Cric

Managerial Economics

Tutorial 5 - Week 7

Ch. 5 - Game Theory and Ch. 6 - Cournot Equilibrium

Problem One

Consider the following simultaneous moves game in normal form:

Player Two

t1 t2

Player One r1 -2,4 0,-2

r2 -4,5 0,1

(a) State the set of Nash equilibrium strategies.

(b) State the payoffs to each player in the Nash equilibrium.

Problem Two

A and B are playing a simultaneous moves game. A can choose either High or Low and B can choose either Near or Far. If A chooses High and B chooses Near, A receives 5 and B receives 5. If A chooses High and B chooses Far A receives 3 and B receives 7. If A chooses Low and B chooses Near A receives 7 and B receives 3. If A chooses Low and B chooses Far, both receive 2.

(a) Write out a table representing each player's strategies and payoffs.

(b) What is/are the Nash equilibrium of this game?

Problem Three

Consider a Cournot duopoly, composed of firms A & B - which produce identical products and face identical costs.

(a) Draw a set of reaction functions in one diagram for this Cournot duopoly.

(b) Label the monopoly outputs that would be produced by firms A & B.

(c) Label the Cournot equilibrium set of outputs.

(d) If the fixed costs of firm A go up - what happens to its reaction curve?

(e) In a new diagram, with identical reaction functions to those used in parts (a) - (c), if the marginal cost for firm A, at every level of output, increases, demonstrate what will happen to its reaction curve. How will the Cournot equilibrium outputs of each firm change?

(f) In a new diagram, with identical reaction functions to those used in parts (a) - (c), if the demand curves for firms A & B shift inwards, demonstrate what will happen to their reaction curves. How will the Cournot equilibrium outputs of each firm change?

Problem Four

Suppose the inverse market demand equation is P = 80 - 4(QA+QB), where QA is the output of firm A and QB is the output of firm B, and both firms have a constant marginal cost of $4 (fixed costs are zero).

(a) Write