Let's consider the following game: Player 1 chooses a (potentially negative) number x, and player 2chooses a (potentially negative) number y. The payoff for player 1 is given by U1 = 100x - x2 - 2xy. Thepayoff for player 2 is given by U2 = 130y - 2y2 - 2xy. Solve for the Nash equilibrium in pure strategies.What is Player 1's payoff in the equilibrium? Enter a numerical answer below. You may round to thesecond decimal if necessary.

Answered: Image /qna-images/answer/b27a0d20-eefb-43b8-93bb-2a9fb3e48897.jpg

Answered: Let's consider the following game:…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 14% chance of returning $11,000,000 profit, a 37% chance of returning $2,000,000 profit, and a 49% chance of losing the million dollars. The second company, a hardware company, has a 8% chance of returning $6,000,000 profit, a 39% chance of returning $2,000,000 profit, and a 53% chance of losing the million dollars. The third company, a biotech firm, has a 5% chance of returning $9,000,000 profit, a 43% of no profit or loss, and a 52% chance of losing the million dollars. Order the expected values from smallest to largest. second, first, third second, third, first first, third, second first, second, third third, second, first third, first, second
A venture capitalist, willing to invest $1,000,000 has three investments to choose from. The first investment, a software company, has a 10% chance of returning $5,000,000profit, a 30% chance of returning $1,000,000 profit, and a 60% chance of losing the million dollars. The second company, a hardware company, has a 20%chance of returning $3,000,000 profit, a 40% chance of returning $1,000,000profit, and a 40%chance of losing the million dollars. The third company, a biotech firm, has a 10% chance of returning $6,000,000 profit, a 70%of no profit or loss, and a 20% chance of losing the million dollars. (a) Construct a PDF for each investment.Enter the exact answers as fractions or decimals. x P(x) −1,000,000 1,000,000 5,000,000 software company^ x P(x) −1,000,000 1,000,000 3,000,000 hardware company^ x P(x) −1,000,000 0 6,000,000 Biotech firm (b) Find the expected value for each investment. Software company: $Hardware…
A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 11% chance of returning $5,000,000 profit, a 29% chance of returning $1,500,000 profit, and a 60% chance of losing the million dollars. The second company, a hardware company, has a 12% chance of returning $5,000,000 profit, a 28% chance of returning $3,500,000 profit, and a 60% chance of losing the million dollars. The third company, a biotech firm, has a 14% chance of returning $10,000,000 profit, a 33% of no profit or loss, and a 53% chance of losing the million dollars. Order the expected values from smallest to largest. third, first, second second, third, first first, second, third third, second, first second, first, third first, third, second
East Coast Athletics is planning to sell its Wilmington, Philadelphia, and Boston gyms. The firm expects to sell its Wilmington gyrn for a cash flow of $A, Its Philadelphia gym for a cash flow of $A, and its Boston gym for a cash flow of $B. The firm expects to sell its Wilmington gym in T years, its Philadelphia gym in 5 years, and its Boston gym in S years. The cost of capital for all three gyms is Y. A > B>0, S > T > 0, and Y> 0. The cash flows from the sales are the only cash flows associated with the various gyms. Based on the information in the preceding paragraph, which one of the following assertions is true? O None of the above assertions is true O The Wilmington gym is the most valuable of the 3 gyms O The Boston gym is the most valuable of the 3 gyms O Two of the three gyms have equal value and those two gyms are more valuable than the third gyms or all three gyms have the same value O The Philadelphia gym is the most valuable of the 3 gyms
A rancher raises chickens and pigs on his 500–acre ranch. Each chicken requires 1 acres of land and needs $25 of veterinary care per year while each pig requires 4 acres of land and needs $50 of veterinary care per year. If the rancher can afford no more than $8,550 for veterinary care this year. If the expected profit is $40 for each chicken and $110 for each pig, how many of each animal should he raise to obtain the greatest possible profit? a). What is the system of inequalities. b) Solve using the graphical method (sketch graph shade, list all corner points) state solution.
A company has $19,310 avallable per month for advertlsing. Newspaper ads cost $160 each and can't run more than 22 times per month. Radio ads cost $620 each and can't run more than 31 times per month at this price. Each newspaper ad reaches 6500 potential customers, and each radio ad reaches 7700 potential customers. The company wants to maximize the number of ad exposures to potential customers. Use n for number of Newspaper advertisements and r for number of Radio advertisements. Maximize P = subject to 22 < 31 < $19, 310 Enter the solution below. If needed, round ads to 1 decimal palace and group exposure to the
1. Suppose two roommates i = 1,2 must decide how much time, 5< tį < 10 (and integer), to spend on cleaning their apartment. The payoff (per unit) to roommate i = 1,2 is given by the following function: (20i Pij (50j – 30i if j 2i if j
Families who have pets are classified as having one, two or three pets. Let say that in a given year, 15% of families with one pet move to have 3 pets, and 5% move to have 2 pets; also 6% of all families with 3 pets move to having only one pet, and 4% move to having 2 pets; finally, 4% of all families having 2 pets move to having 1 pet and 6% move to 3 pets. The cost of having 1 pet is close to $500 a year, for 2 it is $750 and for 3 pets $825. What is the expected cost to having one pet, two pet or three pets? Please do fast ASAP fast
(ii) Explain Nonzero-sum game along with an example. For what value of A, the game with following payoff matrix is strictly determinable? B₂ A₁ A₂ A3 В1 λ -1 -2 6 λ 4 B3 2 -7 λ
6. Solve the following game for optimal strategy based on algebraic method: D1 D2 D3 a=8 b=7 C1 19+a | 12+b 6 c=2 d=9 C2 2 -3 -4 C3 5+d 14+a 7
A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 13% chance of returning $11,000,000 profit, a 25% chance of returning $2,000,000 profit, and a 62% chance of losing the million dollars. The second company, a hardware company, has a 14% chance of returning $6,000,000 profit, a 39% chance of returning $3,000,000 profit, and a 47% chance of losing the million dollars. The third company, a biotech firm, has a 7% chance of returning $6,000,000 profit, a 40% of no profit or loss, and a 53% chance of losing the million dollars.Order the expected values from smallest to largest. third, first, second third, second, first first, second, third first, third, second second, third, first second, first, third
There are three players in a public good game. Each player (i=1,2,3) has 100 dollars to contribute the amount of money cı, i=1,2,3, for a public good. Each player's payoff depend on the following: (i) The amount of her remaining wealth 100-c, i=1,2,3, for spending in private good. 3. (ii) The amount of public good is equal to the sum of contributions from all players. (iii) Each person cares about the amount of public good and her consumption of private goods. Based on the above assumption, each players ui-(100+c)+(c1+c2+c3)(100-c), i=1,2,3 (a) What is the amount of each player contribute to the public good for Nash equilibrium for the non-cooperative simultaneous game? .What is total payoffs for all players in the non-cooperative simultaneous game? What is the amount of each player contributes to the public for social optimum if (b) (c) there are no discrimination of all players? Hint: The social optimum is the maximum total payoff if all players cooperate together. You might think…

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