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- A game involves two players: player A and player B. Player A has three strategies a1, a2 and a3 while player B has three strategies b1, b2 and b3. Player B b1 b2 b3 a1 -40,30 70,20 -10,120 Player A a2 40,60 80,80 60,20 a3 -30,40 -50,110 150, -70 Assuming that this is a one-time game, answer the following questions: Is there any dominant strategy for each player? What is the secure strategy of each player. What is the Nash equilibrium of the game?1. A row of minus signs is written on a whiteboard (can be any number). Two players take turns in replacing either a single minus sign by a plus sign or two adjacent minus signs by two plus signs. The player who makes the last move wins. Discuss the possible strategy for the first mover to force a win.What is the secure strategy for player B in the game presented in Table
- Consider a sequential game between a shopkeeper and a haggling customer. The party who moves first chooses either a high price ($50) or low price ($20) and the second mover either agrees to the price or walks away from the deal and neither party gets anything. Ignore costs and assume the customer values the item at $60.If the shopkeeper goes first and quotes a low price, what is the best response of the customer? Question 33 options: a)Slam the storeowner's door on the way out b)Laugh at the storeowner c)Walk away from the deal d)Accept the low price happily Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.Suppose the following game is played infinite times in the future. Time discount is 0.90. What should be the value of x so that the equilibrium strategy is (Cooperate, Cooperate)? Player 2 Player 1 Cooperate Defect Cooperate (x, x) (2, 14) Defect (14, 2) (5, 5)K mart and Wal-mart are considering establishing either 1 or 2 stores in a town the payoff matrix which gives the profits of each company is as follows (profits are in millions of dollars) Walmart One Two K mart One 10,10 7,12 Two 6,4 5,5 What is the equilibrium outcome in this game? K mart builds _____ store(s) and Wal-mat builds ______ store(s) A. 1,1 B. 2,1 C. 1,2 D. 2,2
- A occurs if all players in a game play their best strategies given what their competitors do.In equilibrium, what is the probability that player 1 will use the pure strategy E in this game?(a) What are the sets of pure strategies of players A and B?(b) Find the subgame perfect equilibrium(c) Provide a brief argument why the SPE is unique (i.e., why there are no more SPE, whether in pure or mixed strategies).
- John enjoys playing two-player zero-sum games. The matrix below shows the losses to John in a particular two-player zero-sum game. His strategies are denoted by I, II, and III, whereas the strategies for his opponent are denoted by A, B, and C. I II III A 3 2 4 B 0 1 1 C 1 3 0 (a) Explain which of John’s strategies is dominated.The opponent now has the option of a fourth strategy, D, which results in none ofJohn’s strategies being dominated.(b) Suggest possible values for the strategy D.In the coin game, two players begin with 13 coins. Players take turns to remove coins. At each turn each player is allowed to remove one, two, or three coins. The winner is the last player to remove coin(s). Suppose there are 9 coins remaining and it is your turn to remove coin(s). Your best strategy is to remove how many coins? a. 0 b. 1 c. 2 d. 31. What are the advantages and disadvantages of collusion? Define Collusion 2. 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? Defining the game and provide an example of the best response.
