2. Consider the following coordination game, where the payos are in dollars.

2. Consider the following coordination game, where the payoffs are in dollars. Player 2 L R Player 1 U (a) Find all Nash equilibria (pure or mixed) for this coordination game. (b) Suppose that before the game is played, there is an initial stage where player 1 chooses whether or not to burn $2. Player 2 observes Player I's action. Then the players play the coordination game shown above. Since player 2 knows that player 1 has the option to burn the money, this "money burning" could be viewed as a way that Player 1 communicates their intention to player 2. Draw an extensive form game that includes both stages of this new game: stage 1, where Player 1 chooses whether or not to burn $2, and stage 2, when the players play the coordination game. Note that whenever Player 1 burns $2, this decreases their own payoff by $2 (this should be reflected in the payoffs of the extensive form game). (c) Indicate each subgame of the extensive form game from the previous step. (d) Write the normal form game for the 2-stage extensive form game and identify any pure strategy Nash equilibria. (e) Use iterative elimination of weakly dominated strategies to reduce the game. There is a way to reduce this (over multiple iterations) to a game where player 1 has 2 remaining strategies and player 2 has 1 remaining strategy. Based on the result, summarize how Player I's option to burn money affects the outcome of this two stage game (compared with the coordination game without money burning). (f) In the previous step, you've reduced to game to one with two remaining strategy profiles. Both remaining strategy profiles give the same payoffs and both are Nash equilibria. Only one of these is subgame perfect. Which one is it?