Six people, named 0, 1, 2, 3, 4, and 5, each have to decide simultaneously and independently whether to go to the beach or to stay home. For each player, the payoff to staying home is zero. For each player, regardless of her name and regardless of the names of the other people who go to the beach, the benefit of going to the beach is 6 minus the total number of people who go to the beach. The cost of going to the beach is 0 for student 0; 1 for student 1; 2 for student 2; etc... Thus, for example, if only players 1 and 4 go to the beach and everyone else stays home, then player l's benefit from going to the beach is 16 - 2] his cost is (1) and so his total payoff is (6 - 2] - [1] = 3; player 4's benefit from going to the beach is 6 - 2 his cost is 4 and so his total payoff is (6 - 2 - [4] = 0; and everyone else's payoff is 0. a. Is it a (pure) Nash equilibrium for players 0, 1, 2, and 3 to go to the beach and for players 4 and 5 to stay home?