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Looking for help with this market entry problem from an economics class but is very closely related to statistics!

Problem 1. Market Entry (65 points) Setup For this problem, you will need to read the paper by Camerer and Lovallo (1999) posted on NYU Courses.We will consider a slightly simplified version in our theoretical analysis below. The setup is as follows: 1. N players privately and simultaneously choose whether to enter a market with some known capacity,c, and profit, 1;. 2. The (N ~— E) players who stay out earn a payment of l].3. The E players who enter are randomly assigned an integer-valued ranking, r, ranging from 1 to E. 4. If the number of entrants, E, does not exceed the industry capacity, c, all entrants earn an equal shareof the profit, v/E. 5. If the number of entrants exceeds capacity, then the c highest-rammed entrants (ranked 3* S c) earn v/c.The remaining (E —» :2) players (ranked r > :2) each suffer a loss of K . Formally, we can denote the strategy space of player 3′ E {1, 2, …,N} by 5′, =6 {0,1}, where 0 denotesnon-entry and 1 denotes entry. Throughout this problem, we assume that players maximize their expectedmonetary payoffs. (a) [10 pts] Explain why player i’s expected payoff can be written as: l] Si=01T5= E s,=1,E5c gxg—Kx(%) s,=1,E>c (b) [5 pts] Show that there are no pure-strategy Nash equilibrium in which the number of entrants isstrictly smaller than c. [Hintz use the payoff functions from (a) to show that in such a scenario, there isalways a profitable deviation for nonentrants.]

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