trip differently, however. Specifically, the friends can be ordered in terms of how much they value the trip in dollar terms. Friend #1 values the trip at v1 = 200, friend #2 values it at v2 = 180, friend #3 has v3 = 160, and so on, with friend #10 valuing the trip at a meager v10 = 20. The payoff to friend i if they choose to go on the trip is vi - (500/m) , where m is the number of friends who decide to go. The payoff to a friend who does not go on the trip is simply 0.
(a) Is this game symmetric? Explain why or why not. (b.) Identify all Nash equilibrium for the road trip game.
(c) Which of the equilibrium that you identified in part (b.) are symmetric, and which are asymmetric?