Q. A large population of players is playing the subsequent version of the beauty-contest game. Each player guesses a number between 100 also 200 (inclusive) also the player closest to p < 1 of the average wins a given prize. If multiple players are closest to p < 1 times the average, the prize is allocated randomly between them.

(a) Illustrate what guesses survive iterated elimination of dominated strategies?
From now on, Assume that a fraction 1 - μ of the players is rational also a fraction μ of the players is irrational. It is known that irrational players like high numbers, so they always guess 200.

(b) Solve for the rationales equilibrium guess as a function of p also μ.

(c) Illustrate what occurs to the rationales guess as p approaches 1 from below? Explain the intuition.

(d) Illustrate what occurs to the rationales guess as μ approaches 0? Explain the intuition.