BundlingSuppose that an arena has a capacity of 20,000 seats. Over the course of a weekend, a tournament will host 3 games between 6teams with each team playing exactly one game. There are 2000 dedicated fans of each team (so 2000*6=12,000 total dedicatedfans), who will each pay up to $150 to see the game with their team playing and up to $10 per game to see the other two games.There are also 2000 general fans who will pay up to $50 per game to see each of the three games. Thus, there are 14,000 fansaltogether (2000*6 + 2000). Assume the marginal cost of admitting one more fan (up to the capacity limit) is $0.a. As the manager of the arena, suppose you could perfectly price discriminate. How many tickets would you expect to sell to eachgame? What is your total revenue for all three games?Tickets Sold (per game):Total Revenue: $For the rest of this problem, assume perfect price discrimination is not possible and provide answers to maximize revenue (Since thereare no costs, this is the same as maximizing profit.)b. If you sold individual tickets to each game at a uniform price, how would you price tickets and how many tickets would you expectto sell to each game? What is your total revenue for all three games?Price per ticket: $Tickets Sold (per game):Total Revenue: $(c) If you sold a package ticket that provided entrance to all 3 games and if you did not sell individual tickets, how would you price thepackage ticket and how many package tickets would you expect to sell? What is your total revenue?Price per ticket: $Tickets Sold:Total Revenue: $(d) Now consider the possibility of selling both a package ticket that provided entrance to all 3 games and also individual tickets toeach game. Is it possible to earn greater revenue than in part (c)?(Click to select)

Total Number of seats in arena = 20,000Number of teams = 6Fans of each team = 2000Number of general…

Suppose that an arena has a capacity of 20,000 seats. Over the course of a weekend, a tournament will host 3 games between 6 teams with each team playing exactly one game. There are 2000 dedicated fans of each team (so 2000*6-12,000 total dedicated fans), who will each pay up to $150 to see the game with their team playing and up to $10 per game to see the other two games. There are also 2000 general fans who will pay up to $50 per game to see each of the three games. Thus, there are 14,000 fans altogether (2000*6 + 2000). Assume the marginal cost of admitting one more fan (up to the capacity limit) is $0. a. As the manager of the arena, suppose you could perfectly price discriminate. How many tickets would you expect to sell to each

Suppose that an arena has a capacity of 20,000 seats. Over the course of a weekend, a tournament will host 3 games between 6 teams with each team playing exactly one game. There are 2000 dedicated fans of each team (so 20006-12,000 total dedicated fans), who will each pay up to $150 to see the game with their team playing and up to $10 per game to see the other two games. There are also 2000 general fans who will pay up to $50 per game to see each of the three games. Thus, there are 14,000 fans altogether (20006 + 2000). Assume the marginal cost of admitting one more fan (up to the capacity limit) is $0. a. As the manager of the arena, suppose you could perfectly price discriminate. How many tickets would you expect to sell to each

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.7P

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Anashequilibriumisastrategyprofilesuchthat: a)Both players are playing a best response strategy b)Both players must be playing a dominant strategyc)Both players achieve their highest possible payoff d)a) and c) e)b) and c)
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Two business partners jointly own a firm and share equally the revenues. They individually and simultaneously decide how much effort to put into the firm. Let s₁ and s2 denote the effort choices of partner 1 and partner 2, respectively. Assume si € [0, 4]. The cost of effort is given by s? for i E {1, 2}. The firm's revenue is given by 4(81 +82 + bs182) where 0 ≤ b ≤ 1. (Note that the parameter 6 reflects the synergies between the effort levels. b> 0 implies that the more one partner works, the more productive the other partner is.) The payoffs for partners 1 and 2 are: u₁ (81, 82) u2 (81, 82) - = 1 [4(81 +82 +68182)] − 8² - 1 [4(81 +82 + bs182)] – $²
k : ces As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 50 percent chance of low demand and a 50 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P= 300,000-400Q and P= 500,000 -225Q, respectively. Your cost function is CQ) = 165,000+ 243,750Q. How many new homes should you build, and what profits can you expect? Number of homes you should build: homes Profits you can expect: $1
Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper scissors rock 0. -3 1 1. раper scissors -1 -1 3 (a) Show that xT= (,) and yT= (5) together are not a Nash equilibrium 3'31 for this modified 3'3 game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.
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In a sideshow game. A player gets 3 balls to place into a Clown's mouth. Each ball is swallowed by the Clown and is then deposited into slots that can hold only 1 ball. Slots are numbered 1 to 9 and prizes are allocated to a player depending on the slot value of the three balls. If for example the first ball landed in slot 8, the second in slot 2 and the third in slot 1, the resulting prize number would be 821 as shown in Figure 3. 3rd 2nd 1st dol 1 2 3 4 5 6 7 8 9 Figure 3: A prize number of 821 is shown for a side show game. a) How many resulting prize numbers are possible in this game? b) How many resulting prize numbers are possible that end with the number 1?
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