Question 6 Two firms, Omo and Dynamo, are the only producers of laundry detergen

Question

Question 6

Two firms, Omo and Dynamo, are the only producers of laundry detergent in the market. They could produce the detergent in either liquid or powder form. If both firms produce a liquid detergent, each makes $2 million economic profit. If Omo produces a liquid detergent and Dynamo produces powder, Omo incurs an economic loss of $1 million and Dynamo increases its profit to $3 million. If Omo produces powder and Dynamo produces a liquid detergent, Omo earns an economic profit of $1 million and Dynamo makes an economic loss of $1 million. If both firms produce the powder form of the detergent, both firms will earn normal profit. Neither firm has any way of policing the other’s actions.

a. Construct the payoff matrix. (1 Mark)

b. Does either player have a dominant strategy? If so, please state. (2 Marks)

c. What is the Nash equilibrium for this game? (2 Marks)  

Explanation / Answer

The game is played by two players: Omo and Dynamo. The strategy set faced by each player is {Liquid, Powder}

Assign a payoff of $2 when both produce liquids. Assign a payoff of $10 to the one who Liquids (if he survives) and $5 to the one who Powders. A payoff of $0 is given when both produce powder. If Omo produces a liquid detergent and Dynamo produces powder, Omo incurs an economic loss of $1 million and Dynamo increases its profit to $3 million. If Omo produces powder and Dynamo produces a liquid detergent, Omo earns an economic profit of $1 million and Dynamo makes an economic loss of $1 million

a)

After assigning the payoffs, construct the payoff matrix akin to the one described below:

Dynamo

Omo

Liquid

Powder

Liquid

(2, 2)

(-1, 3)

Powder

(1, -1)

(0, 0)

b)

The game certainly has adominant strategy for any Dynamo. Note that when Omo choses to produce Liquid, Dynamo is better off in choosing Powder since it gives a payoff of $3 million while producing liquid gives a profit of $2 million. When Omo choses to produce Powder, Dynamo is again better off in choosing to produce Powder. Hence whatever Omo does, Dynamo will produce powdered detergent.

In a similar manner, when Dynamo choses to produce Liquid, Omo is better off in choosing Liquid detergent and when Dynamo choses Powder, Omo is better off in choosing Powdered detergent

c) Nash equilibrium is the set of strategies that players choose as their best response, given the actions by the rest of the players. So there is one pure strategy Nash equilibria and that is given by (Powder, Powder)

Dynamo

Omo

Liquid

Powder

Liquid

(2, 2)

(-1, 3)

Powder

(1, -1)

(0, 0)

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