10. Here's another game that has interested researchers, especially those of the type who work in the MaxGluskin House on campus at UofT. It's also a two-player game, but this time the payment is integralto describing the game. There is no direct Researcher involvement in the game, other than potentiallyas the source of a payout.For the sake of describing the game, imagine that Anson and Kanav are our two players and that theyare playing the game virtually via Zoom for bitcoins, denoted B. There are always two piles of bitcoinin play: a larger one and a smaller one. Ahead of the game Anson and Kanav decide the maximumnumber 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. Ansoncan either take the bitcoin or pass. If Anson (4 B) takes the bitcoin he gets the larger pile, Kanavgets 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 Kanavcan either take the bitcoin or pass. If he takes the bitcoin, Kanav leaves with 8 B, Anson leaveswith 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 passthe 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 orpass. 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, howmany rounds do you think they usually play to? You can state your guess as either a number oras a percentage of 2n, depending on what you guess. Give a reason that doesn't have anythingto do with math.(b) How many rounds will the game end in if both players are playing entirely strategically, and theyboth know that each other is playing strategically? Here, a strategic approach means that youcare only about maximizing your amount of money. Prove your answer using an induction-typeargument.(c) What can you say about the number of rounds the game will last if only one player is playingstrategically? (Economists have found that even when both players are aware of the best strategythey do not play strategically.)

Given, There are two players : Anson and Kanav They are playing a game virtually on Zoom for…

Answered: Here's another game that has interested…

Principles of Microeconomics (MindTap Course List)

8th Edition

ISBN:9781305971493

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Oligopoly

Section: Chapter Questions

Problem 9PA

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Does each individual in a prisoners dilemma benefit more from cooperation or from pursuing self-interest? Explain briefly.
3. Suppose that the various Balls of basketball or internet fame Lavar, Lamelo, Liangelo, Lonzo,and Spalding are considering playing in a 1-on-1 tournament. They get a payoff of 0 if theydecide not to participate. The following table illustrates their payoffs across the variousscenarios. 1 Player 2 Players 3 Players 4 Players 5 Players Lavar 10 4 2 -2 -5 Lamelo 10 7 5 2 -1 Liangelo 10 7 5 2 -1 Lonzo 10 8 7 6 5 Spalding 10 9 8 7 6 a. Find and describe all pure strategy Nash Equilibria.b. Suppose now Spalding, since it is in fact a literal basketball, gets a payoff of 0 in anycircumstance, being an inanimate object. The table is now as follows: 1 Player 2 Players 3 Players 4Players 5 Players Lavar 10 4 2 -2 -5 Lamelo 10 7 5 2 -1 Liangelo 10 7 5 2 -1 Lonzo 10 8 7 6 5 Spalding 0 0 0 0 0 Find and describe all pure strategy Nash Equilibria.
12. Consider a game where each player picks a number from 0 to 60. The guess that is closest to half ofthe average of the chosen numbers wins a prize. If several peopleare equally close, then they share theprize. The game theory implies that (A) all players have dominant strategies to choose 0 (B) all players have dominant strategies to choose 30 (C) there is a Nash equilibrium where all players pick 0 (D) there is a Nash equilibrium where all players pick positive numbers 13. Behavioral data in such games suggests that (A) most subjects choose 0; (B) most subjects choose 30; (C) common answers include 30, 15, 7.5, and 0; (D) most subjects use randomization. Can you help me answer number 13 please?
7. A farmer can either invest in irrigation for their farm or not. There's a 30% chance that they will receive adequate rain such that the irrigation is not necessary, and a 70% chance that the irrigation will be useful if acquired. Assume that the farmer will receive $5,000 if their crops are adequately watered, and $1,000 otherwise. Irrigation costs $3,000. For simplicity, assume this is a one-off game and that nature is not perverse.a. Draw the extensive form of this game, with the farmer acting first and nature second.b. What is the expected value of each strategy for the farmer?c. What is the expected value of perfect information on the weather?
Paramter y = 0 If ⟨a, d⟩ is played in the first period and ⟨b, e⟩ is played in the second period, whatis the resulting (repeated game) payoff for the row player?
8. Two states, A and B, have signed an arms-control agreement. This agreementcommits them to refrain from building certain types of weapons. The agreement is supposed tohold for an indefinite length of time. However, A and B remain potential enemies who wouldprefer to be able to cheat and build more weapons than the other. The payoff table for A (player1, the row player) and B (player 2, the column player) in each period after signing thisagreement is below. a) First assume that each state uses Tit-for-Tat (TFT) as a strategy in this repeated game.The rate of return is r. For what values of r would it be worth it for player A to cheat bybuilding additional weapons just once against TFT? b) For what values of r would it be worth deviating from the agreement forever to buildweapons? c) Convert both values you found in parts a and b to the equivalent discount factor dusing the formula given in lecture and section. d) Use the answers you find to discuss the relationship between d and r:…
Consider the following two-player game.First, player 1 selects a number x≥0. Player 2 observes x. Then, simultaneously andindependently, player 1 selects a number y1 and player 2 selects a number y2, at which pointthe game ends.Player 1’s payoff is: u1(x; y1) = −3y21 + 6y1y2 −13x2 + 8xPlayer 2’s payoff is: u2(y2) = 6y1y2 −6y22 + 12xy2Draw the game tree of this game and identify its Subgame Perfect Nash Equilibrium.
Consider the extensive form game portrayed below. The top number at aterminal node is player 1’s payoff, the middle number is player 2’s payoff,and the bottom number is player 3’s payoff.a. Derive the strategy set for each player. (Note: If you do not want to listall of the strategies, you can provide a general description of a player’sstrategy, give an example, and state how many strategies are in thestrategy set.)b. Derive all subgame perfect Nash equilibria. c. Derive a Nash equilibrium that is not a SPNE, and explain why it isnot a SPNE.
Imagine that two firms in two different countries want to bring a new product tomarket. Due to economies of scale, if both firms do this, they will both lose £50million. But if only one firm does this, it will gain £300 million.(a) What is the best strategy for firm A, if firm B has not yet entered the market, andwhy?(b) Illustrate this with a game theory diagram, showing appropriate payouts.(c) What is the welfare-maximising strategy for a government, and why?

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