1Y You have to decide whether to invest $100 in a friend's enterprise, where in a year's time the money will increase to $150. You have agreed that your friend will split the profits evenly each year with you. Your alternative is to keep at the bank at an interest rate of r. Suppose this game is played repeatedly infinitely often. The rate of interest between any two successive periods is r, the same as that in the bank and the same for you and your friend. What is the cut-off interest rate which will make cooperation possible? KI02

1Y You have to decide whether to invest $100 in a friend's enterprise, where in a year's time the money will increase to $150. You have agreed that your friend will split the profits evenly each year with you. Your alternative is to keep at the bank at an interest rate of r. Suppose this game is played repeatedly infinitely often. The rate of interest between any two successive periods is r, the same as that in the bank and the same for you and your friend. What is the cut-off interest rate which will make cooperation possible? KI02

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

4. Finding Nash equilibria in sequential games Hubert and Larry are trying to decide what movie to see together. There are two theaters in town, each playing one movie. Hubert would prefer to see one movie (call it movie H) and Larry would prefer to see the other movie (movie L), but both would prefer to see one of the movies together rather than their preferred movies separately. As they are discussing where to meet, Larry's cell phone loses power, cutting the conversation short. Both movies start in 10 minutes; therefore, each person must decide which movie to see without being able to communicate with the other. The following payoff matrix represents the game they are playing. Hubert Movie H Movie L Hubert Larry Movie H 45, 30 0,0 Suppose Larry is near home and quickly starts charging his phone. At home, however, he gets terrible phone service but a strong wireless signal. Therefore, instead of calling Hubert, he uses a smartphone app to observe Hubert's location using GPS. Because…
4. Consider the following model of a bank run. Depositors may either Hold or Withdraw their funds from a bank. Both players hold deposits of 6, which earn interest of 1 if kept in the bank. If either depositor withdraws then the bank fails. If both try to withdraw then each depositor can only recover half of their deposits. The payoffs for a two-player version of this game are given below: Player 2 Player 1 Hold Withdraw Hold 7,7 6,0 Withdraw 0,6 3,3
4. Consider the following game matrix, where a and c are some fixed numbers strictly between -1 and 1: 1 -2 -1 -2 -1 C 2 2 -1 -1 1 1 1 -2 a Argue that an optimal mixed strategy of the column player is y* = (1/2,0, 0, 1/2,0), and write down an optimal mixed strategy of the row player with exactly 3 nonzero entries (probabilities). 2.
Assume the following game situation: If Player A plays UP and Player B plays LEFT then Player A gets $1 and Player B gets $3. If Player A plays UP and Player B plays RIGHT then Player A gets $2 and Player B gets $5. If Player A plays DOWN and Player B plays LEFET then Player A gets $4 and Player B gets $2. If Player A plays DOWN and Player B plays RIGHT then Player A gets $1 and Player B gets $1 What is the Mixed Strategy Equilibrium for Player B? O. (LEFT, RIGHT) = (1/8, 3/8) O. (LEFT, RIGHT) = (1/4, 3/4) O. (LEFT, RIGHT) = (1/2, 1/2) O. (LEFT, RIGHT) = (3/8, 1/8)
2. Consider the following simultaneous move stage game. In each cell, player l's payoff is shown first. Player 2 L C R T 3, 1 0 ,0 5 , 0 Player 1 M 2, 1 I, 2 3 , 1 В 1, 0 , 1 4, 4 This game is played twice, without discounting of the second stage payoffs. Both players observe the outcome of the first stage prior to making their second stage choices. Determine whether or not (4,4) can be the first stage payoffs from a pure strategy subgame perfect Nash equilibrium. Explain your answer carefully.
Consider the two-player game depicted below w А 1,5 2,2 0,4 3,11 В 13,0 4,1 2,5 4,2 с 1,3 2,6 5,2 2,0] a. What is Player 2's best response if Player 1 plays B? b. What is Player l's best response if Player 2 plays z? c. What are the pure strategy Nash Equilibria? సా
6.
ABC Inc. Offer Rebate No Rebate XYZ Corp offer Rebate 20.10 30,0 No Rebate 12, 16. 20, 4 In the game above, in the equilibrium strategies: Lutfen birini seçin O A are for XYZ to offer a rebate, and ABC not to offer a rebate. O B are for ABC to offer a rebate, and XYZ not to offer a rebate. O C are for both firms to effer no rebate OD are for both firms to offer rebates
D5
2. Consider the two-player strategic form game represented in the following payoff table: t 1 m b 7,2 1,2 3,7 2 M 2,4 3,4 1,6 R 1,3 7,1 4,2 Player 1 chooses between rows, S₁ = {t, m, b), and receives the first listed payoff in each cell. Player 2 chooses between columns, S₂ = {L, M, R), and receives the second listed payoff in each cell. a. Does either player have a strictly dominant strategy? Explain. b. Explaining your steps carefully, identify the set of rationalizable strategies in this game. c. Making sure to explain your solution method, solve for all pure strategy Nash equilibria in this game.
9
3. Find ALL Nash equilibria of the following game: Nature begins by choosing one of the 2x2 games. It chooses the left game with probability a, and the right game with probability 1- a. Player 2 is INFORMED about nature's choice but player 1 IS NOT informed. L KR R 0,0| 5, 0,0 U 2, 2 0, 3 U D 3, 1, 1 D 1 Are there values of a for which there exists a mixed strategytequilibrium?