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 people are 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 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.

We are going to use a few game theory concepts to answer this question.A player has to pick a number from 0 to 60 and guess closest to half of all the selection will win the price. Now every one will figure out the half of provided number set is 30, therefore it is illogical to choose anything above 30. Now every one rationally will figure out that half of 30 is 15 and then again half of that. It goes on until the number reaches to 0. Therefore if we use K-level rationalisation then the unique Nash equilibrium is "0". This is the state where every player has chosen the best possible strategy for themselves given everyone else playing, and no individual player can benefit by choosing differently. In other words Pareto optimal outcome of thje game. But in real life the above result is not evident. A sample who is involved into the game keep on choosing different numbers in an attempt to predict the result. In this game people will choose between 7.5 and 30. This happens because each player is not perfectly rational or an individual player dont believe that other players are not rational. Hence option C is correct in both scenarios.

Answered: Consider a game where each player picks…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider a game where each player picks a number from 0 to 60. The guess that is closest to half of

the average of the chosen numbers wins a prize. If several people are equally close, then they share the

prize. The game theory implies that

(A) all players have dominant strategies to choose 0

(B) all players have dominant strategies to choose 30

(D) there is a Nash equilibrium where all players pick positive numbers

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.

Definition Definition Economic decision-making framework that analyzes how different players optimize their outcomes with given pay-offs corresponding to their available strategies. The assumptions of game theory are: The number of players or competitors are finite/limited; All participants are rational The rules of the game are known to every player; and Each participant has a finite set of actions. A common way in which game theory is presented as an ( m x n ) matrix in which m represents the strategies of row player and n represents the strategies of column player. There are several limitations of game theory: Many businesses have a large number of competitors, and selecting an optimal strategy in these circumstances is difficult; Real-life business operating environments are full of uncertainty and difficult to model as a game theory; and The assumption of rationality and utility maximization isn't always an accurate portrayal of human nature.

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