game theory problem

Suppose there is a (continuum) mass of people occupying the real line segment [0, 2] in total. That is, each person is labeled by a unique real number as, With a: e [0, 2]. They are the audience of a ShOW, and each person is contemplating about Whether to give a standing ovation or not at the end of the show. Each person can either choose to Sit (S) or give a standing ovation (O). 1. (5pts) For the agent labeled a: E [0, 2], his utility for ovation is 1 if there is at least (a: + 1) / 2 mass of people standing (to give ovation), and -1 otherwise. Utility of sitting is normalized to be 0 for each person. If each person simultaneously chooses to sit or give a standing ovation, What is the pure NE (Nash Equilibrium) of this game? Who is standing and Who is sitting in this equilibrium? NOTE: There are multiple equilibria in this game. For this part, focus on the one Where not everyone stands and not everyone sits