Ayudantía 3 Solución

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PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE
Facultad de Ciencias Económicas y Administrativas
EAA200B-5 Fundamentos de Dirección de Empresas
Ayudant́ıa # 2
Raicho Bojilov
Valentina Diaz Valenzuela
Francisca Ignacia Stange Mart́ınez
Second Semester 2020
1 Iterated Elimination of Dominated Strategies
Consider the following strategic game:
A\B L C R
U 10,4 5,3 3,2
M 0,1 4,6 6,0
L 2,1 3,5 2,8
1. Find the Nash equilibrium of this game.
2. Eliminate dominated strategies. What is the Nash equilibrium of the reduced game?
2 Problem of Collective Action: Continuous Setting
Two partners, i = 1, 2, work on a common project. Each decides how much e↵ort to put into the project,
ei. The total value of the project is given by the formula:
q(e1, e2) = e1 + e2 + e1e2
They split the gains equally between themselves. Their individual payo↵ is the di↵erence between the value
of the project and the e↵ort that they make, e2i .
ui(e1, e2) = 0.5(e1 + e2 + e1e2)� e2i
1. What is the Nash equilibrium?
2. What are levels of e↵ort that maximize the joint (partnership) surplus? This surplus is defined as:
(e1 + e2 + e1e2)� e21 � e22
3. Can you propose a scheme of organization and division of the partnership between 1 and 2 that achieves
the socially optimal outcome?
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