Problem 1 (Games of Strategy. Best response, Nash Equilibrium, Strictly Dominated Strategies) Thing One and Thing Two are having a dinner party. Thing One is cooking, Thing Two is bringing the drinks. Thing One knows that Thing Two will bring sake, wine, or Soda. Thing Two knows that Thing Two is cooking Asian food, Pasta, or BBQ. The table below illustrates how the friends rank the possible meals. Higher numbers correspond to higher utility. It is common knowledge that the two friends are rational. 1. Consider the possible meals. Which meal gives 'Thing One and Thing Two the highest combined utility? 2. Now, suppose that Thing One cooks BBQ. What is Thing Two's best response? 3. In the matrix, using circles illustrate 'Thing One's best responses. Then, using diamonds illustrate Thing Two's best responses. 4. Is there a Nash equilibrium in this game? Is there more than one? What is the most likely outcome of this interaction? You can solve this game using a different method. A player's strategy is called 'strictly dominated' if the player has an alternative strategy that yields him higher payoffs for any action taken by the other player. 5. Consider Thing Two. Is bringing wine a strictly dominated strategy? Is bringing Soda a strictly dominated strategy? Briefly explain. 6. Now, keep in mind that rationality is common knowledge and consider Thing One. Does Thing One have any reason to believe that Thing Two will bring Soda? Does Thing One have any reason to cook BBQ? 7. Now, keep in mind that rationality is common knowledge and consider Thing Two. Given your finding in Part 6 , does Thing Two have any reason to believe that Thing One will cook BBQ? Does Thing Two have any reason to bring Wine? 8. Last, consider Thing One. Given your findings in part 6. and 7., what drink does Thing One believe that Thing Two will bring? What should Thing One cook? Suppose that Thing One and Thing Two live in Pennsylvania where alcoholic beverages (Sake, Wine) are not sold on Sunday. The two friends could decide to hold the dinner party on Saturday or Sunday. 9. On what day of the week you would suggest that they hold their party? Why