There is a class of games called coordination games. The game below is one example of such a game 2. Jones and Smith own the only tourist stops in a small village. Jones's shop is licensed to sell milk or beer, but not both. Smith's shop is licensed to sell pretzels or cookies, but not both. If Jones sells milk and Smith sells cookies, Jones wins 4 and Smith wins 3. If Jones sells milk and Smith sells pretzels each loses 1. If Jones sells beer and Smith sells cookies, each loses 2. If Jones sells beer and Smith sells pretzels, Jones wins 3 and Smith wins 4. a. Write down the game in normal form (bimatrix). Let Jones be player 1 and Smith player 2. Player 1 should be on the left side of the matrix as is the usual convention 1 and player 2 on top. b. Find the pure strategy Nash equilibria. Prove that they are pure strategy Nash equilibria. Show using two methods you have learned in class (the "definition method" and the "arrow method"). Show that the nonequilibrium profiles are not Nash using the "definition method." c. If Smith and Jones are on friendly terms, what is likely to happen (even though this is a non-cooperative game)? Why do we get a different answer to this question when we ask it of the players in problem 1? 3. Consider the Coordination game from lecture. Make up a game with two equilibria in which John and Joan will have an easy time coordinating. 4. Two doctors are competing in a neighborhood. Each has two strategies: Buy an MRI machine. Don't buy an MRI machine. The normal form game modeling their competition is a Prisoners' Dilemma: Dr. 2 Buy don't buy Buy 3,3 9,2 Dr. 1 Dont buy 2,9 8,8 A. Write a little story that explains why the payoffs are what they are. B. How could the doctors avoid the dilemma? Come up with at least two ideas for them