(DSR, Chp 6, U7) The members of a hierarchical group of three hungry lions face a piece of prey. If lion 1 does not eat the prey, the game ends. If it eats the prey, it becomes fat and slow, and lion 2 can eat it. If lion 2 does not eat lion 1, the game ends; if it eats lion 1 then it may be eaten by lion 3. Each lion prefers to eat and stay alive (payoff=4) than to stay alive but go hungry (payoff =3), but prefers to be hungry than to be eaten (payoff=2). (a) Draw the game tree, with payoffs, for this hungry lion game, and find the subgame perfect equilibrium. (b) Write out this game in normal form. Make lion 1 the row player, lion 2 the column player, and lion 3 the page/table player. (c) Find all of the Nash equilibria for the game. (d) You should have found Nash equilibria that are not subgame-perfect. For each of those equilibria, which lion is making a noncredible treat? Explain.

(DSR, Chp 6, U7) The members of a hierarchical group of three hungry lions face a piece of prey. If lion 1 does not eat the prey, the game ends. If it eats the prey, it becomes fat and slow, and lion 2 can eat it. If lion 2 does not eat lion 1, the game ends; if it eats lion 1 then it may be eaten by lion 3. Each lion prefers to eat and stay alive (payoff=4) than to stay alive but go hungry (payoff =3), but prefers to be hungry than to be eaten (payoff=2). (a) Draw the game tree, with payoffs, for this hungry lion game, and find the subgame perfect equilibrium. (b) Write out this game in normal form. Make lion 1 the row player, lion 2 the column player, and lion 3 the page/table player. (c) Find all of the Nash equilibria for the game. (d) You should have found Nash equilibria that are not subgame-perfect. For each of those equilibria, which lion is making a noncredible treat? Explain.

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

If we solve this game by elimination of dominated strategies, what payoff does Gino receive? (Gino's payoffs are located on the right of each cell, after the comma.) Gino Left Right Up (18.5, 7.4) (11.1, 33.3) Maria Down (25.9, 29.6) (14.8, 11.1) Answer:
Tom and Jerry are each given one of two cards. One card is blank, while the other has a circle on it. A player can draw a circle on the blank card or erase the circle on one that has already been drawn. Tom and Jerry make their decision separately and hand in the card at the same time.Nobody wins anything unless the two cards are handed in with one and only one circle on them. The player who hands in the card with the circle receives $20, while the one who hands in the blank card receives $10. Answer the following questions. (1) Represent the game in strategic form.(2) Find the Nash equilibria of the game (in pure strategies).
Players 1, 2, and 3 are playing a game in which the strategy of player i isdenoted yi and can be any nonnegative real number. The payoff function for player 1 is V1(y1,y2,y3) = y1 + y1y2 - (y1)2,for player 2 is V2(y1,y2,y3) = y2 + y1y2 - (y2)2,and for player 3 is V3(y1,y2,y3) = (10 - y1 - y2 - y3)y3.These payoff functions are hill shaped. Find a Nash equilibrium. (Hint: Thepayoff functions are symmetric for players 1 and 2.)
Two players play the following game for infinite times. For the player to continue to cooperate what would be the ranges of their discount factor, δ_1 and δ_2, respectively? cooperate betray cooperate (10,20) (-25,30) betray (15, -22) (-12, -18)
In this version of the ultimatum game experiment, one participant is given £100, and is told to offer to split that amount with another participant. The second player can either refuse to accept the division, in which case the participant receiving the £100 has to give it back, or can accept the division, in which case, the player receiving the money splits the £100 as proposed. For the participant who has to accept or reject the offer A) The best strategy is to accept any offer which meets the social norm for fairness. B) The best strategy is to threaten to turn down any transfer of less than £100 to ensure that the person receiving the money makes a fair offer. C) There is a dominant strategy to accept any offer because gaining some money is better than gaining no money D) There is a dominant strategy to turn down any offer other than £50 because an unequal split would be unfair.
A crime is witnessed by 3 citizens. Every citizen would like the police to be informed about the crime, but prefers that someone else reports it (filing a report is a hassle). Each of the three citizens chooses simultaneously (and independently) whether to call the police or not. When no one makes a call, every citizen receives payoff 0. If at least one citizen calls the police, citizens who call get payoff 5, and those who don't call get payoff 9. (a) Find all Nash equilibria in pure strategies. (b) Compute a symmetric Nash equilibrium in mixed strategies (i.e., an equilibrium in which every citizen calls with the same probability p E (0, 1)). (c) Does the game have a Nash equilibrium in pure or mixed strategies different from those you identified in (a) and (b)? If yes, construct one. If not, argue why not.
Two players bargain over 1 unit of a divisible object. Bargaining starts with an offer of player 1, which player 2 either accepts or rejects. If player 2 rejects, then player 1 makes another offer; if player 2 rejects once more, then player 2 makes an offer. If player 1 rejects the offer of player 2, then once more it is the turn of player 1 where he makes two consecutive offers. As long as an agreement has not been reached this procedure continues. For example, suppose that agreement is reached at period 5, it follows that player 1 makes offers in period 1,2 then player 2 makes an o er in period 3, then player 1 makes offers in 4,5. Negotiations can continue indefinitely, agreement in period 't' with a division (x, 1- x) leads to payoffs ( , (1-x)).(The difference from Rubinstein's alternating offer bargaining is that player one makes two consecutive offers, whereas player 2 makes a single offer in her turn.) a. Show that there is a subgame perfect equilibrium in which player 2's…
In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A.
Which of the following conditions correctly describes a Nash equilibrium when two firms are in the market? Multiple Choice n91s1. $2)2 (51. $2) for all s1 and 12(51, $2)212(51. 52) for all s2. aqls1, s2)22(s1, s2) for all s1 and a2(s1, 52) 2 n1ls1.52) for all s2. Rylsi. s2)2 als1. 52) for all s as1. 52)22(1. s2) for all sy and a2(s. s2)2 a1(s1, s2) for all s2
The dominant strategy of player 2 in the accompanying game is Player 1 Multiple Choice ********* 11. 12. 13. S1 S2 nonexistent. t1 11,0 10,100 Player 2 t2 6,1 5,0 t3 4,-200 0,-100
In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. Is there a pure strategy? Why or why not? Determine the optimal strategies and the value of this game. Does the game favor one player over the other? Suppose Player B decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should Player A do to improve Player A’s winnings? Comment on why it is important to follow an optimal game theory strategy.
UNIT 9 CHAPTER 5 In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. Is there a pure strategy? Why or why not? Determine the optimal strategies and the value of this game. Does the game favor one player over the other? Suppose Player B decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should Player A do to improve Player A’s winnings? Comment on why it is important to follow an optimal game theory strategy.