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The 2/3 of Average Game • You have n players that are allowed to choose a number between 1 and 100. as a normal form game and find its mixed strategy Nash equilibria. We then pick a number in the range uniformly randomly. ² Result from an experiment with p =2/3. • The players coming closest to 2/3 of the average over all numbers win. So to win this game, you have to guess, you have to guess the average and then 2/3 of it, right? In the 19th century, scientists used the idea of random motions of molecules in the development of statistical mechanics to explain phenomena in thermodynamics and the properties of gases. So the typical average in this game is around 26-30, and you should guess 18-20. 1.3 Does game theory work? You will be guessing this number with 72 other people. The average guess was about 13.235418197890148 (a number which probably contains as much entropy as its length), meaning that the winning guess is the one closest to 8.823612131926765. Then the average of all the numbers written on paper is taken and the person whose guess is closest to 2/3 of the average is the winner. Lecture 2 - Putting Yourselves into Other People's Shoes Overview. For example, if the average of all guesses is 60, the correct guess will be 40. So a little bit below the average guess. If you actually want to win, it is usually best to guess in the range 15-25. Each one has to pick a number between 0 and 100. For this game, if you look at real world data sets for how many people chose each number, there tend to be 3 large spikes: one around 50, one around 33, and one around 22, with the largest being around 33. First, A picks a real number between 0 and 1 (both inclusive), then B picks a number in the same range (after knowing A's choice and different from it) and finally C picks a number, also in the same range, (different from the two chosen numbers). Suggest the best strategy available to each player and what number should they guess. Lucas Husted explains. And if Bob is told 21, he does not know if Alice was told 20 or 22. Case 1: The guessing game (hand run) Guess a number between 0 and 100. The game is played under conditions known to game theorists as “common knowledge:” every player has the same information— they also know that everyone else does too. the board game where you try to guess which character your opponent has before they find out yours. It would take 12 k-levels to reach 0. This number appears to be significantly below the number typical for groups of ordinary people, but not dramatically so. Those who pick this number behave as if all ‐ other competitors are naïve and simply submit a random number, so urn:x-wiley:01432095:media:smj2660:smj2660-math-0001 = 50. In this game the computer chooses a random number between 1 and 100, and the player tries to guess the number in as few attempts as possible. At k-level 2, they’d assume that everyone else was playing at level 1, leading them to guess 22. (5) Multiply Numbers By Drawing Lines. How to predict opponents’ play and respond optimally? Each agent’s outcome depends not only on his actions, but also on the actions of other agents. Given a range of integers from 0 to 100, what would the whole number closest to 2/3 of the average of all numbers guessed be? Next lesson. Consider a game where each player picks a number from 0 to 60. For example, if Alice is told 20, she does not know if Bob was told 19 or 21. The Game Theory Tim writes down a number from 1 to 1,000,000. Intro to algorithms. Please write your guess down before scrolling At the start of the lecture, we introduce the “formal ingredients” of a game: the players, their strategies and their payoffs. The 2/3 of the average problem posed on Friday is a well known puzzle in game theory, and it illustrates some fundamental game theoretic concepts.To recap, here’s the problem statement: Suppose everyone in your town selects a real number between 0 and 100, inclusive (i.e. On each turn you try to guess my number. Ties will be broken randomly. Up Next. We then pick a number in the range uniformly randomly. The easiest way to answer this question is with a simple example. (If you haven't read it yet, Introduction to Game Theory might be a useful prerequisite.) Assuming you play … Game theory has been applied to a number of disciplines, including economics, political science, psychology, sociology, biology, and computer science. The game theory implies that (A) all players have dominant strategies to choose 0 (B) all players have dominant strategies to choose 30 The guess closest to two-thirds of the average number wins. In case of a tie the prize is split amongst those who tie. Then you try to guess his number. View Syllabus. The simplicity can often be the biggest source of confusion, which is evident in the number of implausible answers. Game theory; Information theory; Pattern recognition; Probability theory; Quantum mechanics; Statistical mechanics; Statistics; In the physical sciences. Nash Equilibrium, Game Theory, Strategic Planning. Route-finding. Game Theory is the formal study of strategic interaction. We study optimal strategies for players in these games … 13. This experiment only takes a few minutes to run. Solution: Game can be formally represented as follows: N={1,…., n} where n>2 is the number of players What is an algorithm and why should you care? If your guess is not correct, I add or subtracts 1 from my number (always constructing a new number from 1 to 2011). The winner may be determined in various ways; for example, a winner can be a player whose guess is closest in magnitude to the target or a winner can be a player coming closest without guessing higher than the target. Empirically, this is rarely true. A guessing game. They are told the two numbers are consecutive, but neither knows the other person’s number. A person playing at k-level 0 would approach our game naively, guessing a number at random without thinking about the other players. At k-level 1, a player would assume everyone else was playing at level 0, resulting in an average of 50, and thus guess 33. level 1 of reasoning = best response to level 0 which is picking at random leads to 50) ² winning guess … Route-finding. ² 2 min game: mean = 23.9 ² (2/3)*(23.9)=15.9 ² typical game: mean ¼ 30 (i.e. N people announces a number in the set f1, players whose chosen numbers wins a.! Be the biggest source of confusion, which is evident in the range 15-25 Shoes Overview of people! 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