Suppose there are only two firms that sell smartphones: Flashfone and Pictech. The following payoff matrix shows the profit (in millions of dollars) each company will earn, depending on whether it set

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Question:

Suppose there are only two firms that sell smartphones: 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.

Pictech Pricing Pictech Pricing
High Low
Flashfone Pricing High 11,11 3,15
Flashfone Pricing Low 15,3 9,9

For example, the lower-left cell shows that if Flashfone prices low and Pictech prices high, Flashfone will earn a profit of $15 million, and Pictech will earn a profit of $3 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 _____ price, and if Flashfone prices low, Pictech will make more profit if it chooses a _____ price.

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

Considering all of the information given, pricing low _____ a dominant strategy for both Flashfone and Pictech.

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

(i) Flashfone will choose a low price, and Pictech will choose a high price.

(ii) Both Flashfone and Pictech will choose a high price.

(iii) Flashfone will choose a high price, and Pictech will choose a low price.

(iv) Both Flashfone and Pictech will choose a low price.

The game between Flashfone and Pictech is an example of the prisoners’ dilemma

(i) True

(ii) False

Game Theory:

Game theory is a part of economics and mathematics that analyzes strategic situations where player results are interconnected. Economists often use game theory to evaluate the outcomes for firms who are rivals.

Answer and Explanation:

In a simultaneous game, both parties make choices independently and at the same time, so there is no first-mover advantage. To solve these types of game you should circle the best outcome for either player given the choices of the other player. For example, when Flashfone chooses a high price, Pictech must choose between setting a high or low price. They should choose the low price in this case because 15 (million) is more than 11 (million). Follow this process for both firms until all options are exhausted. Both firms are always better off to choose a low price, economists call this a dominant strategy.

Here is the game solved:

Now you just need to read the solution to fill in the answers to these prompts.

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

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

Considering all of the information given, pricing low is a dominant strategy for both Flashfone and Pictech.

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

(i) Flashfone will choose a low price, and Pictech will choose a high price.

(ii) Both Flashfone and Pictech will choose a high price.

(iii) Flashfone will choose a high price, and Pictech will choose a low price.

(iv) Both Flashfone and Pictech will choose a low price.

This is the solution to the game and because both firms will make that choice, it is known as a Nash Equilibrium. It is also the dominant strategy equilibrium because both firms are acting on their own dominant strategy.

The game between Flashfone and Pictech is an example of the prisoners’ dilemma

(i) True

(ii) False

A prisoners’ dilemma is a game where both players acting in their own best intersts will come to an outcome that is worse for both players. In this case, they could be better off if they both chose a high price, however, they won’t because each firm has an incentive to charge a lower price and outsell the other firm.

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