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The hero is facing off with the bully, who might do nothing or do something

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The hero is facing off with the bully, who might do nothing or do something. The hero could respond with one of three strategies: run, hide, or fight. If he fights, he will win, but public opinion will favor the bully if he did nothing (and favor the hero if the bully did something). If the hero hides, his payoff is nil. If the hero runs, his reputation is severely tarnished, and the bully is delighted if he did something to cause the hero's flight. Bully Do Nothing (N) Do Something (S) Hero Run (R) -10,1 -10, 10 Hide (H) 0,2 0,1 Fight (F) -5,5 Identify the Nash equilibrium of the stage game and any cooperative profile that makes both players better off. What is the minimum value for the discount factor that allows both players to cooperate in an infinitely repeated game? (Hint: only one of them needs to play a trigger strategy.)