et’s recall the location game we considered in Lecture 1-9. In the lecture, we examined a case in which two ice-cream vendors compete for customers on one street. In this problem, we consider other scenarios, i.e., there are three or four vendors on the same street.Note that venders choose a location in [0,1][0,1], and the rules of the game are the same as in the lecture:Customers are uniformly distributed along the street.Customers go to the nearest vendor. If multiple vendors occupy the same position, they split the customers equally.The vendor’s payoff is the number of customers.Examples: Three vendors compete on a street.

Consider a location game with two ice cream vendors, where there are five possible locations: 0, 1/4, 1/2, 3/4, and 1. There are many customers, and they are uniformly distributed along the street between 0 and 1. Each customer goes to the nearest vendor. If vendors are located at the same place, they split their customers equally. A vendor’s payoff is the number of customers she/he gets. Vendors simultaneously choose their locations.QuestionWhat is the Nash equilibrium of this game?Hint: If you are unsure about this question, review lecture 1-9.1 pointVendors are located on 0 and 1. None of the above. Both choose 1/2. Vendors are located on 1/4 and 3/4.

Consider the location game between two bakeries, Pie Belly and the Lazy Croissant. Pie Belly moves first, chooses to locate either in the Mall or on the Side Alley. Observing this, the Lazy Croissant then chooses its location, which can similarly be in the Mall or on the Side Alley. The payoffs are as follows: if both firms choose Mall the payoffs are (50, 30) to Pie Belly and the Lazy Croissant; if Pie Belly chooses Mall and the Lazy Croissant the Side Alley the payoffs are (40, 40); if Pie Belly chooses the Side Alley and the Lazy Croissant opts for the Mall, the payoffs are (60, 35); and if both firms opt for the Side Alley the payoffs are (30, 20) respectively. Which statement is true?Group of answer choicesIn the credible equilibria, we observe Pie Belly choosing Mall and then the Lazy Croissant the Side Alley; there is a second-mover advantageIn the credible equilibria, we observe Pie Belly choosing Side Alley and then the Lazy Croissant the Side Alley; there is a second-mover advantageIn the credible equilibria, we observe Pie Belly choosing Side Alley and then the Lazy Croissant the Side Alley; there is a first-mover advantageIn the credible equilibria, we observe Pie Belly choosing Side Alley and then the Lazy Croissant the Mall; there is a first-mover advantageNone of the above statements are true

Two restaurant proprietors, James and May, must simultaneously decide on the locations of their restaurants. The choices are on Pitt Street (P) or King Street (K). If both opt for P, the payoffs are (10, 20) to James and May, respectively. If both proprietors opt for K the payoffs are (10, 8). If James choose P and May chooses K, the payoffs are (5, 4). Finally, if James chooses K and May chooses P, the payoffs are (7, 3). The Nash equilibrium/equilibria is/are . This is a game

(In this and all other questions in which a game matrix is given, Player 1 chooses the row, Player 2 chooses the column, and if there is a Player 3, she chooses the matrix.)  restaurant cricket restaurant  8, X 0, 5 cricket  1, 12 10, 7We say that Players 1 and 2 meet if and only if they choose the same strategy. Suggest a value in the range  such that the above game matrix reflects that- Player 1 prefers being at cricket over being at the restaurant, while Player 2 prefers being at the restaurant over being at cricket, and- each player prefers meeting at a location over being alone at that location, and- meeting is more important to Player 1 than being in their preferred location, and- being at their preferred location is more important to Player 2 than meeting

You live in a town with 300 adults and 200 children,and you are thinking about putting on a play to entertain your neighbours and make some money. A play has a fixed cost of $2000, but selling an extra ticket has zero marginal cost.Here are the demand schedules for your two types of customer: Price: 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 Adults: 0, 100, 200, 300, 300, 300, 300, 300, 300, 300, 300 Children: 0, 0, 0, 0, 0, 100, 200, 200, 200, 200, 200 a) To maximise profit,what price would you charge for an adult ticket? For a child's ticket? How much profit do you make? b) The city council passes a law prohibiting you from charging different prices to different customers. What price do you set for a ticket now? How much profit do you make? c) Who is worse off because of the law prohibiting price discrimination? Who is better off? (If you can, quantify the changes in welfare.) d) If the fixed cost of the play were $2500 rather than $2000, how would your answers to parts (a), (b) and (c) change?