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What is a tit for tat strategy? Why might it be a rational strategy in and infinitely repeated prisoner’s dilemma?
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- Imagine that there are two snowboard manufacturers (FatSki and WideBoard) in the market. Each firm can either produce ten or twenty snowboards per day. The table below (see attached) shows the profit per snowboard for each firm that will result given the joint production decisions of these two firms. Draw the game payoff matrix for this situation. Does either player have a dominant strategy? If so, what is it? What is the Nash equilibrium solution and how many boards should each player produce each day? Since FatSki and WideBoard must play this game repeatedly (i.e. make production decisions every day), what strategy would you advise them to play in order to maximize their payoff over the long term?We can see from the payoff matrix that there are no pure strategy Nash equilibrium in this game because at least one firm would always have an incentive to change its behavior. From Nash's theorem, we know there must be at least one Nash equilibrium so there must be a mixed strategy Nash equilibrium for this game. Find the mixed strategy Nash equilibrium by first deleting all dominated strategies in the game What's the expected payoff to Firm 2 in the equilibrium?O Cell A O Cell C O Cell E O Cell I None of the above
- Two firms, Tim Horbucks and Startons, consider enter the market for take-out coffee, or not. The profit each firm can make (in dollars) is indicated in the table below, where the fixed cost of producing is F dollars. What is the largest value of F below which the game has a UNIQUE Nash equilibrium in pure strategies? Startons Enter Not Enter Enter 400 - F, 400 - F 600 - F,0 Tim Horbucks Not Enter 0, 600 - F 0 ,0 Enter a positive number below, in dollars.What is meant by dominant strategy?a. b. Each firm has four alternative strategies, and a certain profit/payoff is associated with each strategy. The numbers in the payoff matrix denote firm A's profit (in thousands of dollars). The total amount of profit that can be earned by the two firms together is $20000. (This is called a "constant sum game.") Firm B's profit is therefore $20000 minus firm A's profit. What strategies will the two firms select? Is the game strictly determined? If so, how much does each firm gain? B's strategies A's strategies ↓ Increase Advertising Decrease Price Increase Price Alter Product Increase Advertising 0 11 8 11 Decrease Price 8 10 6 2 Increase Price 7 12 15 Alter Product 4 15 3 12 Suppose now that due to a change in consumer preferences, firm A's "Increase Price" strategy pays off better than before when firm B elects to "Decrease Price," that is, the payoff rises from 6 to 14. What strategies will the two firms now select? Is the game strictly determined? If so, how much does each firm…
- Consider a Stackelberg game of quantity competition between two firms. Firm 1 is the leader and firm 2 is the follower. Market demand is described by the inverse demand function P=1000-4Q. Each firm has a constant unit cost of production equal to 20. Suppose firm 2's unit cost of production is c<20. What value would c have so that in the Nash Equilibrium, the two firms, the leader and the follower, had the same market share?Consider a Prisoners' Dilemma game involving two players, N = {1,2}, each of whom may choose either to co-operate (C) or to defect (D). The payoffs this game are illustrated in the below table. Player 1 receives the first listed payoff in each cell while player 2 receives the second listed payoff in each cell. 2 с 3,3 4,0 D 0,4 1, 1 a. Solve for the pure strategy Nash equilibrium of this static game. Are the players able to co-operate with one another? Explain why or why not. Suppose now that the above game is repeated infinitely many times and let 8 > 0 denote the common discount factor between periods. Suppose that the two players make the following agreement: "Play C in every period. If D is ever played, play D in every period thereafter." b. Explain how the one-deviation principle can be used to check whether the above agreement represents a subgame perfect Nash equilibrium of the infinitely repeated game. c. Use the method described in part b. of this question to calculate the…Please answer fast
- Suppose that Flashfry and Warmbreeze are the only two firms in a hypothetical market that produce and sell air fryers. The following payoff matrix gives profit scenarios for each company (in millions of dollars), depending on whether it chooses to set a high or low price for fryers. Flashfry Pricing High Low For example, the lower-left cell shows that if Flashfry prices low and Warmbreeze prices high, Flashfry will earn a profit of $15 million, and Warmbreeze will earn a profit of $2 million. Assume this is a simultaneous game and that Flashfry and Warmbreeze are both profit-maximizing firms. Warmbreeze Pricing High Low 9,9 2,15 15, 2 8,8 If Flashfry prices high, Warmbreeze will make more profit if it chooses a chooses a price. If Warmbreeze prices high, Flashfry will make more profit if it chooses a chooses a price. Considering all of the information given, pricing low True O False price, and if Flashfry prices low, Warmbreeze will make more profit if it price, and if Warmbreeze…Explain the meaning of a Nash Equilibrium. How does it differ from and equilibrium in dominant strategies?The following market is a duopoly populated only by the companies Alpha and Beta. The pay-off matrix immediately below shows the combinations of pricing strategies available to the two companies. The numbers represent millions of dollars in profit. (The negative sign indicates a loss.) Assuming Beta has a first mover advantage, in a one-shot game, what is liekly to be the Nash equilibrium? Explain your answer. Alpha High price Low price High price 250, 200 200, 100 Beta Low price 50, 150 100, 250
