1. The table below shows a prisoner's dilemma in normal form. Players 1 and 2 each choosebetween D and C.DCD2,21,1010, 15,5Answer the following questions. Remember to explain your reasoning.(a) If the game is played only once, what is the equilibrium in dominant strategies?(b) If the game is played three times in a row, what action does each player choose in everyround?Suppose that the game is repeated indefinitely. The players do not discount the future. How-ever, the game ends with probability p € (0, 1) after each round. Assume that each playeruses the following grim-trigger strategy. Each player chooses C in the first round. Each playerchooses C in the current round if both players chose C in every previous round. Each playerchooses D in the current round if either player chose D in some previous round.(c) If p = 1, is it optimal for each player to use the grim-trigger strategy above given thatthe other player uses the grim-trigger strategy above? [Hint: compare the present valuesof following this strategy and of deviating from this strategy.](d) If p=, is it optimal for each player to use the grim-trigger strategy above given thatthe other player uses the grim-trigger strategy above? [Hint: compare the present valuesof following this strategy and of deviating from this strategy.]

2 1/2 D C 1 D 2,2 10,1 C 1,10 5,5

1. The table below shows a prisoner's dilemma in normal form. Players 1 and 2 each choose between D and C. D с D 2,2 1,10 с 10,1 5,5 Answer the following questions. Remember to explain your reasoning. (a) If the game is played only once, what is the equilibrium in dominant strategies? (b) If the game is played three times in a row, what action does each player choose in every round? Suppose that the game is repeated indefinitely. The players do not discount the future. How- ever, the game ends with probability p € (0,1) after each round. Assume that each player uses the following grim-trigger strategy. Each player chooses C in the first round. Each player

1. The table below shows a prisoner's dilemma in normal form. Players 1 and 2 each choose between D and C. D с D 2,2 1,10 с 10,1 5,5 Answer the following questions. Remember to explain your reasoning. (a) If the game is played only once, what is the equilibrium in dominant strategies? (b) If the game is played three times in a row, what action does each player choose in every round? Suppose that the game is repeated indefinitely. The players do not discount the future. How- ever, the game ends with probability p € (0,1) after each round. Assume that each player uses the following grim-trigger strategy. Each player chooses C in the first round. Each player

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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2 questions refer to the games below. (Fun fact, as an aside: the payoffs reflect the frequencies of the letter pairs formed by the names of the strategies in the English language, per 10,000 words.)
12. An important characteristic of a dominant strategy is that: Select one: a. it is the best strategy to dominate your opponents b. it always leads to a Nash equilibrium where all players equally well off c. it can prevent the game reaching a Nash equilibrium d. it is the best strategy for a player, regardless of whatever strategy the opponent chooses
Use the following game table to answer the question: Player 2 Y A 10, 5 6, 3 0,0 Player 1 B 2,6 1, 3 0,0 3,5 3, 4 3, 3 One of these players has a strictly dominant strategy. Which player, and what strategy is it? Player 2; Y Player 1; A Player 2; X O Player 1; B O Player 1; X
8) Consider the following game: There are 10 players. Each player is asked to write a number between 0 and 100. The player whose choice is closest to half of the average is the winner. Describe the game and discuss what would you expect to be the average number if the game were played in class with your colleagues. Do you expect them to play the Nash equilibrium strategy? Explain.
1. Consider the following game matrix. Player A Answer: Top Bottom Left a, b e, f Player B Right c, d g, h (a) If top and left are strictly dominant strategies, then what do we know the relationship of the parameters? (b) If (top, left) is a Nash equilibrium, then what do we know the relationship of the parameters? Answer: (c) If top and left are strictly dominant strategies, will (top, left) be a Nash equilibrium? Why? Answer: (d) If (top, left) is a Nash equilibrium, must the strategies be strictly dominant strategies? Why? Answer:
on Mary, UE, BD UF, AC DF, BC UF, BD DE, AC DE, BC Nancy U D Nancy -5,4 Mary -0,2 -6,2 -2.6 Which of the following answers is a subgame perfect Nash equilibrium in this game? Check all that apply. (Answers below are formatted as Mary's strategy, Nancy's strategy.)
Player 1 Cooperate (C) Defect (D) Cooperate (C) 3,3 8,0 Player 2 Defect (D) 0,8 1,1 In general, a combination of strategies is a Nash equilibrium if ... Every player is choosing a best response against the other players' strategies. Every player has a positive payoff. The players maximize the sum of their payoffs. The players choose identical strategies. If the game is repeated, which cooperative actions could benefit both players? O Both players choose C. Player 1 chooses C, Player 2 chooses D. O Player 1 chooses D, Player 2 chooses C. Both players choose D.
I have attracted a picture of my question because I don't know how to insert a table, if possible, can you please answer the question in typing because I fell hard to understand hand written works, thanks