Homework Answers
The correct option is D because cooperation is not needed in every game where single player is there in the game but strategy, players and payoffs are components of almost every game.
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7) Which of the following is NOT a key component of every game? A) Strategies B)...
(a) (5 points) Do the players have any strategies which are dominated? Any dominant strategies? (b)...
(a) (5 points) Do the players have any
strategies which are dominated? Any dominant strategies?
(b) (2 points) Suppose you could create a new strategy (D) which
consisted of A x = 75% of the time and C 1 − x = 25% of the time.
If your payoff from this new strategy is the average of your
payoffs from A and C (given the percentages), what is the payoff of
D? Add it to the matrix.
(c) (3 points)...
5. [Subgame perfection] Consider the following game. Two friends, Anne (A) and Bob (B), are trying...
5. [Subgame perfection] Consider the following game. Two friends, Anne (A) and Bob (B), are trying to coordinate on a joint activity, which can be either knitting (K) or fencing (F). Both friends prefer coordinating (i.e., choosing the same activity) to not coordinating but, conditional on coordinating, A prefers K to F while B prefers F to K. In the game, A chooses K or F first; B observes A’s choice and then chooses K or F himself. 3 a....
Which of the following statements is not correct? : a) A Cournot equilibrium is an example...
Which of the following statements is not correct? : a) A Cournot equilibrium is an example of a Nash equilibrium b) There may not be a Nash equilibrium in pure strategies c) A Nash equilibrium maximizes the aggregate payoffs of the players of the game d) A Nash equilibrium is a situation in which each player chooses their best strategy given the strategies chosen by the other players in the game
6. The following stage game is played repeatedly for 2 periods. Note that both players observe...
6. The following stage game is played repeatedly for 2 periods. Note that both players observe the decisions made in period 1 before they play again in period 2. The final payoffs to each player are the sum of the payoffs obtained in each period. 112 L R T 1,1 5,0 B 0,3 7,7 (a) Represent this game in extensive form (tree diagram. How many subgames are there? (b) Using backward induction, find all subgame perfect Nash equilibria (SPE) in...
Problem #2: Nash Equilibrium with Continuous Strategies (8pts) Consider a game with continuous strategies, in which...
Problem #2: Nash Equilibrium with Continuous Strategies (8pts) Consider a game with continuous strategies, in which the two players have the following continuous payoff functions: (S1,2)= (20-4s,)s,-s 2(s1,82) (20-6s)s-s The players choose their strategies from the set s, E (-00, 00). a) Find a best-response function for cach firm. b) Using your answer to part a), solve for the Nash Equilibrium of this game.
Choose a,b,c,d 12. In the game above, who has dominant strategy? A) Player A has a...
Choose a,b,c,d
12. In the game above, who has dominant strategy? A) Player A has a dominant strategy C) B) Player B has a dominant strategy Both players have dominant strategies. D) Neither player has a dominant strategy 13. Which one is the Nash equilibrium? A) firm A competition, firm B competition. C) firm A collusion, firm B competition. B) firm A competition, firm B collusion. D) firm A collusion, firm B collusion. In the following game, all payoffs are...
4. Consider the following game that is played T times. First, players move simultaneously and independently....
4. Consider the following game that is played T times. First, players move simultaneously and independently. Then each player is informed about the actions taken by the other player in the first play and, given this, they play it again, and so on. The payoff for the whole game is the sum of the payoffs a player obtains in the T plays of the game A 3,1 4,0 0,1 В 1,5 2,2 0,1 C 1,1 0,2 1,2 (a) (10%) Suppose...
(20 points) Exercise 3: (Midterm 2018) Consider the following normal-form game, where the pure strategies for...
(20 points) Exercise 3: (Midterm 2018) Consider the following normal-form game, where the pure strategies for Player 1 are U, M, and D, and the pure strategies for Player 2 are L, C, and R. The first payoff in each cell of the matrix belongs to Player 1, and the second one belongs to Player 2. Player 2 IL CR u 6,8 2,6 8,2 Player 1 M 8,2 4,4 9,5 8,10 4,6 6,7 (7) a) Find the strictly dominated (pure)...
A game tree differs from a decision tree in that a) A game tree contains the...
A game tree differs from a decision tree in that a) A game tree contains the payoffs of only the firm making the decision b) A decision tree contains the payoffs of all players in the game. c) A game tree contains the payoffs of all of the players in the game. d) A game tree has more branches than a decision tree.
Consider the game in strategic form above where A, B, C, and D are strategies and...
Consider the game in strategic form above where A, B, C, and D are strategies and a, b, c, d, e, f, g, and h, are payoffs. Select all that apply. a. If A is weakly dominated and C is weakly dominant then (B,D) is a Nash equilibrium. b. If b > f and d = h then D is weakly dominated. c. If (A,C) is a Nash Equilibrium then it must be that . d. If a > b...
(a) (5 points) Do the players have any
strategies which are dominated? Any dominant strategies?
(b) (2 points) Suppose you could create a new strategy (D) which
consisted of A x = 75% of the time and C 1 − x = 25% of the time.
If your payoff from this new strategy is the average of your
payoffs from A and C (given the percentages), what is the payoff of
D? Add it to the matrix.
(c) (3 points)...
6. The following stage game is played repeatedly for 2 periods. Note that both players observe the decisions made in period 1 before they play again in period 2. The final payoffs to each player are the sum of the payoffs obtained in each period. 112 L R T 1,1 5,0 B 0,3 7,7 (a) Represent this game in extensive form (tree diagram. How many subgames are there? (b) Using backward induction, find all subgame perfect Nash equilibria (SPE) in...
Problem #2: Nash Equilibrium with Continuous Strategies (8pts) Consider a game with continuous strategies, in which the two players have the following continuous payoff functions: (S1,2)= (20-4s,)s,-s 2(s1,82) (20-6s)s-s The players choose their strategies from the set s, E (-00, 00). a) Find a best-response function for cach firm. b) Using your answer to part a), solve for the Nash Equilibrium of this game.
Choose a,b,c,d
12. In the game above, who has dominant strategy? A) Player A has a dominant strategy C) B) Player B has a dominant strategy Both players have dominant strategies. D) Neither player has a dominant strategy 13. Which one is the Nash equilibrium? A) firm A competition, firm B competition. C) firm A collusion, firm B competition. B) firm A competition, firm B collusion. D) firm A collusion, firm B collusion. In the following game, all payoffs are...
4. Consider the following game that is played T times. First, players move simultaneously and independently. Then each player is informed about the actions taken by the other player in the first play and, given this, they play it again, and so on. The payoff for the whole game is the sum of the payoffs a player obtains in the T plays of the game A 3,1 4,0 0,1 В 1,5 2,2 0,1 C 1,1 0,2 1,2 (a) (10%) Suppose...
(20 points) Exercise 3: (Midterm 2018) Consider the following normal-form game, where the pure strategies for Player 1 are U, M, and D, and the pure strategies for Player 2 are L, C, and R. The first payoff in each cell of the matrix belongs to Player 1, and the second one belongs to Player 2. Player 2 IL CR u 6,8 2,6 8,2 Player 1 M 8,2 4,4 9,5 8,10 4,6 6,7 (7) a) Find the strictly dominated (pure)...
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