04 Jun Question ECON 402. Fall 2014
Question
ECON 402. Fall 2014
HOMEWORK 3
Due in class on Tuesday, September 30th
1. Find the set of undominated strategies in the following games.
(a)
(b)
1
2. Find the set of rationalizable strategies for the following game.
3. Suppose that you manage a rm and are engaged in a dispute with one of your
employees. The process of dispute resolution is modeled by the following game, where
your employee chooses either to \settle” or to \be tough in negotiation”, and you choose
either to \hire an attorney” or to \give in”. Suppose the game can be represented as
follows:
Suppose x is a number that both you and the employee know. For what values of x
can you rationalize selecting the strategy \give in”? Explain what your beliefs need to
satisfy for this to be the case.
4. Consider a duopoly game in which two rms simultaneously and independently select
prices. Assume that prices cannot be negative. Let p1 denote the price set by rm
2
1 and p2 let the price set by rm 2. Unlike Bertrand competition (see Chapter 10),
we assume that products are dierentiated. To be precise, once prices are set by both
rms, consumers demand 10 ???? p1 + p2 units from the good that rm 1 produces, and
they demand 10 ???? p2 + p1 units from the good that rm 2 produces. Assume that
each rm must supply the number of units demanded. Also assume that the cost of
producing qi units is equal to 1
2 qi for rm i = 1; 2.
(a) Write the payo functions for both players (as functions of their strategies p1 and
p2).
(b) Characterize each player’s best response function (as a function of the price set
by the other player). That is, characterize BR1(p2) and BR2(p1). Are prices
strategic substitutes or complements in this game?
(c) Can you determine the set of rationalizable strategies in this game by inspection
of players’ best-response functions? What is the set of rationalizable strategies?
(d) What is the Nash equilibrium in this game? Is the equilibrium an ecient
outcome?
5. Consider the following game:
(a) Characterize the set of rationalizable strategies in this game.
(b) Find all the Nash equilibria in the game. Are these equilibria ecient?
3
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