Sample Exam(4)

Spring 2023 Version E 1 Player 2 Left Center Right Player 1 Up 14, 4 32, 6 18, 8 Middle 8, 22 12, 18 20, 17 Down 16, 14 8, 8 4, 4 Use the information in the game matrix above to answer questions #1 and #2. 1. If this is a simultaneous move game, the pure strategy Nash equilibrium is _____________ . a. (Up, Center) b. (Up, Right) c. (Middle, Left) d. (Middle, Right) e. (Down, Left) 2. If this is a sequential game where Player 1 moves first, the SPE is _____________. a. (Up, Center) b. (Up, Right) c. (Middle, Left) d. (Middle, Right) e. (Down, Left) 3. Use backward induction to find the SPE of the game depicted on the game tree shown above. Player 1’s payoffs are written first followed by Player 2’s payoffs. What is Player 1’s payoff in the SPE of this game? a. 2 b. 3 c. 4 d. 8 e. 10

Spring 2023 Version E 2 A consumer has utility 𝑢𝑢 ( 𝐼𝐼 ) = √𝐼𝐼 and income $1,600. When sick, the consumer must go to the doctor, which costs a whopping $1,150 without insurance. If the consumer goes to the gym, the probability of getting sick is 20%, but if she does not go to the gym, the probability of getting sick is 80%. The cost of going to the gym is $150. An insurance company is offering a health insurance plan with a premium of $230 and a co-pay of $110 (the consumer pays the $110 copay only if she goes to the doctor). Use this information to answer #4 and #5. 4. The consumer’s expected utility from purchasing insurance and going to the gym is a. 31.6 b. 33.3 c. 37.0 d. 34.6 e. 34.9 5. Given this insurance contract with cost-sharing, the $110 copay a. Fixes the moral hazard problem. b. Fixes the adverse selection problem. c. Is too high and prevents people from purchasing insurance. d. Is too low to fix the adverse selection problem. e. Is too low to fix the moral hazard problem. Firm 1 and Firm 2 are Stackelberg competitors in the market for popsicles. Firm 1 is the leader and Firm 2 is the follower. Each firm has the same cost of producing popsicles, such that 𝐶𝐶 ( 𝑞𝑞 1 ) = 0.4 𝑞𝑞 1 and 𝐶𝐶 ( 𝑞𝑞 2 ) = 0.4 𝑞𝑞 2 . Market demand for popsicles is given by 𝑃𝑃 = 10 – 0.2 𝑄𝑄 , where the market quantity is equal to the sum of the popsicles produced by each firm ( 𝑄𝑄 = 𝑞𝑞 1 + 𝑞𝑞 2 ). Use this information to answer questions #6, #7, and #8. 6. What is Firm 2’s best response function? a. 𝑞𝑞 2 = 24 − 0.5 𝑞𝑞 1 b. 𝑞𝑞 2 = 48 − 2 𝑞𝑞 1 c. 𝑞𝑞 2 = 12 − 0.25 𝑞𝑞 1 d. 𝑞𝑞 2 = 26 − 0.5 𝑞𝑞 1 e. 𝑞𝑞 2 = 50 − 𝑞𝑞 1 7. What is the market price of popsicles in the SPE of this game? a. $5.20 b. $3.60 c. $2.80 d. $2.50 e. $0.40 8. Now suppose the firms described above competed on price in a Bertrand competition model. What is the market price of popsicles in equilibrium? a. $5.20 b. $3.60 c. $2.80 d. $2.50 e. $0.40

Spring 2023 Version E 4 Player 2 Player 1 Cooperate Defect Cooperate 100, 100 80, 110 Defect 110, 80 90, 90 12. If the game presented above is played only once and players must choose their actions simultaneously, then a. neither player has a dominant strategy. b. both players have a dominant strategy to “Cooperate”. c. both players have a dominant strategy to “Defect”. d. the players’ best response is to randomize – playing “Cooperate” with probability p = 0.5 and “Defect” with probability p = 0.5. e. there is not a Nash Equilibrium in pure strategies. 13. Now suppose that the simultaneous game presented in #12 is repeated infinitely. For what range of interest rates would the players be able to sustain an agreement to cooperate? a. r ≤ 200% b. r ≤ 100% c. r ≤ 90% d. r ≤ 50% e. r ≤ 0% A risk-neutral worker can choose to exert either low or high effort. The manager cannot observe the worker’s action, but the manager can observe the realized revenue for the firm - either $800 or $1,000. The relationship between effort and revenue is shown below. Use this information to answer questions #14 and #15. Low Effort High Effort Cost for worker= $0 Cost for worker= $40 Prob(Rev = $800) = 80% Prob(Rev = $800) = 40% Prob(Rev = $1,000) = 20% Prob(Rev = $1,000) = 60% 14. Instead of offering a flat wage, the manager offers the worker 40% of the firm’s realized revenue. Given this labor contract, the firm’s expected profit will be a. $336 b. $504 c. $552 d. $840 e. $880 15. What’s the smallest percentage of revenue the firm can offer to incentivize the worker to choose high effort? a. 20% b. 30% c. 40% d. 50% e. 60%

Spring 2023 Version E 5 16. Of the duopoly models that we studied, industry profits are highest in _______________, and consumers are happiest in _____________________. a. Cournot, Stackelberg b. Stackelberg, Bertrand c. Cournot, Bertrand d. Stackelberg, Cournot e. Bertrand, Cournot Blanche Rose Stay In Go Out Stay In 2, 2 0, 1 Go Out 1, 0 3, 3 Blanche and Rose can’t remember what they planned to do this evening. Both would prefer to go out, but not on their own. They live in the 1980s and don’t have cell phones, so they must make their choice without knowing the other’s plans. Their payoffs are described in game the matrix above. Use this information to answer questions #17 and #18. 17. If Blanche chooses to “Stay In” with 𝑝𝑝 = 0.5 and “Go Out” with 𝑝𝑝 = 0.5 , what is Rose’s best response? a. Rose chooses “Stay In” with 𝑝𝑝 = 0.5 and “Go Out” with 𝑝𝑝 = 0.5 . b. Rose chooses “Stay In” with 𝑝𝑝 = 0.25 and “Go Out” with 𝑝𝑝 = 0.75 . c. Rose chooses “Stay In” with 𝑝𝑝 = 1 and “Go Out” with 𝑝𝑝 = 0 . d. Rose chooses “Stay In” with 𝑝𝑝 = 0 and “Go Out” with 𝑝𝑝 = 1 . e. Any strategy or combination of strategies is a best response for Rose. 18. Is Blanche’s strategy described in question #17 part of a mixed strategy Nash Equilibrium (NE)? a. Yes. This strategy is part of the mixed strategy NE for this game. b. No. There is not a mixed strategy NE for this game. c. No. There is a mixed strategy NE for this game, but it does not include this strategy. d. No. This strategy is part of a pure strategy NE. e. There is not enough information provided to answer this question. 19. When buyers lack information about product quality, warranties can serve as a credible signal only if a. Consumers are risk averse. b. The cost of providing the warranty is higher for firms that provide low-quality products. c. The cost of providing the warranty is the same for firms that provide high- and low-quality products. d. The warranty is offered regardless of the quality of the product. e. The cost of providing the warranty is higher for firms that provide high-quality products. 20. In order for a set of strategies to constitute a Nash Equilibrium a. Each player must adopt a dominant strategy b. Each player must adopt a mixed strategy c. Players must coordinate to adopt the set of strategies that will maximize their joint payoffs. d. Each player must adopt a strategy that is a best response to the strategies of the other players. e. Each player must adopt a strategy that results in the best outcome for the other player.

Spring 2023 Version E 7 Player 2 Player 1 Left Right Up 4, 12 6, 15 Down 3, 20 5, 18 25. Which of the following is true about the simultaneous, one-shot game presented above? a. Player 1 does not have a dominant strategy. b. Player 2 does not have a dominant strategy. c. There is more than one pure strategy Nash Equilibrium. d. This is an example of a prisoner’s dilemma game. e. All the above statements are true.

Spring 2023 Version E 8 Answers 1. E 2. B 3. B 4. D 5. E 6. A 7. C 8. E 9. D 10. E 11. C 12. C 13. B 14. B 15. D 16. C 17. D 18. C 19. B 20. D 21. A 22. D 23. D 24. B 25. B