Consider the following "location game." There are two ice cream sellers (Seller 1 and Seller 2) in a small city. Residents are uniformly located on a straight street of length 1. The ice cream sellers need to choose where to set up their carts, and each resident will purchase one unit of ice cream from the nearest seller. The city council has fixed the price of the ice cream, and as a result, each seller just wants sell as much ice cream as possible.

Consider the following "location game." There are two ice cream sellers (Seller 1 and Seller 2) in a small city. Residents are uniformly located on a straight street of length 1. The ice cream sellers need to choose where to set up their carts, and each resident will purchase one unit of ice cream from the nearest seller. The city council has fixed the price of the ice cream, and as a result, each seller just wants sell as much ice cream as possible.

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter15: Oligopoly And Strategic Behavior

Section: Chapter Questions

Problem 17P

See similar textbooks

Similar questions

Please no written by hand Two players bargain over how to split $10. Each player i ∈ {1, 2} choose a number si ∈ [0, 10] (which does not need to be an integer). Each player’s payoff is the money he receives. We consider two allocation rules. In each case, if s1 + s2 ≤ 10, each player gets his chosen amount si and the rest is destroyed. 1. In the first case, if s1 + s2 > 10, both players get zero. What are the (pure strategy) Nash equilibria? 2. In the second case, if s1 + s2 > 10 and s1 6= s2, the player who chose the smallest amount receives this amount and the other gets the rest. If s1 + s2 > 10 and s1 = s2, they both get $5. What are the (pure strategy) Nash equilibria? 3. Now suppose that s1 and s2 must be integers. Does this change the (pure strategy) Nash equilibria in either case?
Let us see the example of Juan and María given but modify their preferences. It is still the case that they are competitive and are deciding whether to show up at their mom’s house at 8:00 A.M., 9:00 A.M., 10:00 A.M., or 11:00 A.M. But now they don’t mind waking up early. Assume that the payoff is 1 if he or she shows up before the other sibling, it is 0 if he or she shows up after the other sibling, and it is 1 if they show up at the same time. The time of the morning does not matter. Find all Nash equilibria.
Two firms A and B compete on price. They can choose a low or high price. Firm A is smaller than firm B, and typically earn a lower payoff. For instance if both firms offer a low price firm A earns $400, and B $500, and if they both offer a high price Firm A earns just $400, while firm B earns $1,000. However, when Firm A offers a low price and B a high price firm A can gain an advantage and will earn $600, while B will earn $400. Finally, if the situation is reversed and B offers a low price and B a high price, B will steal the market and earn $1,500 while A will earn nothing. Please construct a payoff matrix for this situation Does Firm A have a dominant strategy?
Two farmers have unlimited access to a common plot of land and can let their cows graze on it. The matrix below shows the benefits they get from grazing either 1 or 2+ cows on the land. Farmer 2 Farmer1 1 cow 2+ cows 1 cow 8,8 2,10 2+cows 10,2 4,4 What kind of game is this? What is/are the Nash equilibrium/equilibria? What is/are the Pareto efficient outcome(s) in this game? (Hint: Remember that Pareto efficiency occurs when no one person can be made better off without someone else being made worse off) The government offers a reward or subsidy for communities where farmers only allow 1 cow to graze on the common field, resulting in a new payoff matrix:…
Consider the example at the beginning of the chap- ter. Suppose that there are only two blockbusters jockeying for position: Warner Bros.'s Harry Potter and Fox's Narnia. Suppose that blockbusters released in November share a total of $500 million in ticket revenues, whereas blockbusters released in Decembershare a total of $800 million(a) Formulate the game played by Warner Bros. and Fox.
Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are given in the following table: Player 1 Player 2 Left Right Top 6 1 9 4 Bottom 2 4 5 3 where the number on the left is the payoff to Player 1, and the number on the right is the payoff to Player 2. D) What is Player 1’s maximin strategy?E) What is Player 2’s maximin strategy?F) If the game were played with Player 1 moving first and Player 2 moving second, using the backward induction method we went over in class, what strategy will each player choose?
6)Game Theory: The Prisoners’ Dilemma: Assume that the Wilson and Spalding athletic equipment companies are in a one-shot game for market share and profits, but that they have the option of choosing only one of two possible price strategies for basketballs: $20 or $80. Obviously if they choose different strategies, the firm with the lower price will win the entire market. The firms face the following payoff matrix (See Chap. 10). Wilson\ \Spalding Wilson $ 20 Price Wilson $ 80 Price Spalding $ 20 Price $ 400, $ 400 $ 1500, $ 0 Spalding $ 80 Price $ 0, $ 1500 $ 1000, $ 1000 What strategy will each firm choose? Why? Which strategy is dominant? Which strategy is preferred by each firm? What will be the outcome of the one-shot game? Where is the Nash equilibrium? Which outcome would be best for the two firms? What will happen if the game is repeated an infinite number of times?
5 Suppose two players play one of the two normal-form games shown in Figure 1. L U 0,-1 D 2,4 R 2,0 6,0 L U | 4,-1 D 2,-2 R 2,0Now suppose that Player 2 knows which game is being played, but Player 1 does not. Find the pure strategy Bayesian Nash equilibrium of this game.
Exercise 7: The facility location game. Our example is a game in which two firms compete through their choice of locations. Suppose that two firms A and B are each planning to open a store in one of six towns located along six consecutive exits on a highway. We can represent the arrangement of these towns using a six-node graph as in Figure 1 Now, based on leasing agreements, Firm 1 has the option of opening its store in any of towns 1, 3, or 5, while Firm 2 has the option of opening its store in any of towns 2, 4, or 6. These decisions will be executed simultaneously. Once the two stores are opened, customers from the towns will go to the store that is closer to them. So for example, if Firm A open its store in town 3 and Firm B opens its store in town 2, then the store in town 2 will attract customers from 1 and 2, while the store in town 3 will attract customers from 3, 4, 5, and 6. If we assume that the towns contain an equal number of customers, and that payoffs are directly…
True or False?Please Explain Thoroughly: In a Nash equilibrium of a strategic game, each player must best respond to her opponents’ actions, therefore, no other action profile can be unanimously preferredby all the players to a Nash equilibrium.