Determine an optimal mixed strategy for the row player, R, for the game whose payoff matrix is given below, solving the question graphically: 52 24
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Could you please do all parts and provide written solutions , with explanations
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- . The table below states the payoffs in political points (measured in billions of rubles) to two nations that are rivals in world politics, Russia and Ukraine. Each country can take one of two courses: peace; or war. In each cell, the first payoff is for Russia, and the second payoff is for Ukraine. (a) Assume that neither country observes the military strategy of its rival, and solve the game (if it can be solved). Explain your solution step-by-step. Does this outcome maximize total political points? (b) In general, what is a Nash equilibrium? Is the solution to this game a Nash equilibrium? (c) Suppose that each country deposits a fund of two billion rubles with the United Nations. Either country would forfeit this fund if it wages war. What is the solution now to the game? Is this a Nash equilibrium? Russia, Ukraine Peace War Peace 4,4 1, 5 War 5, 1 2,2The table below states the payoffs in profits (of millions of tenge each day) to two grocery supermarkets that are rivals in Almaty, Blue Foods and Ladymart. Each supermarket can take one of two courses: Low prices; or high prices. In each cell, the first payoff is for Blue Foods, and the second payoff is for Ladymart. (a) Assume that neither store observes the pricing by the other store, and solve the game (if it can be solved). Explain your solution step-by-step. Does this outcome maximize total profits to the two stores? (b) Now assume that each store can observe the pricing by the other store, and solve the game. Blue Food, Ladymart High prices Low prices High prices 2, 2 0, 3 Low prices 3, 0 1,1d) Consider the following two-person zero-sum game: 3 -2 1) A = (-1 4 2 2 6/ 2 Using linear programming, verify that the value of a game, v = 2 and strategies (0,0,1) for player I and ,,0) for player Il are optimal solutions.
- There are two players who simultaneously call out one of the numbers oneor two. Player I’s name is James; he wins if the sum of the numbers is odd. Player II’s name is Louis; she wins if the sum of the numbers is even. The amount paid to the winner by the loser is always the sum of the numbers in pesos. Find the table for the payoff function P, and analyze the game to find the value and optimal strategies of the players. Is the game fair?2. Give an example of a 2-player, zero-sum game with the following properties (by giving its payoff matrix from the perspective of the row player): • The row player has strategy set {1, 2} and the column player has strategy set {C1, C2} • The security levels of r₁, r2, C1, and c₂ are respectively −1, −2, 4, and 3.Solve the following game using Graphical Method: + 2. 3. a₁ az a3 a4 a₁ PRACTICAL NO: 9 GAME THEORY -3 az a₁ az аз b₁ 19 7 12 8 b₁ 6 20 b₁ 3 2 -2 b2 6 3 8 7 b2 7 12 b3 7 14 18 13 b₂ -4 5 8 b4 5 6 4 -1 b3 15 10
- If a salesperson has gross sales of over $600,000 in a year, then he or she is eligible to play the company's bonus game: A black box contains 3 one-dollar bills, 1 five-dollar bill and 1 twenty-dollar bill. Bills are drawn out of the box one at a time without replacement until a twenty-dollar bill is drawn. Then the game stops. The salesperson's bonus is 1,000 times the value of the bills drawn. Complete parts (A) through (C) below. (A) What is the probability of winning a $23,000 bonus? (Type a decimal or a fraction. Simplify your answer.) CIf a salesperson has gross sales of over $600,000 in a year, then he or she is eligible to play the company's bonus game: A black box contains 2 one-dollar bills, 1 five-dollar bill and 1 twenty-dollar bill. Bills are drawn out of the box one at a time without replacement until a twenty-dollar bill is drawn. Then the game stops. The salesperson's bonus is 1,000 times the value of the bills drawn. Complete parts (A) through (C) below. (A) What is the probability of winning a $20,000 bonus? (Type a decimal or a fraction. Simplify your answer.) (B) What is the probability of winning the maximum bonus by drawing out all the bills from the box? Type a decimal or a fraction. Simplify your answer.) (C) What is the probability of the game stopping at the third draw? Type a decimal or a fraction Simplify your answer.)a) Consider the following two-person zero-sum game: 1 3 1 4 2 -3 5 6120 A = (-3 75)" Use graphical method to determine the optimal strategies for both player A and player B and give the value of the game.
- Ant Co. has developed a new product, the A-Warren. It is now time to bring the A-Warren product to market. There are two alternatives for Ant-Co either market the product only in the local area, or market the product nationally. If Ant Co. rolls out the A-Warren product locally and it is successful, then the company will receive $1.4M from product sales. However, if the local rollout is unsuccessful, then the company will lose $100,000 ($0.1M) due to the costs of advertising. If Ant Co. rolls out the A-Warren product nationally and it is successful, then the company will receive $3M from product sales. However, if the national rollout is unsuccessful, then the company will lose $1M due to the costs of advertising. Historically, 40% of Ant Co.'s product rollouts have been successful. What is the most that Ant Co should pay for any information regarding the success of the A-Warren product? $0.00M $0.54M None of the answers are correct. $1.14M $0.60MAnt Co. has developed a new product, the A-Warren. It is now time to bring the A-Warren product to market. There are two alternatives for Ant-Co either market the product only in the local area, or market the product nationally. If Ant Co. rolls out the A-Warren product locally and it is successful, then the company will receive $1.4M from product sales. However, if the local rollout is unsuccessful, then the company will lose $100,000 ($0.1M) due to the costs of advertising. If Ant Co. rolls out the A-Warren product nationally and it is successful, then the company will receive $3M from product sales. However, if the national rollout is unsuccessful, then the company will lose $1M due to the costs of advertising. Historically, 40% of Ant Co.'s product rollouts have been successful. Which of the following statements are true? A decision alternative is to rollout the A-Warren product successfully. O An event outcome is a successful national A-Warren rollout with a payoff of $1.4M. An…Ant Co. has developed a new product, the A-Warren. It is now time to bring the A-Warren product to market. There are two alternatives for Ant-Co either market the product only in the local area, or market the product nationally. If Ant Co. rolls out the A-Warren product locally and it is successful, then the company will receive $1.4M from product sales. However, if the local rollout is unsuccessful, then the company will lose $100,000 ($0.1M) due to the costs of advertising. If Ant Co. rolls out the A-Warren product nationally and it is successful, then the company will receive $3M from product sales. However, if the national rollout is unsuccessful, then the company will lose $1M due to the costs of advertising. Historically, 40% of Ant Co.'s product rollouts have been successful. Ant Co. could choose to use a focus group to provide feedback on the A-Warren. In the past when Ant Co.'s products were successful (locally or nationally), the focus group predicted this 80% of the time.…