Exercise 3.12. Three players, Avinash, Brian and John, play the following game.Two cards, one red and the other black, are shuffled well and put face down on thetable. Brian picks the top card, looks at it without showing it to the other playersGAME THEORY - Giacomo Bonanno124(Avinash and John) and puts it back face down. Then Brian whispers either "Black"or "Red" in Avinash's ear, making sure that John doesn't hear. Avinash then tellsJohn either "Black" or "Red". Finally John announces either "Black" or "Red" andthis exciting game ends. The payoffs are as follows: if John's final announcementmatches the true color of the card Brian looked at, then Brian and Avinash give $2each to John. In every other case John gives $2 each to Brian and Avinash.(a) Represent this situation as an extensive-form game.(b) Write the corresponding strategic form (or normal form) assuming that theplayers are selfish, greedy and risk neutral.

(a) The extensive-form game representation of this situation can be illustrated as follows (b) The…

Answered: Exercise 3.12. Three players, Avinash,…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Make sure you clearly write your name and submission:. 1. Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player chooses one of 3 strategies: rock, paper, or scissors. Then, both players reveal their choices. The outcome is determined as follows. If both players choose the same strategy, neither player wins or loses anything. Otherwise: • "paper covers rock": if one player chooses paper and the other chooses rock, the player who chose paper wins and is paid 1 by the other player. • "scissors cut paper": if one player chooses scissors and the other chooses paper, the player who chose scissors wins and is paid 1 by the other player. • "rock breaks scissors": if one player chooses rock and the other player chooses scissors, the player who chose rock wins and is paid 1 by the other player. We can write the payoff matrix for this game as follows: rock paper -1 0 1 rock 0 paper 1 scissors -1 (a) Show that this game does not have a pure Nash equilibrium. 1 X 3 (b) Show that…
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.
Felix and Jocelyn are arrested and charged with armed robbery. The police interview both suspects separately about their involvement in the crime. Each suspect has to make a decision. They can betray the other suspect by confessing that they both committed the crime, or they can cooperate with the other suspect by remaining silent. The table shows the sentences that Felix and Jocelyn will receive given their choices. Use the table to answer the question. What will be the dominant strategy outcome for Felix and Jocelyn? They both get 12 years. O They both get 10 years. Felix gets 5 years, and Jocelyn gets 15 years. Jocelyn gets 5 years, and Felix gets 15 years. Felix Stay silent Confess Stay silent Jocelyn gets 10 years Felix gets 10 years Jocelyn Jocelyn gets 15 years Felix gets 5 years Confess Jocelyn gets 5 years Felix gets 15 years Jocelyn gets 12 years Felix gets 12 years
You and I play the following game. Hidden from you, I put a coin in my hand: with probability p it is a 10 pence coin and otherwise it is a 20 pence coin. You now guess which coin is in my hand: you guess it is 20 pence with probability s and otherwise you guess it is a 10 pence coin. You get to win the coin if you guess correctly and otherwise win nothing. What (in terms of p and s) is your expected gain in pence from playing this game once with me? Challenge: suppose we are going to play repeatedly and you want to maximise your gain and I wish to minimise my loss. What value of p should I choose and what value of s should you choose? (This question is somewhat ill-defined, but it does have an interesting possible answer.) (Note: anything labelled "challenge" will not be part of the hand-in.)
Dairy King Advertise Doesn't Advertise Advertise 7,7 12, 3 Creamland Doesn't Advertise 3, 12 10, 10 For example, the upper right cell shows that if Creamland advertises and Dairy King doesn't advertise, Creamland will make a profit of $12 million, and Dairy King will make a profit of $3 million. Assume this is a simultaneous game and that Creamland and Dairy King are both profit-maximizing firms. If Creamland decides to advertise, it will earn a profit of not advertise. million if Dairy King advertises and a profit of million if Dairy King does If Creamland decides not to advertise, it will earn a profit of does not advertise. million if Dairy King advertises and a profit of million if Dairy King If Dairy King advertises, Creamland makes a higher profit if it chooses If Dairy King doesn't advertise, Creamland makes a higher profit if it chooses Suppose that both firms start off not advertising. If the firms act independently, what strategies will they end up choosing? ◇ Creamland will…
Two roommates John and Joe are playing a simultaneous game of cleaning the apartment. If neither of them clean, the apartment gets filthy and both get a utility of 2. If John cleans and Joe doesn’t, John gets a utility of 1 and Joe gets a utility of 4. If Joe cleans and John doesn’t, Joe gets a utility of 1 and John gets a utility of 4 and if both clean up the apartment, they each get a utility of 3.What is the Nash equilibrium of this game? Group of answer choices Joe cleans, John doesn’t John cleans, Joe doesn’t Both of them clean the apartment Neither of them clean the apartment
Find all ESS, if any, in the following symmetric game. Please check all that apply: Stop OMixed 1/4 Go and 3/4 Stop OMixed 1/2 Go and 1/2 Stop OMixed 2/3 go and 1/3 Stop Go There are no ESS Go Stop Go 2.2 5,3 Stop 3,5 2,2
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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?
Ann and Stella want to watch a movie together this weekend. There are 8 movies playing in theatres on Saturday, and 11 movies playing in theatres on Sunday. Ann first chooses a day - either Saturday or Sunday. Then, knowing the day that Ann picked, Stella chooses one movie from those playing in theatres on that day. How many pure strategies does Stella have?

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