Question 3: Finding NE [30 points] Consider the following 5 x 5 game between Player 1 (row) and Player 2 (column). The first element in any square represents the payoff of Player 1 and the second element, the payoff to Player 2. F G H I J A 8, 5 2, 2 3, 6 6, 1 7, 7 B 3, 4 3, 3 7, 2 6, 2 8, 4 C 2, 4 1, 3 5, 3 3, 2 4, 2 D 1, 5 0, 5 1, 8 2, 3 3, 6 E 6, 5 5, 2 4, 4 3, 1 2, 5 1. Specify the strategies for Player 1 and Player 2, respectively. See if you can find any strategies for Player 1 that are strictly dominated by another; do the same for Player 2. Eliminate these strictly dominated strategies, and consider the reduced game. Repeat this same step of eliminating strictly dominated strategies in the reduced game. Continue this process until you can reduce the game no further, i.e., no player has a strictly dominated strategy. [10 points] 2. At this point, you should have arrived at a 2 x 2 game. Final all the Nash equilibria for this game, including pure and mixed strategy ones. [10 points] 3. Instead of the simultaneous game, consider transforming the above 2 x 2 game into a sequential one. Player 1 acts in the first stage given the same two options as in the 2 x 2 game. After that, player 2 acts in the second stage. Player 2 is also endowed with the same two options as in the 2 x 2 game for each decision point following player 1's choice. All final payoffs are the same as specified before. For example, as in the original 5 x 5 game, player 1 choosing A and player 2 choosing F leads to payoffs of (8, 5). Draw the game tree. Specify the available strategies for each player. Find all the subgame perfect equilibria. [10 points]