Suppose a group of chess players gather and decide to rank themselves in "popularity". The popularity score of a player in the gathering is the number of other players in the gathering that player has previously played a game against. Prove that there will be ties in this score among the players in the gathering

Suppose a group of chess players gather and decide to rank themselves in "popularity". The popularity score of a player in the gathering is the number of other players in the gathering that player has previously played a game against. Prove that there will be ties in this score among the players in the gathering

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter17: Making Decisions With Uncertainty

Section: Chapter Questions

Problem 1MC

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Two players bargain over 1 unit of a divisible object. Bargaining starts with an offer of player 1, which player 2 either accepts or rejects. If player 2 rejects, then player 1 makes another offer; if player 2 rejects once more, then player 2 makes an offer. If player 1 rejects the offer of player 2, then once more it is the turn of player 1 where he makes two consecutive offers. As long as an agreement has not been reached this procedure continues. For example, suppose that agreement is reached at period 5, it follows that player 1 makes offers in period 1,2 then player 2 makes an o er in period 3, then player 1 makes offers in 4,5. Negotiations can continue indefinitely, agreement in period 't' with a division (x, 1- x) leads to payoffs ( , (1-x)).(The difference from Rubinstein's alternating offer bargaining is that player one makes two consecutive offers, whereas player 2 makes a single offer in her turn.) a. Show that there is a subgame perfect equilibrium in which player 2's…
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When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, the auctioneer actively woos representatives of other museums that have no chance of winning to attend anyway. Suppose a piece of art has recently become available for sale and will be auctioned off to the highest bidder, with the winner paying an amount equal to the second highest bid. Assume that most collectors know that Valerie places a value of $15,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Valerie simply bids $15,000/2=$7,500 and wins the piece of art. The expected price paid by Valerie, with no other bidders present, is $________.. Suppose the owner of the artwork manages to recruit another bidder, Antonio, to the auction. Antonio is known to value the art piece at $12,000. The expected price paid by Valerie, given the presence of the second bidder Antonio, is $_______. .
A bag of n players chooses one number between 0 and 10. The winner is the one who chooses the second smallest number. For example, if the selected numbers are [2, 2, 3, 5, 9, 10], the winner will be the one who chose 3. In the event that multiple people choose the second smallest number, the winner is randomly selected from among them. For example, if the selected numbers are [2,2, 2, 3, 3, 3, 3, 5, 9, 10], each player who chose 3 will win with a probability of 1/4. Even if everyone chooses the same number (meaning there is no second smallest number), the winner is randomly selected from among them. Each player wants to choose the number that will give them the greatest chance of winning. Find the Nash equilibrium for this problem.
A bag of n players chooses one number between 0 and 10. The winner is the one who chooses the second smallest number. For example, if the selected numbers are [2, 2, 3, 5, 9, 10], the winner will be the one who chose 3. In the event that multiple people choose the second smallest number, the winner is randomly selected from among them. For example, if the selected numbers are [2, 2, 3, 3, 3, 3, 5, 9, 10], each player who chose 3 will win with a probability of 1/4. Even if everyone chooses the same number (meaning there is no second smallest number), the winner is randomly selected from among them. Each player wants to choose the number that will give them the greatest chance of winning. Find the Nash equilibrium.
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Microsoft is one of the leading software companies. Prior to 2000, Microsoft’s share of the market for personal computer operating systems stood above 80 per cent. However, since the twenty-first century Microsoft’s market share has steadily declined to 40 per cent. This is due to the rise in competing software producers such as Apple macOS (10%), Google's Android OS (35%), Linux Operating System (35%), and Apple iOS (5%). The market share of each company is provided in parentheses. Google and Linux have decided that it would be in their best interest to work together to serve the market. This is not common knowledge to the person’s outside of the companies. State what market structure existed prior to the 2000 and illustrate how equilibrium price and quantity are determined in this industry. Can excess profit be earned by Microsoft in the long run prior to the 2000. Explain. [3 marks] State what market structure exists in the twenty first century. Explain if excess profit will exist…
Microsoft is one of the leading software companies. Prior to 2000, Microsoft’s share of the market for personal computer operating systems stood above 80 per cent. However, since the twenty-first century Microsoft’s market share has steadily declined to 40 per cent. This is due to the rise in competing software producers such as Apple macOS (10%), Google's Android OS (35%), Linux Operating System (35%), and Apple iOS (5%). The market share of each company is provided in parentheses. Google and Linux have decided that it would be in their best interest to work together to serve the market. This is not common knowledge to the person’s outside of the companies. i. State what market structure existed prior to the 2000 and illustrate how equilibrium price and quantity are determined in this industry. Can excess profit be earned by Microsoft in the long run prior to the 2000. Explain. State what market structure exists in the twenty first century. Explain if excess…
Microsoft is one of the leading software companies. Prior to 2000, Microsoft’s share of the market for personal computer operating systems stood above 80 per cent. However, since the twenty-first century Microsoft’s market share has steadily declined to 40 per cent. This is due to the rise in competing software producers such as Apple macOS (10%), Google's Android OS (35%), Linux Operating System (35%), and Apple iOS (5%). The market share of each company is provided in parentheses. Google and Linux have decided that it would be in their best interest to work together to serve the market. This is not common knowledge to the person’s outside of the companies. State what market structure existed prior to the 2000 and illustrate how equilibrium price and quantity are determined in this industry.
An experiment consists of asking 3 women at random if they wash their dishes with brand X detergent. List the elements of S corresponding to event E that at least 2 of the women use brand X