9 Using a payoff matrix to determine the equilibrium outcome

9. 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. Pictech Pricing High Low High 11,11 2,18 Low 18, 2 10,10 Flashfone Pricing 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 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 aprice, and if Pictech prices low, Flashfone will make more profit if it chooses a price Considering all of the information given, pricing high a dominant strategy for both Flashfone and Pictech

Solution

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.

Pricing high is not a dominant strategy for both Flashfone and Pictech.

If the firms do not collude:

- Both Flashfone and Pictech will choose a low price

This is an example of Prisoners\' dilemma (inefficient outcome is chosen)

MC = MC2

price = $40 per ticket

According to the kinked demand curve model, if one firm decreases its price, other firms will do likewise to retain their market share, but if one firm increases its price, other firms will not follow suit. Therefore, if Happyland decreases its price to below the price you just found for Happy land, its competitors will follow suit.

This explains why the D2 portion of the kinked demand curve is relatively less elastic than the D1 portion.

For both cases, Happyland would charge the same price. (P is chosen corresponding to the quantity where MR=MC)