Using a payoff matrix to determine the equilibrium outcome Suppose there are onl

Question

Using a payoff matrix to determine the equilibrium outcome

Suppose there are only two firms that sell smart phones, Flashfone and Pictech. 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 phones.

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

If Flashfone prices high, Pictech will make more profit if it chooses a (high/low) price, and if Flashfone prices low, Pictech will make more profit if it chooses a (high/low)price.

If Pictech prices high, Flashfone will make more profit if it chooses a(high/low)price, and if Pictech prices low, Flashfone will make more profit if it chooses a (high/low) price.

Considering all of the information given, pricing low(high/low)a dominant strategy for both Flashfone and Pictech.

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

Flashfone will choose a high price and Pictech will choose a low price.

Both Flashfone and Pictech will choose a low price.

Flashfone will choose a low price and Pictech will choose a high price.

Both Flashfone and Pictech will choose a high price.

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

True

False

Explanation / Answer

Answer.

According to the payoff matrix in the question:

If Fashfone chooses to price high then Pictech will prefer to price low as 18>11.

If Fashfone chooses to price low even then Pictech will prefer to price low as 10>2.

Thus Pictech has a dominant strategy of pricing low.

Similar is the case of Fashfone. If Pictech prices high, Fasfone prefers to price low as 18>:11 and If Pictech prices low even then Fashfone prefers low pricing as 10>2.

Thus in case both do no collude, both will have pricing low as a dominant strategy. Both will end up choosing a low price.

Part b. True. the above situation is an example of prisoner's dilemma because if both of them cooperate and price high they end up earning higher payoffs than without cooperating.

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