Consider a location game with nine regions like the one discussed in this chapter. But instead of having the customers distributed uniformly across the nine regions, suppose that region 1 has a different number of customers than the other regions. Specifically, suppose that regions 2 though 9 each has ten customers, whereas region 1 has x customers. For what values of x does the strategy of locating in region 2 dominate locating in region 1?

Consider a location game with nine regions like the one discussed in this chapter. But instead of having the customers distributed uniformly across the nine regions, suppose that region 1 has a different number of customers than the other regions. Specifically, suppose that regions 2 though 9 each has ten customers, whereas region 1 has x customers. For what values of x does the strategy of locating in region 2 dominate locating in region 1?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.5P

See similar textbooks

Similar questions

Suppose that there are only two firms in a market in which demand is given by p = 64 - Q, where Q is the total production of the two firms. Each firm can choose either a low level of output, qL = 15, or a high level of output, qH = 20. The unit cost of production for both firms is $4. Write down the normal-form representation of the game in which the strategic variable for each firm is the quantity of output and the firms make their choices simultaneously. Find the pure strategy Nash equilibrium of this game (quantities produced and market price).
Consider the following static game with two firms as the players. Each firm must decide either to upgrade (U) an existing good to a new version; or not upgrade it (N). The decisions are simultaneous. If a firm chooses to upgrade, they have to pay a fixed cost of 7. If they don’t upgrade, there is no fixed cost. The marginal cost is always equal to 3. The demand side of the market is as follows: If neither firm upgrades, each firm sells 2 units at price 4. If both firms upgrade, each firm sells 3 units at price 5. If only one firm upgrades, the one who upgrades sells 5 units at price 5, and the other firm does not sell anything.
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. 12 11 9 10
2. 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. (a) We think of this "location game" as a simultaneous-move game, in which each player's payoff is the proportion of residents that buy from her cart. Is this game with discrete strategies or continuous strategies? Please state the set of (pure) strategies for both sellers. Is this game zero-sum or non-zero-sum? (b) Find all NE(s) of this game. (c) Is there an alternative pair of locations for the sellers such that the residents’ total walking distance is reduced but neither seller is hurt? Is it an NE? (d) Suppose now that there are…
2. 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. (a) We think of this "location game" as a simultaneous-move game, in which each player's payoff is the proportion of residents that buy from her cart. Is this game with discrete strategies or continuous strategies? Please state the set of (pure) strategies for both sellers. Is this game zero-sum or non-zero-sum? (b) Find all NE(s) of this game.
In 2003, Saudi Arabia and Venezuela produced an average of 8 million and 3 million barrels of oil a day, respectively. Production costs were about $10 a barrel and the price of oil averaged $28 per barrel. Each country had the capacity to produce an additional 1 million barrels per day. At that time, it was estimated that each country 1-million-barrel increase in supply would depress the average price of oil by $3. A. Draw a normal form representation of a game where Saudi Arabia has 2 possible actions to produce 8 million or 9 million barrels of oil and Venezuela has 2 possible actions: to produce 3 or 4 million barrels of oil. Fill in the payoffs for each player and action. Draw a table. B. What action should each country take and why? C. Does the asymmetry in the countries' sizes cause them to take different attitudes towards expanding out? Explain why or why not.
Imagine two Pizzerias are playing a static game where the firms have to choose their strategies simultaneously, selecting a strategy that maximizes its profit given what it believes the other firm will do. Their decision is how many pizzas to produce. They can choose between producing 100, 150 or 200 pizzas each. The profit for respective firm is showed in the payoff matrix below. a) What is the solution (if there is one) and also describe the characteristic features of this game. b) If this game was played repeatedly, could that potentially change the outcome of the game? In your answer, you are expected to motivate and describe how.
Which of the following is the COLLUSIVE OUTPUT in the Game Theory Matrix below? * Firm B Payoff = Expected Profit ($m) High Price Low Price High Price $4m; $4m $-1m, $6m Firm A Low Price $6m; $-1m $1m, $1m Both firms choose High Price Both firms choose Low Price Firm A chooses Low Price; Firm B chooses High Price O Firm A chooses High Price; Firm B chooses Low Price
In the following two-user game, the payoffs of users Alice and Bob are exactly negative of each other in all the combinations of strategies (a,a), (a,b), (b,a), (b,b). This models an extreme case of competition, and is called a zero-sum game. Please point out every pure-strategy Nash equilibrium of this game, and explain why it is. a b a (1, -1) (3, -3) (2, -2) (5, -5)
Imagine a game where individuals can be either cooperative (like splitting a resource) or selfish (like grabbing the entire resource). Depending on the relative costs and benefits of interacting and the resource, there might be a variety of possible payoff matrices for such an interaction. Of the following matrices, which one illustrates the largest “temptation to cheat?”
There is a beach with nine regions in it and two pop sellers must choose in which region to situate. Customers in each region walk to the closest seller to buy a pop. Each pop is sold for $1 each. Suppose that the customers are not distributed evenly across the regions. Regions 2 through 9 each have 10 customers but region 1 has x customers. For what values of x does the strategy of locating in region 2 dominate locating in region 1? In particular, what is the maximum value of x for this to be true? Please show all your calculations in your written solution.
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 11