Lets again consider the same two firms from the previous question. In this game, both firms have already entered the market and now decide what price to charge. For concreteness, suppose that there are 10 million customers, each of whom will buyfrom one of the two firms, and that each firm decides whether to charge $20 or $30 (with costs of zero). If both firms charge the same price, they will each sell to 5 million customers, but if one charges the low price ($20) and the other charges the highprice ($30), 8 million will buy from the low-price firm and 2 million will buy from the high-price firm.(a) Create a payoff matrix for this game.(b) Identify any dominant strategies for either of the two players.(C) Identify any Nash equilibrium in the game, using the best response analysis.(d) Is this a Prisoner's Dilemma situation?

Given information Two firms are in the Market Firm 1 and Firm 2 Total customer are 10 million in the…

Answered: Lets again consider the same two firms…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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First 4 blanks: high/low Last blank: is not/is
There are two firms in the market. Denote the price and the quantity of firm j by p; and q; , respectively. Those two products are differentiated and the demand system is given by 91 = 100 – 2p1 + P2 92 = 100 + pi – 2p2 For simplicity, assume zero production costs, meaning that profit is equal to revenue. Consider the two-stage game in which firm 1 decides the price first and then firm 2 choose its price after observing firm 1's price. If firm 1's price is 24, what is the best response price of firm 2? Report only the value . Answer:
Player 1 can stay at home or fly to New York, in which case Player 2 can meet Player 1, who can then buy a drink for Player 2. See the game below. Which of the following completely describes a possible strategy for Player 1? 1 Fly to New York Stay home Stay home Stay home and Don't buy drink Fly to New York and Meet Stay home or Fly to New York 2 Meet Don't meet 0,0 1 Buy drink Don't buy drink -2,0 1,2 -1, -1
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?
Once again, two ice cream truck vendors, A and B, are playing a simultaneous pricing game. If only one of the vendors prices low, he gets all the customers for a payoff of 12, while the other vendor gets no customers and a payoff of zero. If both vendors price high, they each get a payoff of 6. If both price low, they each get a payoff of 5. Suppose that the above game is repeated indefinitely, and together the vendors adopt a trigger strategy such that they would start charging the low price only if the other vendor charged a low price last time. Provided that the vendors stick to their new strategy, what would be the Nash equilibrium going forward? a) Both the vendors price high b) Both the vendors price low c) Vendor A prices high, vendor B prices low d) Vendor B prices high, vendor A prices low
Suppose that Creamland and Dairy King are the only two firms that sell ice cream. The following payoff matrix shows the profit (in millions of dollars) each company will earn depending on whether or not it advertises: Dairy King Advertise Doesn't Advertise Advertise 8, 8 15, 2 Creamland Doesn't Advertise 2, 15 11, 11 For example, the upper right cell shows that if Creamland advertises and Dairy King doesn't advertise, Creamland will make a profit of $15 million, and Dairy King will make a profit of $2 million. Assume this is a simultaneous game and that Creamland and Dairy King are both profit- maximizing firms. If Creamland decides to advertise, it will earn a profit of s million if Dairy King advertises and a profit of $ million if Dairy King does not advertise. If Creamland decides not to advertise, it will earn a profit of s million if Dairy King advertises and a profit of s million if Dairy King does not advertise. If Dairy King advertises, Creamland makes a higher profit if it…
Consider a Bertrand game between two firms. The demand for firm 1's product is given by q1 = 100 - 3p1 + 2p2. The demand for firm 2's product is given by q2 100- 3p2 +2p1. In terms of notation, p1 is the price of firm 1's product and pa is the price of firm 2's product. The two firms choose their prices simultaneously. For your calculations below, assume zero costs and that prices are measured in dollars per unit. Find the equilibrium prices. as b Derive the firms' best-response functions and explain whether the prices are strategic substitutes or complements in this game.
Consider the following two player game. In each cell the first number refers to the payoff to Player 1 while the second number refers to the payoff to Player 2. Suppose the two players move simultaneously (at the same time). Which one of the following statements is CORRECT? Player #1 Player #2 Top Bottom Left 7.7 4.0 Right 0,4 4,4 O There are three equilibria in this game: two pure strategy equilibria at [Top, Left] and [Bottom, Right) and al third equilibrium in mixed strategies. In the mixed strategy equilibrium of this game. Player 1 should play Top with probability 2/5 and Bottom with probability 3/5; Player 2 should play Left with probability 2/5 and Right with probability 3/5. O There are three equilibria in this game; two pure strategy equilibria at (Top. Left) and (Bottom, Right) and a third equilibrium in mixed strategies. In the mixed strategy equilibrium of this game, both players should randomize over the strategies with probability and %. O There is a unique dominant…
A secluded off-ramp on a highway through the Prairie of Prax has two gas stations, the only gas stations for miles, Northgoings and Southgoings. Suppose Northgoings and Southgoings must simultaneously display their prices, choosing between a high price and low price gas. The payoff matrix for this game, showing potential daily profit, is displayed below. Assume both stations know all of the information in the matrix, and that this is a one-time payoff. Northgoings Decisions High Price Low Price N: $500 N: $800 High Price S: $400 S: $50 Southgoings Decisions N: $100 N: $250 Low Price S: $700 S: $200 (a) According to our model of game theory, Northgoings has a dominant strategy to [Select] (b) According to our model of game theory, Southlgoings has a dominant strategy to [ Select] V (c) According to our model of game theory, the competitive outcome, or Nash Equilibrium, Northgoings will earn [ Select] and Southgoings will earn [ Select] (d) On the other hand, if these two companies…
The inverse market demand for fax paper is given by P=100-Q. There are two firms who produce fax paper. Firm 1 has a cost of production of C1= 15*Q1 and firm 2 has a cost of production of C2=20*Q2 a) Suppose that firm play a Stackelberg game. First firm 1 sets the quantity in t=1, then, knowing which quantityfirm 1 has set, firm 2 chooses the quantity in t=2. What are the Stackelberg quantities and prices? What arethe profits od firm 1 and 2? Compared to part a) which firm benefits and which firm loses?
To advertise or not to advertise Suppose that Creamland and Dairy King are the only two firms that sell ice cream. The following payoff matrix shows the profit (in millions of dollars) each company will earn depending on whether or not it advertises: Dairy King Advertise Doesn't Advertise Creamland Advertise 10, 10 18, 2 Doesn't Advertise 2, 18 11, 11 For example, the upper right cell shows that if Creamland advertises and Dairy King doesn't advertise, Creamland will make a profit of $18 million, and Dairy King will make a profit of $2 million. Assume this is a simultaneous game and that Creamland and Dairy King are both profit-maximizing firms. If Creamland decides to advertise, it will earn a profit of _________ million if Dairy King advertises and a profit of ________ million if Dairy King does not advertise. If Creamland decides not to advertise, it will earn a profit of __________ million if Dairy King advertises and a profit of _________…
Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player chooses one of 3 strategies: rock, paper, or scissors. Then, both players reveal their choices. The outcome is determined as follows. If both players choose the same strategy, neither player wins or loses anything. Otherwise: • "paper covers rock": if one player chooses paper and the other chooses rock, the player who chose paper wins and is paid 1 by the other player. "scissors cut paper": if one player chooses scissors and the other chooses paper, the player who chose scissors wins and is paid 1 by the other player. "rock breaks scissors": if one player chooses rock and the other player chooses scissors, the player who chose rock wins and is paid 1 by the other player. We can write the payoff matrix for this game as follows: rock paper scissors rock 0 -1 1 paper 1 0 scissors -1 1 -1 0 2. Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper…

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