Game Theory Academic Essay

Game Theory Problem 1 Consider a homogeneous product, quantity choosing, duopoly. Inverse demand is given by p = 25;000- Q where p is unit price and Q = q1 + q2 is total industry output. Firm 1 has a constant marginal cost of c1 = 10;000, while firm 2 has a constant marginal cost of c2 = 14;000. Both firms have fixed costs of $10 million. Wages and salaries make up about two-thirds of marginal cost for each firm. The government is considering a 5% payroll (i.e., wage and salary) tax on firms in this industry. The firms argue that this will drive at least one of them out of business, with undesirable consequences for state employment. Should the government take this possibility seriously? Problem 2 Consider a small town that has a population of dedicated pizza eaters but is able to accommodate only two pizza shops, Donnas Deep Dish and Pierces Pizza Pies. Each seller has to choose a price for its pizza, but for simplicity, assume that only two prices are available: high and low. If a high price is set, the sellers can achieve a profit margin of $12 per pie; the low price yields a profit margin of $10 per pie. Each store has a loyal captive customer base that will buy 3,000 pies per week, no matter what price is charged by either store. There is also a floating demand of 4,000 pies per week. The people who buy these pies are price conscious and will go to the store with the lower price; if both stores charge the same price, this demand will be split equally between them. (Cartel Pricing) (a) Draw the payoff matrix for the pizza-pricing game, using each store profits per week (in thousands of dollars) as payoff. Find the Nash equilibrium of this game. (b) Now suppose that Donnas Deep Dish has a much larger loyal clientele that guarantees it the sale of 11,000 (rather than 3,000) pies per week. Profit margins and the size of the floating demand remain the same. Draw the payoff matrix for this new version of the game and find the Nash equilibrium. (c) How does the existence of the larger loyal clientele for Donnas Deep Dish help solve pizza stores dilemma? Problem 3 Consider a new version of the tax evasion game, in which the cost of monitoring has tripled, going from 10 to 30. (a) Represent the new game in matrix form. (b) Find the mixed strategy equilibrium Nash Equilibrium of the new game. (c) Comment on the common argument: ?if the cost of monitoring goes up, Authority should decrease the level (frequency) of the monitoring activity. PLACE THIS ORDER OR A SIMILAR ORDER WITH US TODAY AND GET A GOOD DISCOUNT

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