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Advanced Management Accounting代写-EF5407-Assignment 3

时间：2021-04-04

EF5407: Topics in Microeconomics Sem B 2020-2021

Assignment 3

Due: Friday, April 16

Maximum Marks: 100

IMPORTANT NOTE: Please submit your assignment online through canvas,

latest by the due date. Upload a pdf document only. Please note that the ques-

tions are based on the material covered in lectures 7-9. There are four questions

and each question carries equal mark. Your submissions must be written clearly.

Question 1: Two people are involved in a dispute. Person 1 does not know whether person

2 is strong or weak; she assigns probability ↵ to person 2’s being strong. Person 2 is fully

informed. Each person can either fight or yield. Each person’s preferences are represented

by the expected value of a payo↵ function that assigns the payo↵ of 0 if she yields (regardless

of the other person’s action) and a payo↵ of 1 if she fights and her opponent yields; if both

people fight, then their payo↵s are (-1,1) if person 2 is strong and (1,-1) if person 2 is weak.

Formulate this situation as a Bayesian game and find its Bayes-Nash equilibria if ↵ < 1/2

and if ↵ > 1/2.

Question 2: Consider the Cournot duopoly model with imperfect information about costs

as discussed in class. That is, consider the situation where firm 1’s unit cost (c) is known

by both firms, but only firm 2 knows its own unit cost. Firm 1 believes that firm 2’s cost

is cL with probability ✓ and cH with probability 1 ✓, where 0 < ✓ < 1 and cL < cH . Now

assume that the (inverse) demand in the market is given by: P (Q) = ↵Q for Q ↵ and

P (Q) = 0 for Q > ↵. Assuming that all outputs are positive in the Bayes Nash equilibrium,

what is the equilibrium?

Question 3: Consider a variant of the Bayesian game of first-price auction discussed in class

in which the players are risk averse. Specifically, suppose each of the n players’ preferences

are represented by the expected value of the payo↵ function x1/m, where x is the player’s

monetary payo↵ and m > 1. Suppose also that each player’s valuation is distributed uni-

formly between 0 and 1. Find the symmetric Bayes-Nash equilibrium bidding function.

Page 1 of 2

靐

EF5407: Topics in Microeconomics Sem B 2020-2021

Question 4: Specify a pooling Perfect Bayesian Equilibrium in which both sender types

play R in the following signaling game.

Page 2 of 2

学霸联盟

Assignment 3

Due: Friday, April 16

Maximum Marks: 100

IMPORTANT NOTE: Please submit your assignment online through canvas,

latest by the due date. Upload a pdf document only. Please note that the ques-

tions are based on the material covered in lectures 7-9. There are four questions

and each question carries equal mark. Your submissions must be written clearly.

Question 1: Two people are involved in a dispute. Person 1 does not know whether person

2 is strong or weak; she assigns probability ↵ to person 2’s being strong. Person 2 is fully

informed. Each person can either fight or yield. Each person’s preferences are represented

by the expected value of a payo↵ function that assigns the payo↵ of 0 if she yields (regardless

of the other person’s action) and a payo↵ of 1 if she fights and her opponent yields; if both

people fight, then their payo↵s are (-1,1) if person 2 is strong and (1,-1) if person 2 is weak.

Formulate this situation as a Bayesian game and find its Bayes-Nash equilibria if ↵ < 1/2

and if ↵ > 1/2.

Question 2: Consider the Cournot duopoly model with imperfect information about costs

as discussed in class. That is, consider the situation where firm 1’s unit cost (c) is known

by both firms, but only firm 2 knows its own unit cost. Firm 1 believes that firm 2’s cost

is cL with probability ✓ and cH with probability 1 ✓, where 0 < ✓ < 1 and cL < cH . Now

assume that the (inverse) demand in the market is given by: P (Q) = ↵Q for Q ↵ and

P (Q) = 0 for Q > ↵. Assuming that all outputs are positive in the Bayes Nash equilibrium,

what is the equilibrium?

Question 3: Consider a variant of the Bayesian game of first-price auction discussed in class

in which the players are risk averse. Specifically, suppose each of the n players’ preferences

are represented by the expected value of the payo↵ function x1/m, where x is the player’s

monetary payo↵ and m > 1. Suppose also that each player’s valuation is distributed uni-

formly between 0 and 1. Find the symmetric Bayes-Nash equilibrium bidding function.

Page 1 of 2

靐

EF5407: Topics in Microeconomics Sem B 2020-2021

Question 4: Specify a pooling Perfect Bayesian Equilibrium in which both sender types

play R in the following signaling game.

Page 2 of 2

学霸联盟