If there are a known finite number of repeated games to be played, the two players will cooperate until the last game, at which point both will try to defect. true or false? explain.
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- Two firms are competing on price. If they have the same price, they share the market otherwise the one with the lowest price captures all demand Market demand follows Q(P)=100-3P Cost is C(Q)=10Q Firms can only choose between the following prices: 9, 10, 11, 12. In the Nash equilibrium of this game, what prices are charged? Suggestion: calculate the profits they obtain for each of the price combinations, write down the game in its normal form (payoff matrix), and then use the underlining method to match best responses. U ப U 9 12 10 110 11A two-person game in which each person has access to only two possible strategies will have at most one Nash equilibrium. True FalseTwo firms are competing on price. If they have the same price, they share the market - otherwise the one with the lowest price captures all demand Market demand follows Q(P)=100-3P Cost is C(Q)=10Q Firms can only choose between the following prices: 9, 10, 11, 12. In the Nash equilibrium of this game, what prices are charged? Suggestion: calculate the profits they obtain for each of the price combinations, write down the game in its normal form (payoff matrix), and then use the underlining method to match best responses. 12 11 9 10
- In a small town there are two pizza restaurants . If neither restaurant advertises, its revenue will not change. If only one firm advertises, the firm that advertises will double its revenue and the firm that doesn't advertise will see a decrease in its revenue, but if both firms advertise, their revenue will not change. What outcome would be predicted by game theory in this market? Both restaurants will advertise. Game theory would predict chat sometimes one restaurant would advertise, and the rest of the time both will advertise. Neither restaurant will advertise Game theory is only a theory and cannot predict real-world events. One restaurant will advertise.Refer to the normal-form game of price competition in the payoff matrix below. Suppose the game is infinitely repeated, and the interest rate is 10 percent. Both firms agree to charge a high price, provided no player has charged a low price in the past. (a) If both firms stick to this agreement, then what is the present value of firm A's payoffs? Please show your calculations. (b) If firm A cheats, what is the present value of the returns for Firm A for cheating? Please show your calculations.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?
- Two firms are competing to establish one of two new wireless communication standards, A or B. A strategy is a choice of standard, and an outcome of this game is a choice of standard by each firm – for example, (A, B) represents the case where Firm 1 decides to develop standard A and Firm 2 develops standard B. Here, the first letter will always correspond to Firm 1’s decision, and the second letter to Firm 2’s decision. Firm 1 has the following preferences over outcomes, in order of highest to lowest preferred: it prefers (A, A) to (B, A) to (A, B) to (B, B). Firm 2 prefers (A, B) to (A, A) to (B, A) to (B, B). Suppose that firms simultaneously decide which standard to develop. What is the pure strategy Nash equilibrium?Two firms are competing to establish one of two new wireless communication standards, A or B. A strategy is a choice of standard, and an outcome of this game is a choice of standard by each firm – for example, (A, B) represents the case where Firm 1 decides to develop standard A and Firm 2 develops standard B. Here, the first letter will always correspond to Firm 1’s decision, and the second letter to Firm 2’s decision. Firm 1 has the following preferences over outcomes, in order of highest to lowest preferred: it prefers (A, A) to (B, A) to (A, B) to (B, B). Firm 2 prefers (A, B) to (A, A) to (B, A) to (B, B). Suppose that firms simultaneously decide which standard to develop. What is the pure strategy Nash equilibrium? Is the answer (B,B)? If not please explian what is the answer?Three married couples in the state of Maryland—Bob and Carol, Ted and Alice, and Ross and Mike (remember, same-sex marriage is legal in the state of Maryland)—are thinking about renting a boat to go sailing on the Chesapeake Bay. The cost of a boat rental is $600. Each of the three couples puts some amount of money in an envelope. Thus, each player in this game is a couple. If the total amount collected is at least $600, then the boat is rented. If the amount collected is more than $600, then the money left over after renting the boat is spent on wine. If the total amount collected is less than $600, then they do not rent the boat, and the money is spent on a dinner. Assume the benefit to a couple from the boat trip is 400, the benefit from each dollar spent on wine is 50 cents, the benefit from each dollar spent on dinner is 40 cents, and the personal cost of the contribution to a couple equals the amount of contribution. For example, if the boat is rented, $50 of wine is purchased…
- Consider a game in which there is $4 to be divided, and the first mover is only permitted to make one of three proposals: (a) $3 for the first mover and $1 for the second mover, (b) $2 for each, or (c) $1 for the first movier and $3 for the second mover. The second mover is shown the proposal and can either accept, in which case it is implemented, or reject and cause each to earn $0. Show this game in extensive (tree) form. Be sure to show the payoffs for each person, with the first mover listed on the left, for each of the six terminal nodes.A large group of players each guesses a number between 0 and 300. The winner is the person whose number is closest to three-fifth of the average guess. What is the Nash equilibrium? Will it be observed? What do you expect for the outcome of this game with next year's 203 class? (Considering that they have similar sophistication to your class but they have not covered game theory yet.)Consider a game with two players who cannot communicate, and in which each player is asked a question. The players can answer the question honestly or lie. If both answer honestly, each receives $100. If one player answers honestly and the other lies, the liar receives $500 and the honest player gets nothing. If both lie, then each receives $50. a) Describe the strategies and payoffs of this game b) Construct the payoff matrix c) Compare this game to the prisoners' dilemma. Are the two games similar or different? Briefly explain your answer.