This payoff matrix shows a two-player variant of the sushi game, but where B really loves sushi, so her payoffs from getting to eat sushi are higher than A's, and her payoffs from there not being enough sushi are lower than A's. Payoffs are ordered A, B. B B N A B 10, 15 10, 25 N 20, 15 0,-5 A. Find and state all of the mixed strategy Nash equilibria of the game. If there are multiple equilibria, number them in preparation for answering part "c." B. (From the week 6 lectures) Draw a graph of the expected payoffs for each player. Use these graphs to formulate the decision rule for each player. C. (From the week 6 lectures) Draw a graph of the best replies of the two players. Carefully label each Nash equilibrium.

Jane is interested in buying a car from a used car dealer. Her maximum willingness to pay for thecar is 12 ($12,000). Bo, the dealer, is willing to sell the car as long as he receives at least 9($9,000). What is the Nash bargaining solution to this game?

Problem 2. Consider the partnership-game we discussed in Lecture 3 (pages 81-87 of the textbook). Now change the setup of the game so that player 1 chooses x = [0, 4], and after observing the choice of x, player 2 chooses y ≤ [0, 4]. The payoffs are the same as before. (a) Find all SPNE (subgame perfect Nash equilibria) in pure strategies. (b) Can you find a Nash equilibrium, with player 1 choosing x = 1, that is not subgame perfect? Explain.

How expected Nash Equilibrium would be achieved in case of game with no Nash Equilibrium?