Answer all of the question with a clear precise and correct answers

5. In the ancient Chinese historical novel Three Kingdoms, by Luo Guanzhong, defeated General Cao Cao must choose which of two roads on which to try to escape from victorious General Kongming, who must simultaneously choose which of the roads to wait in ambush on. If Cao Cao is captured, Cao Cao loses 2 and Kongming gains 2. Whether or not Cao Cao is captured, both Cao Cao and Kongming gain 1 additional unit of payoff by taking the comfortable Main Road instead of the awful Huarong Road (However, because 2 > I they both think that whether Cao Cao is captured is more important than being comfortable.) The payoff matrix is: Kongming Main Road (q) Huarong Road Main Road (p) 3 -1 Cao Cao 2 Huarong Road -2 (a) Compute the mixed strategy equilibrium in the game, letting p be the probability with which Cao Cao takes the Main Road and q be the probability with which Kongming takes the Main Road. (b) Assuming that a level-0 Cao Cao or Kongming randomizes 50-50 between Main Road and Huarong Road, which strategy would a level-1 Cao Cao choose? Which would a level-1 Kongming choose? Which would a level-2 Cao Cao choose? Which would a level-2 Kongming choose? Which would a level-3 Cao Cao choose? Which would a level-3 Kongming choose? (c) Suppose both Cao Cao and Kongming are equally likely to be level-1, level-2, or level-3. Using your answer to (b), compute the probabilities with which Cao Cao and Kongming take the Main Road.6. Consider an Intersection game like Alphonse and Gaston, in which two drivers meet at the intersection of two roads, with one on each road and no way to distinguish between their roles. The payoffs are: Go Stop 0 Go Stop 0 (a) Letting p be the probability that each driver plays Go, find the mixed-strategy Nash equilibrium and explain why it is an equilibrium. Compute players' equilibrium expected payoffs. (b) If the players have no way to distinguish between their roles, would you expect them to be able to coordinate on one of the Pareto-efficient pure-strategy equilibria? Why or why not? For part (c), assume that players are repeatedly paired at random from a single large population to play the Intersection game, with no way to distinguish their roles once paired; and that they adjust their strategies over time in a way that increases the population frequency of a pure strategy that has higher expected payoff, given the current mix of strategies in the population. (c) How would you expect the mixture of strategies, Go or Stop, to evolve over time? Explain.Return to considering a single two-person interaction as in parts [a}-(b}. But for pans {d}- (f}, imagine that a stoplight is installed at the intersection, which both players can see before they decide whether to Go or Stop. The stoplight is Green for one driver if and only if it is Red for the other driver, and at any given time when they meet, it is equally likely to be Green for Row and Red for Column or Red for Row and Green for Column. {d} Show in a new payoff matrix how the stoplight changes the game and its setof equilibria. (Hint: The payoffs for the various combinations of Stop and Go are still m in the above payoff matrix, but now players have more strategies because they can make their decision to Go or Stop depend on whether the light is Red or Green, for example choosing strategies such as \"Stop on Green, Go on Red\" [there are no traffic laws in the game, so this is just as possible as \"Go on Green, Stop on Red"}. Further, to evaluate the consequences of their strategies, you now have to make expected-payoff calculations that take into account their uncertainty about whether the light will be Green or Red for them and the effect this has on the nal outcome, given their strategies. For example, if they both choose the strategy \"Stop on Green, Go on Red\4) In economic policy, there is an ongoing debate over when, if ever, it is appropriate for the government to subsidize specific industries. The normal argument against subsidies is that they arise from inappropriate politics - e.g. political contributions from the industry being helped - and they only serve to freeze out more efficient foreign producers. Potentially, however, there are other cases. Several years ago, Paul Krugman created this example: Consider the civilian aircraft industry where there are now two large competitors in Europe/America - Boeing and Airbus. Developing a new airliner involves large initial costs and so each company needs, say, 300 new orders over the first three years to break even. The problem is that the world market is likely to generate only 400 orders over the next three years. Suppose Boeing and Airbus are each considering developing a new passenger airliner. Given the nature of the market, the pay off matrix for profit looks like this (Boeing's profit is the first in each pair). Airbus Develop Do not Develop Develop (-7, -7) (25, 0) Boeing Do Not Develop (0, 25) (0,0) a) Does this competition have a Nash equilibrium? Explain. b) Suppose that while the two companies are examining their positions, the U.S. government announces that it will give Boeing a subsidy of 9 units to develop the airplane - i.e. a payment that would not have to be returned as long as Boeing developed the plane and brought it to market. How might that influence how the game evolves. 5) As you walk down the aisles of a supermarket, you will see that many firms engage in "product proliferation". Nine-Lives Cat Food produces about a dozen different flavors of cat food - Seafood Delight, Tuna in Sauce, several meat-flavored cat foods that cannot be mentioned here. Tide laundry detergent produces five or six different varieties of Tide - Tide Original, Tide with Fresh Scent, Tide with Bleach Substitute, liquid Tide etc. Typically, these varieties all sell for about the same price so they are not a way of achieving price discrimination. Rather, as the kinked demand curve suggest, product proliferation is a form of non- price competitive strategy. One part of the strategy involves appealing to various consumer tastes. In the context of a supermarket, what other strategic reason might these manufacturers have for producing so many similar products