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- 5.Each of Player 1 and Player 2 chooses an integer from the set {1, 2, ..., K}. If they choose the same integer, P1 gets +1 and P2 gets -1; if they choose different integers, P1 gets -1 and P2 gets +1. (a) Show that it is a NE for each player to choose every integer in {1, 2, ..., K} with equal probability, K1 . (b) Show that there are no NE besides the one you found in (a).The Nash equilibrium of the accompanying game is Player 1 Multiple Choice O O O (Y. B). (X, B). X Y Z (Z. C). Player 2 A 9, 8 5, 6 10, 9 none of the provided answers because there is no Nash equilibrium in this game. B 10, 12 12, 20 13, 4 C 3, 15 4, 10 8, 12Determine the optimum strategies and the value of the game with the followingpayoff matrix of player A where A1, A2 are the strategies for player A and B1, B2 are for player B.B1 B2A1 5 1A2 3 4
- The mixed stratergy nash equalibrium consists of : the probability of firm A selecting October is 0.692 and probability of firm A selecting December is 0.309. The probability of firm B selecting October is 0.5 and probability of firm selecting December is 0.5. In the equilibrium you calculated above, what is the probability that both consoles are released in October? In December? What are the expected payoffs of firm A and of firm B in equilibrium?Q56 A Nash equilibrium is an outcome... a. Achieved by cooperation between players in the game. b. That is achieved by collusion where no party has an incentive to change their behaviour. c. Where each player's strategy depends on the behaviour of its opponents. d. That is achieved when players in the game have jointly maximized profits and divided those profits according to market share of each player. e. Where each player's best strategy is to maintain its present behaviour given the present behaviour of the other players.What is the secure strategy for player B in the game presented in Table
- True/False a. Consider a strategic game, in which player i has two actions, a and b. Let s−i be some strategy profile of her opponents. If a IS a best response to s−i, then b is NOT a best response to s−i. b. Consider the same game in (a). If a IS NOT a best response to s−i, then a does NOT weakly dominates b. c. Consider the same game in (a). If a mixed strategy of i that assigns probabilities 13 and 23 to a and b, respectively, IS a best response to s−i, SO IS a mixed strategy that assigns probabilities 32 and 13 to a and b, respectively. d. Consider the same game in (a). If a mixed strategy of i that assigns probabilities 13 and 23 to a and b, respectively, is NOT a best response to some strategy profile of her opponents, s−i, NEITHER is a mixed strategy that assigns probabilities 32 and 13 to a and b, respectively. e. Consider the same game in (a). If a IS a best response to s−i, SO IS any mixed strategy that assigns positive probability to a. f. Consider the same game in (a). If a…onsider the game described by the ff table. what is thE best response for the column player if he/she knows that the row player will make the Y move?A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spend C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (36 + J )C - 2C 2 and the profits of the jeweler will be (30 + C )J - 2J 2. The clothing store gets to choose its amount of advertising first, knowing that the jeweler will find out how much the clothing store advertised before deciding how much to spend. The amount spent by the clothing store will be Group of answer choices $17. $34. $51. $8.50. $25.50.
- Consider the following ‘war of attrition’. Two animals are in a stand off for a prey. Theyindependently decide when to give up. Waiting is costly, but the animal giving up last winsthe prey (they each get nothing if they walk away at the exact same time). Getting the preygives a benefit of 80 while waiting costs 2 per unit of time. Formally payoffs are given asfollows:u1(t1, t2) =(−2t1 if t1 ≤ t280 − 2t2 if t1 > t2u2(t1, t2) =(80 − 2t1 if t1 < t2−2t2 if t1 ≥ t2,where ti is the amount of time animal i decided to wait. Assuming that animals aim tomaximize payoffs (consciously or not), figure out the Nash equilibria of this game by answeringthe following questions (similar to how we proceeded to solve the Bertrand game).(a) Show that there is no Nash equilibrium where both animals wait a strictly positiveamount of time. For this, consider two subcases: (i) both wait the same amount oftime, or (ii) one gives in earlier than the other.(b) Assume now that one animal, say the first one,…Three players (Allen, Mark, Alice) must divide a cake among them. The cake is divided into three slices.The table below shows the value of each slice in the eyes of each of the players. S1 S2 S3 Allen $7.00 $6.00 $5.00 Mark $4.00 $4.00 $4.00 Alice $5.00 $4.00 $6.00 Which of the slices does Allen deem fair? Group of answer choices S1 and S2 S1 and S3 S2 and S3 S1, S2, and S3 S1 onlyMatthew is playing snooker (more difficult variant of pool) with his friend. He is not sure which strategy to choose for his next shot. He can try and pot a relatively difficult red ball (strategy R1), which he will pot with probability 0.4. If he pots it, he will have to play the black ball, which he will pot with probability 0.3. His second option (strategy R2) is to try and pot a relatively easy red, which he will pot with probability 0.7. If he pots it, he will have to play the blue ball, which he will pot with probability 0.6. His third option, (strategy R3) is to play safe, meaning not trying to pot any ball and give a difficult shot for his opponent to then make a foul, which will give Matthew 4 points with probability 0.5. If potted, the red balls are worth 1 point each, while the blue ball is worth 5 points, and the black ball 7 points. If he does not pot any ball, he gets 0 point. By using the EMV rule, which strategy should Matthew choose? And what is his expected…