Problem 3. Consider the strategic-form game represented by the following matrix:: LR T 6,6 2,8 B 8,2 0,0 Player 1 chooses between T and B and receives the first payoff in the cells. Player 2 chooses between L and R and receives the second payoff in the cells. 1. What are the Nash equilibria (including any mixed) of this game, and what are the players' expected payoffs in each equilibrium? Suppose a single (fair) coin is tossed, the outcome of which is publicly observed. If it is heads player 1 is told to play T, and player 2 is told to play R; if it is tails, player 1 is told to play B, and player 2 is told to play L. 2. Would each player be willing to follow these instructions, given that the other player did so? What would be the expected payoffs? Comment. A "three-sided coin" is tossed, with equal probability assigned to each of three outcomes: x, y, and z. The players do not observe the outcome. However, if x is thrown, player 1 is told to play T, and player 2 is told to play R. If y is thrown, player 1 is told to play T, and player 2 is told to play L. If z is thrown, player 1 is told to play B, and player 2 is told to play L. 3. Show that each player would be willing to follow these instructions, given that the other player does so. What would be the expected payoffs? Comment. 4. Does this notion of correlated equilibrium provide a reasonable generalisation of mixed-strategy Nash equilibrium