Alice and Bob are playing a repeated game in which a certain stage game is played twice in succession. All behaviour in the first period is observed by both players before the second period commences. In the stage game, Alice has 3 pure strategies and Bob has 2 pure strategies. How many pure strategies does Bob have in the repeated game? (If necessary, use a calculator to compute this number.) 2 6 2187 3 36 64 7 729 128 216 Please do fast ASAP fast

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A route in the city has trains that depart from station every 20 minutes. It takes a train 40 minutes to make a trip from the station to its destination. For commuters, shorter trips are considered better. Suppose that one such train with 200 commuters on it is about to depart when an additional commuter (who is running slightly late) blocks the doors in order to get on the train, which delays the train by 15 seconds. If this commuter had chosen not to block the train doors, they would have to catch the next train after this one. Question: (Please show the detailed calculation process) What is the private marginal gain of the commuter who barges on the train? What is the marginal spillover effect to all the commuters on the train in terms of travel time? What is the change in the total travel time to all the commuters on the train?

Individual A Cooperate Defect Individual B Cooperate 28, 28 34,8 Defect 8, 34 12, 12 Suppose individuals live in villages that are homogeneous by type and a fractions of their interactions takes place in their village, the rest occurring in the city where the types were mixed. The fraction of the population who are cooperators is a. a) Write the expected return functions for cooperate and defect as a function of s and a. b) Under which conditions does an interior equilibrium exist for the fraction of the population playing cooperate (a) c) If the interior equilibrium for a exists, is the interior equilibrium unstable or stable? d) Find the impact of higher s on the interior equilibrium for a. What intuitively does this outcome mean? Discuss your answer.

A1

How many total pure and mixed-strategy equilibria does the game below have? Player 2 y a 3. 3 4, 2 Player 1 6, 3 2, 6 5,3 3, 2 Numerical answer b.

Firm B Q=5 Q=6 Q=5 (24, 24) (30, 10) Q=6 (10, 30) (19, 19) Firm A This table shows a game played between two firms, Firm A and Firm B. In this game each firm must decide how much output (Q) to produce: 5 units or 6 units. The profit for each firm is given in the table as (Profit for Firm A, Profit for Firm B). Refer to Table. The dominant strategy For Firm A is to produce 5 units and the dominant strategy for Firm B is to produce 6 units. 5 units and the dominant strategy for Firm B is to produce 5 units. 6 units and the dominant strategy for Firm B is to produce 5 units. 6 units and the dominant strategy for Firm B is to produce 6 units.

Answer these questions on a separate sheet of paper. -3 1 Consider the game defined by the matrix: P = 4 -3 1. If Row Player uses the strategy R = [0.4 0.6], calculate the matrix R1P to determine what strategy the Column Player should use. What will be the expected payout of the game? 2. If Row Player uses the strategy R2 = [0.7 0.3], determine what strategy the Column Player should use. What will be the expected payout of the game? %3D 3. Which of the strategies R1 and R2 will end up being better for Row Player? Explain.

Determine all of the Nash equilibria (pure-strategy and mixed-strategy equilibria) of the following game:

q52 If you advertise and your rival advertises, you each will earn 14 million in profits. If neither of you advertises, you will each earn 20 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn 10 million and the non-advertising firm will earn 16 million. If you and your rival plan to be in business for only one year, the Nash equilibrium is a. for each firm to advertise. b. for the other firm to advertise and your firm not to advertise. c. for your firm to advertise and the other not to advertise. d. for neither firm to advertise.