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(3) [Dutta, Ch 2 Exercise 2.5 and 2.10 Consider the following "divide the dollar" game. Two...
Consider the following extensive form game P1 RP:2 L2 R2 L1 R1 (2,2) (0,3) 1. How many sub-games are there in this game...
Consider the following extensive form game P1 RP:2 L2 R2 L1 R1 (2,2) (0,3) 1. How many sub-games are there in this game? What is the Subgame Perfect Equilibrium? 2. Represent this game as a Normal form game and find all pure strategy Nash Eq. Is there a mixed Nash eq. in this game? If yes, show one. If not, argue why not 3. Now assume that P2 cannot observe P1's action before he makes his move. As such, he...
IDSDS= Iterative Deletion of Strictly Dominated Strategies Exercise 3- Unemployment benefits. Consider the following simultaneous-move game...
IDSDS= Iterative Deletion of Strictly Dominated Strategies
Exercise 3- Unemployment benefits. Consider the following simultaneous-move game between the government (row player), which decides whether to offer unemployment benefits, and an unemployed worker (column player), who chooses whether to search for a job. As you interpret from the payoff matrix below, the unemployed worker only finds it optimal to search for a job when he receives no unemployment benefit; while the government only finds it optimal to help the worker when...
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2....
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2. After having observed the choice of A, Player B chooses between two projects Pl or P2. The payoffs are as follows: If A chooses TI and B chooses P1 the payoffs are (12, 8), where the first payoff is for A and the second for B; if A chooses T1 and B opts for P2 the payoffs are (20, 7); if A chooses T2...
2. (The Dynamic Model of the Market for Lemon) Consider the dynamic version of the model...
2. (The Dynamic Model of the Market for Lemon) Consider the dynamic version of the model of the market for lemon with a buyer (player 1) and a seller (player 2). The seller owns a car whose quality is low (L), medium (M), or high (H), each with equal probability (1/3). The seller knows the quality of the car, but the buyer does not. The seller assigns value 0 to low-quality car, value 3 to a medium-quality car and value...
(2) Consider the following game: P U M D LR 3,1 0,2 1,2 1,1 0,4 3,1...
(2) Consider the following game: P U M D LR 3,1 0,2 1,2 1,1 0,4 3,1 (a) Show that M is a dominated strategy when mixed strategies are used. (b) Using the observation in part (a) above, find the mixed strategy NE for this game. (3) (Bertrand Model with sequential move) Consider a Bertrand duopoly model with two firms, F and F2 selling two varieties of a product. The demand curve for Fi's product 91 (P1.p2) = 10 - P1...
Problem 2.(20 points) Consider the following game: In the first step, Alice has two $10 bills...
Problem 2.(20 points) Consider the following game: In the first step, Alice has two $10 bills and can take one of the following two actions: (i) she can give S20 to Bob or (ii) she can give one of the S10 bills to Bob. All the money will be used to buy popcorns before the movie they will see. Each one dollar of popcorn gives one unit of payoff for the player who buys it. In the second step, they...
Problem 2.(20 points) Consider the following game: In the first step, Alice has two $10 bills...
Problem 2.(20 points) Consider the following game: In the first step, Alice has two $10 bills and can take one of the following two actions: (i) she can give S20 to Bob or (ii) she can give one of the S10 bills to Bob. All the money will be used to buy popcorns before the movie they will see. Each one dollar of popcorn gives one unit of payoff for the player who buys it. In the second step, they...
Consider the following extensive form game P1 RP:2 L2 R2 L1 R1 (2,2) (0,3) 1. How many sub-games are there in this game? What is the Subgame Perfect Equilibrium? 2. Represent this game as a Normal form game and find all pure strategy Nash Eq. Is there a mixed Nash eq. in this game? If yes, show one. If not, argue why not 3. Now assume that P2 cannot observe P1's action before he makes his move. As such, he...
IDSDS= Iterative Deletion of Strictly Dominated Strategies
Exercise 3- Unemployment benefits. Consider the following simultaneous-move game between the government (row player), which decides whether to offer unemployment benefits, and an unemployed worker (column player), who chooses whether to search for a job. As you interpret from the payoff matrix below, the unemployed worker only finds it optimal to search for a job when he receives no unemployment benefit; while the government only finds it optimal to help the worker when...
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2. After having observed the choice of A, Player B chooses between two projects Pl or P2. The payoffs are as follows: If A chooses TI and B chooses P1 the payoffs are (12, 8), where the first payoff is for A and the second for B; if A chooses T1 and B opts for P2 the payoffs are (20, 7); if A chooses T2...
2. (The Dynamic Model of the Market for Lemon) Consider the dynamic version of the model of the market for lemon with a buyer (player 1) and a seller (player 2). The seller owns a car whose quality is low (L), medium (M), or high (H), each with equal probability (1/3). The seller knows the quality of the car, but the buyer does not. The seller assigns value 0 to low-quality car, value 3 to a medium-quality car and value...
(2) Consider the following game: P U M D LR 3,1 0,2 1,2 1,1 0,4 3,1 (a) Show that M is a dominated strategy when mixed strategies are used. (b) Using the observation in part (a) above, find the mixed strategy NE for this game. (3) (Bertrand Model with sequential move) Consider a Bertrand duopoly model with two firms, F and F2 selling two varieties of a product. The demand curve for Fi's product 91 (P1.p2) = 10 - P1...
Problem 2.(20 points) Consider the following game: In the first step, Alice has two $10 bills and can take one of the following two actions: (i) she can give S20 to Bob or (ii) she can give one of the S10 bills to Bob. All the money will be used to buy popcorns before the movie they will see. Each one dollar of popcorn gives one unit of payoff for the player who buys it. In the second step, they...
Problem 2.(20 points) Consider the following game: In the first step, Alice has two $10 bills and can take one of the following two actions: (i) she can give S20 to Bob or (ii) she can give one of the S10 bills to Bob. All the money will be used to buy popcorns before the movie they will see. Each one dollar of popcorn gives one unit of payoff for the player who buys it. In the second step, they...
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