Consider the following stage game: ) (0,6) (4,4) For i 1,2, call f the payoff of player i in the above stage game. Consider now an infinite repetition of the above stage game where the payoff of player i is the limit of the average payoffs over time, i.e., T 1 lim supfi(o (ht−1)), T→[infinity] t=1 where he is the history of actions up to time t and ☛ is the strategy profile. 1. Find all Nash equilibria of the stage game. 2. Find a strategy profile that achieves (4,4) as a payoff of the infinitely repeated game. 3. If (4,4) is an equilibrium payoff of the infinitely repeated game, find an equilibrium strategy that achieves this payoff. 4. Is (5,3) as an equilibrium payoff of the infinitely repeated game?