2. Paul and Stella play a game with three strategies each, T, M, and B for Paul, and L,C, and R for Stella. Both move simultaneously. The payoffs are given by thefollowing form:StellaLсRPaulT(8,4)(10, 2)(2,3)M(4,2)(10, 1)(5,7)B(1,4)(10, 3)(9,-4)a. Which strategy is dominated?b. What is the pure-strategy Nash equilibrium? Identify all if there are more than one.c. If Paul moved first, so that Stella observed it, which strategy would Paul choose?Now assume the game is simplified into two strategies for each player. Paul plays T or B,and Stella plays L or R. They move simultaneously. The (new) payoffs are:StellaLRPaulT(3,1)(-1, -3)B(-2,-3)(1,4)d. What is the Nash equilibrium in pure strategies? Identify all if there are more thanone.e. What is the mixed-strategy Nash equilibrium?

Answered: Image /qna-images/answer/154adfbd-448c-4cc3-880d-50e9535c13ca.jpg

Answered: 2. Paul and Stella play a game with…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider a new card game between 2 players: Jim (player 1) and Angella (player 2) Jim is dealt two cards : ♡8 and ♠️9 . Angella is also dealt two cards: ♢6 and ♣️6 . Now, each of the players will play 1 card both at the same time. The payoff of Jim is 4 points if he plays a card of opposite color (red/black) than Angella, and otherwise his payoff is 10 points. The payoff of Angella is 3 points if the difference of the already played card numbers is greater than 4, otherwise her payoff is 2 points. 1. Find the Best Responses for Angella.2. Find all the Nash Equilibriums of the game (if any).
Consider a symmetric game with 10 players. Each player chooses among three strategies: x, y, and z. Let nx denote the number of players who choose x, ny denote the number of players who choose y, and nz denote the number of players who choose z. (So, nz = 10−nx−ny.) The payoff to a player from choosing strategy x is 10−nx (note that nx includes this player as well), strategy y is 13−2ny (again ny includes this player as well), and strategy z is 3. (a) Show that a Nash equilibrium must have at least one person choosing x and at least one person choosing y. (Hint: In a Nash equilibrium, no player can do better by doing something different.) b) Find all Nash equilibria.
In Section 5.5 we showed the following two-person, zero-sum game had a mixed strategy: Player B b1 b2 b3 a1 0 -1 2 Player A a2 5 4 -3 a3 2 3 -4 a. Which strategies are dominated? a1, a2, a3, b1, b2, b3 b. Does the game have a pure or mixed strategy?
Consider a two-player game that is set up with two piles of stones. The two players are taking turns removing stones from one of the two piles. In each turn, a player must choose a pile and remove one stone or two stones from it. The player who removes the last stone (making both piles empty) wins the game. Show that if the two piles contain the same number n ∈ Z+ of stones initially, then the second player can always guarantee a win.
In a Stackelberg game, what is the best response that follower firm 2 can make to the choice y1 already made by the leader, firm 1?
Consider a "modified" form of "matching biased coins" game problem. The matching player is paid Rs.8 if the two coins turn both heads and Rs.12 if the coins turn both tails. The non-matching player is paid Rs.3 when the two coins do not match. Given the choice of being the matching or non-matching player, which one would you choose and what would be your strategy?.
In a game, a participant is given three attempts to hit a ball. On each try, she either scores a hit, H, or a miss, M. The game requires that the player must alternate which hand she uses in successive attempts. That is, if she makes her first attempt with her right hand, she must use her left hand for the second attempt and her right hand for the third. Her chance of scoring a hit with her right hand is .7 and with her left hand is .4. Assume that the results of successive attempts are independent and that she wins the game if she scores at least two hits in a row. If she makes her first attempt with her right hand, what is the probability that she wins the game?
two players A and B agree to play until one of them wins a certain number of games. P(A wins a game)=p and P(B wins a game)=1-p=q. However, they are forced to quit when A still has a games to win and B still has b games to win. How should they divide their stance to be fair?
A three-finger Morra game is a game in which two players simultaneously show one, two, or three fingers at each round. The outcome depends on a predetermined set of rules. Here is an interesting example: If the numbers of fingers shown by A and B differ by 1, then A loses one point. If they differ by more than 1, the round is a draw. If they show the same number of fingers, A wins an amount equal to the sum of the fingers shown. Determine the optimal strategy for each player. (Enter your probabilities as fractions.) Player A should show one finger with probability _____ , two fingers with probability _____ , and three fingers with probability ______ . Player B should show one finger with probability _______ , two fingers with probability ________ , and three fingers with probability ________ . Find the expected value of the game. The expected outcome is the player A will win __________ points per round, on average.
A fast food company is offering a prize promotion game. The company claims that in 0.5 % of all orders will receive $100 cash1% of all orders will receive $ 10 cash and 10\% of orders will receive a coupon for a free soft drink. The remaining orders will receive no prizes. A group of long- time customers were excited about the new promotion, and over the course of the promotion, they placed 651 ordersOf these orders, 2 ended up winning $100,6 won $10 and 52 won a free soft drink. If this group wanted to do a chi-squared goodness of fit test to test the advertised odds, what would be the appropriate null and alternative hypotheses?
I am stuck on this question, Three people are going to play a cooperative game. They are allowed to strategize before the game begins, but once it starts they cannot communicate with one another. The game goes as follows. A fair coin is tossed for each player to determine whether that player will receive a red hat or a blue hat, but the color of the hat (and result of the coin toss) is not revealed to the player. Then the three players are allowed to see one another, so each player sees the other two players’ hats, but not her own. Simultaneously, each player must either guess at the color of her own hat or ‘pass’. They win if nobody guesses incorrectly and at least one person guesses correctly (so they can’t all pass). The players would like to maximize their probability of winning, so the question is what should their strategy be? A naive strategy is for them to agree in advance that two people will pass and one person (designated in advance) will guess either red or blue. This…
if Z = 3 (a) How many pure strategy profiles exist in this game? (b) In the unique subgame perfect Nash equilibrium, what is the sum of the payoffs to the two players?

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