max II₂i (x2i, j) 721 20 Cj (ci + cj)² X2i x2 + x2j where x21 (25) denotes contest investment by i (j) in stage 2. Following Nti (1999), first-order optimality conditions determine the unique pure strategy Nash equilibrium. Equilibrium investments satisfy Ꭱ ; -R-C2i Ci (c + c₂ ) ²² R.

max II₂i (x2i, j) 721 20 Cj (ci + cj)² X2i x2 + x2j where x21 (25) denotes contest investment by i (j) in stage 2. Following Nti (1999), first-order optimality conditions determine the unique pure strategy Nash equilibrium. Equilibrium investments satisfy Ꭱ ; -R-C2i Ci (c + c₂ ) ²² R.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.7P

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Question

max II2i(2, ₁) =
#2120
X2i
X2i
-R-C2i
+ x2j
where x2; (2) denotes contest investment by i (j) in stage 2. Following Nti (1999), first-order
optimality conditions determine the unique pure strategy Nash equilibrium. Equilibrium
investments satisfy
C₂
x2 = (a + c)²R; x2 = (a + c)² R.
X2i
Ꭱ
c₂)²¹

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