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Here's another game that has interested researchers, especially those of the type who work in the Max Gluskin House on campus at UofT. It's also a two-player game, but this time the payment is integral to describing the game. There is no direct Researcher involvement in the game, other than potentially as the source of a payout. For the sake of describing the game, imagine that Anson and Kanav are our two players and that they are playing the game virtually via Zoom for bitcoins, denoted B. There are always two piles of bitcoin in play: a larger one and a smaller one. Ahead of the game Anson and Kanav decide the maximum number 2n of turns, for some n EN greater than or equal to 1.

Here's another game that has interested researchers, especially those of the type who work in the Max Gluskin House on campus at UofT. It's also a two-player game, but this time the payment is integral to describing the game. There is no direct Researcher involvement in the game, other than potentially as the source of a payout. For the sake of describing the game, imagine that Anson and Kanav are our two players and that they are playing the game virtually via Zoom for bitcoins, denoted B. There are always two piles of bitcoin in play: a larger one and a smaller one. Ahead of the game Anson and Kanav decide the maximum number 2n of turns, for some n EN greater than or equal to 1.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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10. Here's another game that has interested researchers, especially those of the type who work in the Max Gluskin House on campus at UofT. It's also a two-player game, but this time the payment is integral to describing the game. There is no direct Researcher involvement in the game, other than potentially as the source of a payout. For the sake of describing the game, imagine that Anson and Kanav are our two players and that they are playing the game virtually via Zoom for bitcoins, denoted B. There are always two piles of bitcoin in play: a larger one and a smaller one. Ahead of the game Anson and Kanav decide the maximum number 2n of turns, for some n E N greater than or equal to 1. • During the first turn the large pile of bitcoin has 4 Band the smaller pile of bitcoin has 1 B. Anson can either take the bitcoin or pass. If Anson (4 B) takes the bitcoin he gets the larger pile, Kanav gets the smaller pile (1 B) and the game ends. If he passes, the size of each pile is doubled. • Now the large pile of bitcoin has 8 Band the smaller pile has a 2 B. During the second turn Kanav can either take the bitcoin or pass. If he takes the bitcoin, Kanav leaves with 8 B, Anson leaves with 2 B, and the game ends. If he passes the piles double. • In general, during odd-numbered turns Anson can either take the bitcoin or pass. After each pass the piles double. If Anson takes the bitcoin the game ends. • (Piles of Bitcoins) In general, during even-numbered turns Kanav can either take the bitcoin or pass. After each pass the piles double. If Kanav takes the bitcoin the game ends. (a) What do you think usually happens when two players engage in a game like this? That is, how many rounds do you think they usually play to? You can state your guess as either a number or as a percentage of 2n, depending on what you guess. Give a reason that doesn't have anything to do with math. (b) How many rounds will the game end in if both players are playing entirely strategically, and they both know that each other is playing strategically? Here, a strategic approach means that you care only about maximizing your amount of money. Prove your answer using an induction-type argument. (c) What can you say about the number of rounds the game will last if only one player is playing strategically? (Economists have found that even when both players are aware of the best strategy they do not play strategically.)
Transcribed Image Text:10. Here's another game that has interested researchers, especially those of the type who work in the Max Gluskin House on campus at UofT. It's also a two-player game, but this time the payment is integral to describing the game. There is no direct Researcher involvement in the game, other than potentially as the source of a payout. For the sake of describing the game, imagine that Anson and Kanav are our two players and that they are playing the game virtually via Zoom for bitcoins, denoted B. There are always two piles of bitcoin in play: a larger one and a smaller one. Ahead of the game Anson and Kanav decide the maximum number 2n of turns, for some n E N greater than or equal to 1. • During the first turn the large pile of bitcoin has 4 Band the smaller pile of bitcoin has 1 B. Anson can either take the bitcoin or pass. If Anson (4 B) takes the bitcoin he gets the larger pile, Kanav gets the smaller pile (1 B) and the game ends. If he passes, the size of each pile is doubled. • Now the large pile of bitcoin has 8 Band the smaller pile has a 2 B. During the second turn Kanav can either take the bitcoin or pass. If he takes the bitcoin, Kanav leaves with 8 B, Anson leaves with 2 B, and the game ends. If he passes the piles double. • In general, during odd-numbered turns Anson can either take the bitcoin or pass. After each pass the piles double. If Anson takes the bitcoin the game ends. • (Piles of Bitcoins) In general, during even-numbered turns Kanav can either take the bitcoin or pass. After each pass the piles double. If Kanav takes the bitcoin the game ends. (a) What do you think usually happens when two players engage in a game like this? That is, how many rounds do you think they usually play to? You can state your guess as either a number or as a percentage of 2n, depending on what you guess. Give a reason that doesn't have anything to do with math. (b) How many rounds will the game end in if both players are playing entirely strategically, and they both know that each other is playing strategically? Here, a strategic approach means that you care only about maximizing your amount of money. Prove your answer using an induction-type argument. (c) What can you say about the number of rounds the game will last if only one player is playing strategically? (Economists have found that even when both players are aware of the best strategy they do not play strategically.)
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