Consider the following dynamic game between two players. Each player chooses one of the actions "keep" or "share" when it is his/her turn to move. There is initially a pot of money with $2 dollars in it. P1 moves first. If he chooses "keep" the game ends with P1 getting all the cash in the pot, and P2 getting nothing. If he chooses "share", $200 dollars is added to the pot, and the game proceeds to the next stage, where P2 gets to choose. If P2 chooses "keep" she gets all the money in the pot, and P1 gets nothing, and the game ends. If she chooses "share", $2000 is added to the pot, and P1 gets to choose one last time. If P1 then chooses "keep" he gets to walk away with all the cash. If he chooses "share", a further $20,000 is added to the pot. Then, in this last round P2 gets a choice: either keep all the cash in the pot or to split the cash in half with P1. The game ends after this choice. How many dollars does P1 earn in the equilibrium?

Consider the following dynamic game between two players. Each player chooses one of the actions "keep" or "share" when it is his/her turn to move. There is initially a pot of money with $2 dollars in it. P1 moves first. If he chooses "keep" the game ends with P1 getting all the cash in the pot, and P2 getting nothing. If he chooses "share", $200 dollars is added to the pot, and the game proceeds to the next stage, where P2 gets to choose. If P2 chooses "keep" she gets all the money in the pot, and P1 gets nothing, and the game ends. If she chooses "share", $2000 is added to the pot, and P1 gets to choose one last time. If P1 then chooses "keep" he gets to walk away with all the cash. If he chooses "share", a further $20,000 is added to the pot. Then, in this last round P2 gets a choice: either keep all the cash in the pot or to split the cash in half with P1. The game ends after this choice. How many dollars does P1 earn in the equilibrium?

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

A small community has 10 people, each of whom has a wealth of $3,000. Each individual must choose whether to contribute $300 or $0 to the support of public entertainment for their community. The money value of the benefit that a person gets from this public entertainment is one half of the total amount of money contributed by all individuals in the community. This game has a Nash equilibrium in which 5 people contribute $300 and for public entertainment and 5 people contribute nothing. This game has a dominant strategy equilibrium in which nobody contributes anything for public entertainment. This game has no Nash equilibrium in pure strategies, but has a Nash equilibrium in mixed strategies. This game has a dominant strategy equilibrium in which all 10 citizens contribute $300 to support public entertainment. This game has two Nash equilibria, one in which everybody contributes $300 and one in which no- body contributes $300.
Up ооооо Down Player 1 Up No EFFICIENT equilibrium exists Down Up Down Player 2 P1 gets $120 P2 gets $5 P1 gets $100 P2 gets $10 P1 gets $95 P2 gets $95 In the game above, what is/are the EFFICIENT sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) (down, down) P1 gets $15 P2 gets $25
Consider the below payoff matrix for a game of chicken. Two players drive their cars down the center of the road directly at each other. Each player chooses SWERVE or STAY. Staying wins you more payoff only if the other player swerves. Swerving loses face if the other player stays. However, the worst outcome is when both players stay. Stay Swerve Stay -0,-0 -6,6 Swerve 6,-6 9,9 Player 1 chooses rows and Player 2 chooses columns. Denote the probability of "Stay" for Player 1 as p and for Player 2 as 9. What is the value of p so that Player 2 is indifferent between Stay and Swerve? Write your answer as a decimal number with 2 decimal places (e.g. 0.05)
Consider a game in which there is $4 to be divided, and the first mover is only permitted to make one of three proposals: (a) $3 for the first mover and $1 for the second mover, (b) $2 for each, or (c) $1 for the first movier and $3 for the second mover. The second mover is shown the proposal and can either accept, in which case it is implemented, or reject and cause each to earn $0. Show this game in extensive (tree) form. Be sure to show the payoffs for each person, with the first mover listed on the left, for each of the six terminal nodes.
Question 28 Consider the following Extended Form Game: 01 O 5 O 3 A 09 (2,3) P1 A' (5,5) A' B (3,8) A P2 B' P2 B' (1,9) Player 1 always plays B. Player 2 chooses the strategy (B', B'). What is the payoff of player 1? P1 B (9,1)
Samiyah and DeAndre decide to play the following game. They take turns choosing either 1, 2, or 3. As each number is chosen, it is added to the previously chosen numbers. The winner is the player who chooses a number that brings the cumulative number to 10. For example, if Samiyah chooses and DeAndre chooses 2 (so the cumulative number is 5) and Samiyah chooses 2 and DeAndre chooses 3 then DeAndre wins as his choice of 3 results in the sum equaling 10. Using SPNE, who wins?
4. Two investors have each deposited 5 (all amounts are in $10,000s) with a bank. The bank has invested these deposits in a long-term project. If both investors make withdrawals at date 1 then each receives 3 and the game ends. If only one investor makes a withdrawal at date 1 then that investor receives 5, the other receives 1, and the game ends. Finally, if neither investor makes a withdrawal at date 1 then the project matures and the investors make withdrawal decisions at date 2. If both investors make withdrawals at date 2 then each receives 7 and the game ends. If only one investor makes a withdrawal at date 2 then that investor receives 9, the other receives 5, and the game ends. Finally, if neither investor makes a withdrawal at date 2 then the bank returns 7 to each investor and the game ends. Show the bi-matrix for dates 1 and 2.
Consider the following game. You will roll a fair, 6-sided die either once or twice. You decide whether to do the second roll after you see how the first one lands. The payoff is $n, where n is the outcome of the last roll. For example, if the first roll lands 4 and the second lands 2, you win $2. If you only do one roll and it lands 4, you win $4. Suppose you make your decision about whether to go for a second roll based on expected monetary value. Then you will go for a second roll if (and only if) the first roll lands x or lower. What is x?
Consider the following sequential game. Player 1 plays first, and then Player 2 plays after observing the choice of Player 1. At the bottom of the decision tree, the first number represents the payoff of Player 1, while the second number represents the payoff of Player 2. For player 2, A stands for Accommodate and F stands for Fight. Player 1 Enter Player 2 A F A Stay out Player 2 F (16,30) (-6,18) In the Nash equilibrium of this game, player 2 earns Player 2 player 1 would play (0,40) (0,20) ✓an incentive to threaten F because, if player 1 believed him then so that player 2 would earn ✓. However, this threat is
Cameron and Luke are playing a game called ”Race to 10”. Cameron goes first, and the players take turns choosing either 1 or 2. In each turn, they add the new number to a running total. The player who brings the total to exactly 10 wins the game. a) If both Cameron and Luke play optimally, who will win the game? Does the game have a first-mover advantage or a second-mover advantage? b) Suppose the game is modified to ”Race to 11” (i.e, the player who reaches 11 first wins). Who will win the game if both players play their optimal strategies? What if the game is ”Race to 12”? Does the result change? c) Consider the general version of the game called ”Race to n,” where n is a positive integer greater than 0. What are the conditions on n such that the game has a first mover advantage? What are the conditions on n such that the game has a second mover advantage?
Not Play 1 Play 11 2 1 Trust Distrust 1 Steal Share 0 2 10 0 55 5 5 Find all of the pure strategy Nash Equilibria of this game. There can be more than one equilibrium. [Here ((Not Play, Steal), (Trust)) indicates that player 1 chooses Not Play at the first decision node and Steal at the second decision node, and 2 chooses Trust at his unique decision node.] a) ((Play, Share), (Trust)) b) ((Not play, Share), (Distrust)) c) ((Not play, Steal), (Distrust)) d) ((Not play, Steal), (Trust)) ☐ e) ((Play, Steal), (Distrust))
Find all of the Nash equilibrium of the following three player game. Player 1 chooses rows (a,b). Player 2 chooses columns (c,d). Player 3 chooses matrices (x.y). Player 3 receives the third listed payoff for cach outcome. 5,5,5 4,4,0 8,8,3 7,7,3 1,3,1 4,2,0 3,2,4 3,1,0 a by A) (b,d.x) and (a,d.y) B) (b.cy) OC) (b,d,x) D) (a,d,x) and (b,c.y) E) (b,c,x) OF) (a,d.x)