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.
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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.
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