QUESTION 2Player 1 and Player 2 will play one round of the Rock-Paper-Scissors game. The winner receives a payoff +1, the loser receives a payoff-1. If it is a tie, then each player receives a payoff of zero. Suppose Player 2is using a non-optimal strategy: he/she plays Rock with probability 35%; Paper with probability 45%; and Scissors with probability 20%. Given that Player 1 knows Player 2 is using this strategy, the best response ofPlayer 1 is to playO a mixed strategy with probability 1/3 each (Rock, Paper and Scissors)O Rock with probability 100%O Paper with probability 100%Scissors with probability 100%O any strategy (any strategy is a best response for Player 1)

from given data we make table: P(Rock)=0.35 P(Paper)=0.45 P(Scissor)=0.20 If win +1 If lose -1 If…

Answered: Player 1 and Player 2 will play one…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A dairy farmer thinks that the average weight gain of his cows depends on two factors: the type of grain that they are fed and the type of grass that they are fed. The dairy farmer has four different types of grain from which to choose and three different types of grass from which to choose. He would like to determine if there is a particular combination of grain and grass that would lead to the greatest weight gain on average for his cows. He randomly selects three one-year-old cows and assigns them to each of the possible combinations of grain and grass. After one year he records the weight gain for each cow (in pounds) with the following results. Is there sufficient evidence to conclude that there is a significant difference in the average weight gains among the cows for the different types of grain? Cow Weight Gain (Pounds) Grass A Grass B Grass B Grain A 163163 287287 305305 267267 304304 325325 198198 348348 172172 Grain B 338338 291291 223223 286286 168168…
Suppose that you watch the game show over many years and find that door #1 hides the car 50% of the time, door #2 has the car 40% of the time, and door #3 has the car 10% of the time. What then is your optimal strategy? In other words, which door should you pick initially, and then should you stay or switch? What is your probability of winning with the optimal strategy? Explain.
In this Decision Point activity, you began to explore game theory: specifically, how your outcomes are dependent not just on your own choices, but also on the reactions of competitors. Use what you learned from this decision point, and information from the chapter to answer the following question. Suppose Nike and Adidas are considering whether to develop new advertising campaigns. For each pair of strategies, the blue triangle shows Nike's payoff and the yellow triangle shows Adidas's payoff, in billions. Use this information to complete the sentences. Adidas's choices Advertise Do not advertise Advertise $6b Nike's choices -$3b $6b $14b Do not advertise $14b $10b -$3b $10b The best outcome for Nike is to choose and for Adidas to choose If Adidas chooses not to advertise, their best result will happen if Nike chooses The Nash equilibrium for this advertising game is for Nike to choose and for Adidas Answer Bank to advertise not to advertise
A man buys a racehorse for $25,000 and enters it in two races. He plans to sell the horse afterward, hoping to make a profit. If the horse wins both races, its value will jump to $105,000. If it wins one of the races, it will be worth $65,000. If it loses both races, it will be worth only $10,000. The man believes there is a 30% chance that the horse will win the first race and a 35% chance that it will win the second one. Assuming that the two races are independent events, find the man's expected profit.
several pows are told by the king of enemies that they will put to sleep by injection and the next morning each of them will wake up with a green or red hat on. Each will see the color of each other but not of their own. The will ask the color of each own hat and the pow will be killed if the guess will be wrong. The pows need to establish a strategy that will guarantee survival of all of them except possibly one.
You are one space short of winning a baord game and must roll a 1 on a die to claim victory. You want to know how many rolls it might take. How would you simulate rolling the die until you get a 1?
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Suppose an oil company is thinking of buying some land for $10,000,000. There is a 60%60% chance of economic growth and a 40%40% chance of recession. The probability of discovering oil is 44%44% when there is economic growth and 32%32% when there is a recession. If there is economic growth and the oil company discovers oil, the value of the land will triple. If they do not discover oil, the value of the land will decrease by 10%.10%. If there is a recession and the company discovers oil, the value of the land will increase by 50%.50%. If they do not discover oil, the land will decrease in value by 75%.75%. What is the expected value of the investment? Give your answer to the nearest dollar. Avoid rounding within calculations. $$ Select the correct interpretation of the expected value. The expected value represents what the actual investment value will be for this land purchase of $10,000,000. The company should make the investment because the expected value…
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A vending machine contains 1000 lollipops. Some of the lollipops are red, and the others are blue. You don’t know how many there are of each color. However, you do know that these two alternatives are equally likely. There are 900 blue lollipops and 100 red ones. There are 500 blue lollipops and 500 red ones. When you put a coin into the vending machine, it gives you a lollipop, chosen at random. Suppose that it gives you a blue lollipop. What is the probability that there are 900 blue lollipops and 100 red ones? Show how you got the answer.
Suppose that after the 2020 presidential election there are three races that are too close to call: Wisconsin,Michigan, and Pennsylvania. In order to become president, a candidate must receive 270 electoral votes ormore. Wisconsin has 10 electoral votes, Michigan has 16, and Pennsylvania has 20. Suppose that in theother decided races, Democrats have 259 electoral votes and Republicans have 233. The Democrat has an80% chance of winning Wisconsin, a 50% chance of winning Michigan, and a 10% chance of winningPennsylvania. A statistician defines a random variableXto be +1 if the Democrat wins,−1 if theRepublican wins, and 0 if neither candidate reaches 270 electoral votes. Find the probability densityfunction ofX. (Hint: Make this easier by figuring out the scenario in which the Republican wins or there isa tie!)
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: scissors rock paper rock 0 -1 paper 1 0 scissors -1 1 Week 10 Coursework Questions 2. Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3…

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