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2. Consider the infinitely repeated game based on the stage game in the figure below. Note that the game is symmetric between players 1 and 2. Player 3: p Player 3: q Player 2 Player 2 x Z X y Z a 3,3,0 9,4,3 1,1,3 a 2,2,2 3,1,5 4,0,1 Player 1 b 4,9,2 7,7,6 3,4,8 Player 1 |b 1,3,4 4,4,4 0,8,6 C 1, 1,1 4,3,2 5,5,5 C 0,4,3 8,0,4 2,2,2 a. Find the stage game Nash equilibria. b. Consider the following strategy profile. Player 1 chooses action b in period 1. In any other period, player 1 chooses b as long as, in all past periods, the outcome was (b,y,p); and, for any other history, player 1 chooses c. Player 2 chooses y in period 1. In any other period, player 2 chooses y as long as in all past periods the outcome was (b,y,p); and, for any other history, player 2 chooses z. Player 3 chooses p in all periods and for all histories. Derive the conditions for this strategy profile to be an SPNE. ECON 590 Spring 2021 Dr. Jalali c. Consider the following strategy profile. Player 1 chooses action b in period 1. In any other period, player 1 chooses b as long as, in all past periods, the outcome was (b,y,p); and, for any other history, player 1 chooses a. Player 2 chooses y in period 1. In any other period, player 2 chooses y as long as in all past periods the outcome was (b,y,p); and, for any other history, player 2 chooses x. Player 3 chooses p in period 1. In any other period, player 3 chooses p as long as, in all past periods, the outcome was (b,y,p); and, for any other history, player 3 chooses