ECO303: Intermediate Microeconomic Theory Benjamin Balak, Spring 2008 Game Theory: FINAL EXAMINATION 1. Under a mixed strategy, A) players move sequentially. B) a player chooses among two or more pure strategies according to pre-specified probabilities. C) the players may never reach a Nash equilibrium. D) players obtain lower payoffs than in a pure strategy equilibrium. 2. Player A and Player B are playing a prisoners' dilemma game. Which of the following statements is false? A) If the players play the game repeatedly with each other, the players may play cooperatively. B) If the game is played only once, the players would not be expected to cooperate. C) If players play the game repeatedly with each other, they are more likely to cooperate if they are patient. D) If the game is played only once, the outcome minimizes total jail time. 3. Consider a repeated prisoner's dilemma game. The likelihood of a cooperative outcome rises when A) they value payoffs in future periods much less than they value payoffs in the current period. B) Interactions between the players are frequent. C) Cheating is difficult to detect. D) The one-time gain from cheating is large in comparison to the eventual cost of cheating. 4. A strategy in which you do to your opponent in this period what your opponent did to you in the last period is a A) Live-and-let-live strategy C) Grim trigger strategy. B) Shoot-to-kill strategy. D) Tit-for-tat strategy. 5. In a sequential game A) A player always obtains a higher payoff by maintaining the maximum flexibility in his or her actions. B) The first mover always obtains a higher payoff than a second mover. C) A player can sometimes obtain a higher payoff by making a move that restricts the flexibility he or she will have later in the game. D) strategic moves include those that are easy to reverse. Page 1
Use the following games to answer the following questions: (Payoffs are listed with the row player's payoffs first & the column player's payoffs second: Player 1, Player 2) 6. In Game 1 above, A) Player A choosing A1 and Player B choosing B1 is a Nash equilibrium. B) Player A choosing A2 and Player B choosing B2 is a Nash equilibrium. C) there is no Nash equilibrium. D) there are multiple Nash equilibria in pure strategies. 7. In Game 1 above, A) Player A has a dominant strategy. C) Both players have dominant strategies. B) Player B has a dominant strategy. D) Neither player has a dominant strategy. 8. In Game 2 above, A) Player A choosing A1 and Player B choosing B1 is a Nash equilibrium. B) Player A choosing A1 and Player B choosing B2 is a Nash equilibrium. C) Player A choosing A2 and Player B choosing B1 is a Nash equilibrium. D) Player A choosing A2 and Player B choosing B2 is a Nash equilibrium. 9. In Game 2 above, A) player A has a dominant strategy. C) both players have dominant strategies. B) player B has a dominant strategy. D) neither player has a dominant strategy. 10. In Game 3 above, A) Player A has a dominant strategy. C) Both players have a dominant strategy. B) Player B has a dominant strategy. D) Neither player has a dominant strategy. 11. In Game 3 above, A) A1 is a dominated strategy for Player A C) A3 is a dominated strategy for Player A B) A2 is a dominated strategy for Player A D) Player A has no dominated strategies. 12. In Game 3 above, A) B1 is a dominated strategy for Player B C) B3 is a dominated strategy for Player B B) B2 is a dominated strategy for Player B D) Player B has no dominated strategy. Page 2
13. In Game 3 above, A) Player A choosing A1 and Player B choosing B1 is a Nash equilibrium. B) Player A choosing A1 and Player B choosing B3 is a Nash equilibrium. C) Player A choosing A3 and Player B choosing B1 is a Nash equilibrium. D) Player A choosing A3 and Player B choosing B3 is a Nash equilibrium. 14. In Game 4 above, A) There is one Nash equilibrium. C) There are three Nash equilibria. B) There are two Nash equilibria. D) There are four Nash equilibria. 15. For Game 4 above, which of the following statements is incorrect? A) Player A choosing A1 and Player B choosing B1 is a Nash equilibrium. B) Player A choosing A3 and Player B choosing B3 is a Nash equilibrium. C) Player A choosing A1 and Player B choosing B3 is a Nash equilibrium. D) Both players in Game 4 have a dominated strategy. 16. Suppose in Game 4 above that the players make their choices sequentially, with Player A choosing first. The Nash equilibrium in this game will be A) Player A choosing A1 and Player B choosing B1. B) Player A choosing A1 and Player B choosing B3. C) Player A choosing A3 and Player B choosing B1. D) Player A choosing A3 and Player B choosing B3. 17. Game 8 shows the payoff matrix in terms of profit (in millions of dollars) for two possible strategies: advertise or do not advertise. If they legally could, why might the two companies agree to a binding contract committing both to not advertise? A) Because advertising is ineffective. B) Because advertising is too expensive. C) Because not advertising would lower the costs and therefore increase the profits to each firm. D) Because not advertising would lower profits. 18. Game 8 shows the payoff matrix in terms of profit (in millions of dollars) for two possible strategies: advertise or do not advertise. Suppose that the two companies can legally make a non-binding agreement to not advertise. Based on the payoff matrix shown above, will the two companies honor such an agreement to not advertise? A) Yes. Both Coke and Pepsi will not advertise. C) No. Pepsi will advertise but Coke will not. B) No. Coke will advertise but Pepsi will not. D) No. Both Coke and Pepsi will advertise. Page 3
19. Game 8 shows the payoff matrix in terms of profit (in millions of dollars) for two possible strategies: advertise or do not advertise. Which of the following is a true statement? A) Coke has a dominant strategy to not advertise. C) The game has one Nash equilibrium. B) Pepsi has a dominant strategy to not advertise. D) The game has multiple equilibria. 20. Game 9 has the structure of a A) prisoner's dilemma. B) sequential game. C) game of chicken. D) tit-for-tat game 21. In Game 9 above, A) There is one Nash equilibrium. C) There are three Nash equilibria. B) There are two Nash equilibria. D) There are four Nash equilibria. 22. Games with structures like Game 9 above have been used to describe A) bank runs. C) dominant strategy equilibria. B) collusion in Sumo wrestling. D) the decision to hire a lawyer. Risk & Uncertainty: 23. Suppose a fair, two-sided coin is flipped. If it comes up heads you receive $5; if it comes up tails you lose $1. The expected value of this lottery is A) $2 B) $3 C) $4 D) $5 24. Consider a lottery with four possible outcomes, A, B, C, and D. The associated payoffs are: A - $10, B - $30, C - $70, and D - $150. The probabilities are P(A) = 0.40, P(B) = 0.20, P(C) = 0.30, and P(D) = 0.10. The expected value of this lottery is A) $23 B) $46 C) $65 D) $260 25. Consider four lotteries, A, B, C, and D, all with an expected value of $100. The associated standard deviations of the lotteries are: A is 10, B is 15, C is 5, and D is 20. Which lottery is the riskiest? A) Lottery A B) Lottery B C) Lottery C D) Lottery D 26. A decision maker can be described with utility which is only a function of income and which exhibits diminishing marginal utility of income. This decision maker is A) risk-averse. B) risk-neutral. C) risk-loving. D) risk-gaining. Page 4
27. Which of the following statements is correct for a decision maker facing a choice between a sure thing and a lottery when the sure thing had the expected payoff of the lottery are equal? A) Risk-loving decision makers will require a positive risk premium to bear risk. B) Risk-neutral decision makers will require a positive risk premium to bear risk. C) Risk-averse decision makers will require a positive risk premium to bear risk. D) The risk premium depends on the characteristics of the lottery, not on the characteristics of the utility function of the decision maker. 28. Your current disposable income is $10,000. There is a 10% chance you will get in a serious car accident, incurring damage of $1,900. (There is a 90% chance that nothing will happen.) Your utility function is U = I, where I is income. What is the most you would be willing to pay for this policy (rather than no insurance)? A) $100 B) $190 C) $199 D) $270 29. A good way to deal with adverse selection faced by an insurance company would not be to A) fully indemnify its policy holders. B) require applicants to take a physical examination. C) require policy holders to pay a deductible. D) insure groups of individuals (such as all employees of a particular firm). 30. The winner's curse refers to A) bidding an amount higher than your maximum willingness to pay in an effort to 'win' in a private values auction. B) winning a private values auction and later determining that you bid more than you had really intended to. C) winning a common values auction and bidding more than the object is worth. D) winning an item in a common values auction that you don't really want. Page 5
Use the decision tree along with the given probabilities to answer the following question(s). Probability Event A = 30% Probability Event B = 70% Probability Event 1 = 58% Probability Event 2 = 42% Probability of Event A given that Event 1 occurs = 16% Probability of Event B given that Event 1 occurs = 84% Probability of Event A given that Event 2 occurs = 50% Probability of Event B given that Event 2 occurs = 50% Page 6
31. If the decision maker chooses Decision A and Event 1 occurs, which decision alternative should the decision maker choose at node D? A) Decision 1 B) Decision 2 C) Either Decision; they both have the same expected value. D) Neither Decision; more information is needed. 32. If the decision maker chooses Decision A and Event 2 occurs, which decision alternative should the decision maker choose at node E? A) Decision 1 B) Decision 2 C) Either Decision; they both have the same expected value. D) Neither Decision; more information is needed. 33. What is the expected value at node B? A) 18.60 B) 16.04 C) 13.76 D) 12.50 34. If the decision maker chooses Decision B, which decision alternative should the decision maker choose at node C? A) Decision 1 B) Decision 2 C) Either decision; they both have the same expected value. D) Neither decision; more information is needed. 35. At node A, which decision has the higher expected value? A) Decision A B) Decision B C) Either decision; they both have the same expected value. D) Neither decision; more information is needed. 36. If the cost of obtaining information to determine Event 1 and Event 2 is $5, what is the value of perfect information? A) 1.96 B) 0 C) 3.04 D) 5 Page 7
Externalities, Public Goods, the Coase Theorem, Property Rights, & Transaction Costs: 37. An environmental economic consulting firm is hired to measure the negative externalities associated with the pollution from an industry. The consultants calculate the marginal social cost of production to be MSC = 2Q + 30 and the marginal private cost of production to be MPC = Q + 30. The market demand curve for the industry can be expressed as P = 60 Q. If the industry currently does not take into account the negative externality in its supply decisions, the industry is by units relative to the social optimum. A) under-producing; 5 B) over-producing; 5 C) under-producing; 8 D) over-producing; 8 38. An environmental economic consulting firm is hired to measure the negative externalities associated with the pollution from an industry. The consultants calculate the marginal social cost of production to be MSC = 2Q + 30 and the marginal private cost of production to be MPC = Q + 30. The market demand curve can be expressed as P = 60 Q. If the consultants have accurately measured the impact of the pollution externality, the deadweight loss from producing at the market equilibrium is A) $30 B) $37.5. C) $55. D) $67.5. 39. Suppose that an industry emits a chemical that pollutes the ground water. Without considering the effects of the pollution, the industry has a marginal private cost curve of MPC = Q +30. The market demand curve is P = 60 Q, while the marginal social cost curve is MSC = 2Q + 30. What is the socially optimal emissions standard? A) 15. B) 10. C) 5. D) 0. 40. The Coase Theorem implies that victims of pollution should be able to pay polluters not to pollute if the victims value a reduction in pollution more than the polluters value the production of the pollution. Which of the following does not explain why this type of payment does not work in real life? A) If there are many victims, the costs to them of organizing may be quite high. B) If there are many firms in the industry, it may be difficult for the victims to negotiate with all of the firms. C) The victims may have trouble quantifying the value to them of reducing the pollution. D) Bargaining costs are likely to be small in this case, so the theorem does not apply. Page 8
41. Suppose that a smoker and a non-smoker are seated next to each other in a restaurant. This restaurant does not offer a non-smoking section. The smoker is indifferent between 1) smoking and 2) not smoking and consuming a $6 dessert. The non-smoker values being able to eat in a smoke-free environment at $10. According to the Coase Theorem, and assuming no bargaining costs, what will happen? A) The smoker will continue to smoke because that is his right. B) The smoker will stop smoking, just to be a nice guy. C) The non-smoker will offer to pay the smoker between $6 and $10 to stop smoking, but the smoker will refuse because he has the right to smoke. D) The non-smoker will offer to pay the smoker between $6 and $10 to stop smoking, and the smoker will accept the money and refrain from smoking. 42. An example of a good that is non-rival but exclusive is A) hunting in a public game area. B) national defense. C) public radio. D) a pay-tv channel. 43. Which of the following is not an example of a free rider problem? A) Sally listens to public radio but never contributes to her local station. B) Fred benefits when the National Guard arrives to help create a flood wall around his town, but he is so poor that he pays no taxes. C) Joe works with two other students on a group project for his intermediate microeconomics class. The grade is based on a group paper, but Joe goes to a movie instead of working on the paper because he knows that the other group members will write it without him. D) John goes into his local corner shop and walks out with an apple without paying for it. That s it! Page 9