1. Two risk neutral players compete to win a prize, P. The probability of winning depends on effort; the probability that player i wins equals e(e++e2), where ei is the effort level of player i. The cost of effort is ciei. a) Find the Nash equilibrium effort levels. b) What is the probability player 1 wins at equilibrium?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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1. Two risk neutral players compete to win a prize, P. The probability of winning
depends on effort; the probability that player i wins equals e(e++e2), where ei is the
effort level of player i. The cost of effort is ciei.
a) Find the Nash equilibrium effort levels.
b) What is the probability player 1 wins at equilibrium?
Transcribed Image Text:1. Two risk neutral players compete to win a prize, P. The probability of winning depends on effort; the probability that player i wins equals e(e++e2), where ei is the effort level of player i. The cost of effort is ciei. a) Find the Nash equilibrium effort levels. b) What is the probability player 1 wins at equilibrium?
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