Question

6. Using a payoff matrix to determine the equilibrium outcome 

Suppose there are only two firms that sell Blu-ray players: Movietonia and Videotech. The following payoff matrix shows the profit (in millions of dollars) each company will earn, depending on whether it sets a high or low price for its players. 

For example, the lower-left cell shows that if Movietonia prices low and Videotech prices high, Movietonia will earn a profit of $18 million, and Videotech will earn a profit of $2 million. Assume this is a simultaneous game and that Movietonia and Videotech are both profit-maximizing firms. 

 If Movietonia prices high, Videotech will make more profit if it chooses a_______ price, and if Movietonia prices low, Videotech will make more profit if it chooses a _______ price. 

If Videotech prices high, Movietonia will make more profit if it chooses a _______ price, and if Videotech prices low, Movietonia will make more profit if it chooses a _______ price. 

Considering all of the information given, pricing low _______ a dominant strategy for both Movietonia and Videotech.

If the firms do not collude, what strategies will they end up choosing?

• Movietonia will choose a low price, and Videotech will choose a high price.

• Both Movietonia and Videotech will choose a high price.

• Movietonia will choose a high price, and Videotech will choose a low price.

• Both Movietonia and Videotech will choose a low price.

True or False: The game between Movietonia and Videotech is an example of the prisoners' dilemma.

• True

• False

Answer 1

If Movietonia prices high, Videotech will make more profit if it chooses a low price , and if Movietonia prices low, Videotech will make more profit if it chooses a low price.

So, Low, Low

If Videotech prices high, Movietonia will make more profit if it chooses a low price , and if Videotech prices low, Movietonia will make more profit if it chooses a low price.

So, low, low in this case as well.

If Movietonia chooses high strategy, then payoffs are: (11, 2)

If it chooses low strategy, then payoffs are: (18, 10)

Movietonia makes higher profit if it chooses low strategy irrespective of whatever Videotech chooses. So, Low is the dominant strategy for Movietonia

Similarly,

If Videotech chooses high strategy, then payoffs are: (11, 2)

If it chooses low strategy, then payoffs are: (18, 10)

Videotech makes a higher profit if it chooses low strategy irrespective of whatever Movietonia chooses. So, Low is the dominant strategy for Movietonia.

Hence, pricing low is a dominant strategy for both Movietonia and Videotech

Game

	High	Low
High	(11, 11)	(2, 18) *
Low	(18, 2) #	(10, 10) *#

As seen from the above table, the Nash Equilibrium (without collusion) is .

So, both Movietonia and Videotech will choose a low price.

Option 4th is correct

Prisonner's Dilemma situation when the players end up choosing a sub-optimal solution which gives them a lower payoff.

As seen from the above, both player benefits if they had choosen as their optimal strategy which would have given them a higher payoff of (11, 11) vis-a-vis the payoff of (10, 10).

So, this game is indeed an example of the prisoner's dilemma. Hence, it is TRUE