Suppose there are N identical firms in a market where the maximum total profit is 12. Assuming an infinite game, if the firms fully cooperate, each would get 12/N in profit. If one firm cheats, it gets the entire market profit for one period, followed by a profit of 1 in all future periods, The discount rate r is .33. How large can N be and still sustain cooperation? That is, how many firms can there be before cooperation breaks down?
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Suppose there are N identical firms in a market where the maximum total profit is 12. Assuming an infinite game, if the firms fully cooperate, each would get 12/N in profit. If one firm cheats, it gets the entire market profit for one period, followed by a profit of 1 in all future periods, The discount rate r is .33. How large can N be and still sustain cooperation? That is, how many firms can there be before cooperation breaks down?
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- 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?Game Theory. Consider a Stackelberg competition game with three firms. Firm 1 chooses q1 first. Firm 2 observes q1 and chooses q2. Firm 3 observes both and chooses q3. These three firms are the only firms in the market, so the sum of their outputs is equal to total market supply, i.e. q1+q2+q3=Q. Suppose demand is given by P=12-Q. For simplicity of calculation, suppose each firm has marginal costs of 0, i.e. c1(q1)=0, c2(q2)=0 and c3(q3)=0. (1) What quantity does Firm 1 produce in the SPNE of the game? (2) What quantity does Firm 2 produce in the SPNE of the game? (3) What quantity does Firm 3 produce in the SPNE of the game?Bob's Product- Strategy Pizza No Pizza Sam's Product Strategy No Pizza A U Pizza -$10 с -$10 $0 $15 B D $15 $10 $0 $10 Refer to the payoff matrix. Bob's Burgers and Sam's Sandwiches are competing restaurants in a small town. Both are considering adding pizza to their line of products. If this is a sequential game but we don't know who moves first, what can we say about the final outcome? A. There is no Nash equilibrium attainable for this game. B. Cell A represents the only Nash equilibrium possible for this game. C. Cell D represents the only Nash equilibrium possible for this game. D. Cells B and C both represent possible Nash equilibrium outcomes for this game.
- Consider two firms choosing quantities sequentially in a duopoly setting (i.e. the Stackelberg game). The two firms have identical products. Each firm has no fixed costs, and faces marginal costs equal to 5 plus the quantity it produces (i.e. MC = 5 + q). Market demand is given by Q = 46 - P, where Q is market quantity and P is market price. In equilibrium, how much will the firm that moves first produce?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 the two-stage, static game depicted in Figure 5.1 involving two companies that enter into an agreement to maximize total profits. The payoffs in this game are in millions of dollars. The optimal strategy for both firms is to: Firm Y A C (3, 3) (1, 1) (1, 1) Firm X (1, 1) (5, 5) (7, 4) C (1, 1) (4, 7) (6, 6) Payoffs: (Firm X, Firm Y) FIGURE 5.1 O Play B in stage 1 and stage 2. O Play B in stage 1 and play A in stage 2. O Play C in stage 1 and stage 2. O Play B in stage 1 and play C in stage 2. O Play C in stage 1 and play B in stage 2.
- Is there a Nash Equilibrium for this game? If so, what is it? O The Nash Equilibrium is for both first to choose the high price. O The Nash Equilibrium is for both first to choose the low price. O The Nash Equilibrium is for Chevron to choose the high price while Shell chooses the low price. O The Nash Equilibrium is for Shell to choose the high price while Chevron chooses the low price. O There is no Nash Equilibrium for this game.Two competing firms must choose their quantity of production simultaneously. Each firm can choose either a High quantity of 3 or a Low quantity of 2. The price for both firms is 9-Q, where Q is the sum of both their quantities. Costs are zero; the profit is simply price times quantity. For example, if firm 1 chooses High and firm 2 chooses Low, then price is 9-(3+2)=4; payoff for firm 1 is 12 while payoff for firm 2 is 8. What is the unique Nash equilibrium? (Firm 1's strategy will be written before firm 2's.)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?Consider the following normal form representation of the standard competition between firm A and firm B. Each firm can choose either standard A or standard B. Their payoffs are given as follows: Firm B A В A Firm A В 1 1 3 1 (1) (10 points) What's Nash equilibrium (NE) in this game? If there are more than one, find them all. But there is no NE, state that there is no NE. (2) (10 points) If you find a NE (or multiple Nash equilibria), is it (or are they) Pareto efficient?Consider a market with two firms, Kellogg and Post, that sell breakfast cereals. Both companies must choose whether to charge a high price ($4.00) or a low price ($2.50) for their cereals. These price strategies, with corresponding profits, are depicted in the payoff matrix to the right. Kellogg's profits are in red and Post's are in blue. Kellogg What is the cooperative equilibrium for this game? Price = $4.00 Price = $2.50 O A. The cooperative equilibrium is for Kellogg to choose a price of $2.50 and Post to choose a price of $4.00. $800 Price = $4.00 $50 %3D O B. The cooperative equilibrium is for Kellogg and Post to both choose a price of $2.50. Post of $4.00. OC. The cooperative equilibrium is for Kellogg and Post to both choose a price $350 O D. The cooperative equilibrium is for Kellogg to choose a price of $4.00 and $350 Price = $2.50 $50 Post to choose a price of $2.50. O E. A cooperative equilibrium does not exist for this game. Clear all Chec 88,092 2 47