Suppose individuals live in villages that are homogeneous by type and a fractions of their interactions takes place in their village, the rest occurring in the city where the types were mixed. The fraction of the population who are cooperators is a. a) Write the expected return functions for cooperate and defect as a function of s and a. b) Under which conditions does an interior equilibrium exist for the fraction of the population playing cooperate (a) c) If the interior equilibrium for a exists, is the interior equilibrium unstable or stable? d) Find the impact of higher s on the interior equilibrium for a. What intuitively does this outcome mean? Discuss your answer.

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
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Individual
A
Cooperate
Defect
Individual B
Cooperate
28, 28
34,8
Defect
8, 34
12, 12
Suppose individuals live in villages that are homogeneous by type and a fractions of
their interactions takes place in their village, the rest occurring in the city where the
types were mixed. The fraction of the population who are cooperators is a.
a) Write the expected return functions for cooperate and defect as a function of s and
a.
b) Under which conditions does an interior equilibrium exist for the fraction of the
population playing cooperate (a)
c) If the interior equilibrium for a exists, is the interior equilibrium unstable or stable?
d) Find the impact of higher s on the interior equilibrium for a. What intuitively does
this outcome mean? Discuss your answer.
Transcribed Image Text:Individual A Cooperate Defect Individual B Cooperate 28, 28 34,8 Defect 8, 34 12, 12 Suppose individuals live in villages that are homogeneous by type and a fractions of their interactions takes place in their village, the rest occurring in the city where the types were mixed. The fraction of the population who are cooperators is a. a) Write the expected return functions for cooperate and defect as a function of s and a. b) Under which conditions does an interior equilibrium exist for the fraction of the population playing cooperate (a) c) If the interior equilibrium for a exists, is the interior equilibrium unstable or stable? d) Find the impact of higher s on the interior equilibrium for a. What intuitively does this outcome mean? Discuss your answer.
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