Question

1. Create an example of duopoly Nash Equilibrium that is similar to the one in the text.  Assume Boeing and Airbus can each choose either a high or low price strategy. If both limit output to keep prices high then both companies get $20 billion profit. If Boeing produces more planes while Airbus keeps output low then there is $24 billion Boeing profit and $12 billion Airbus profit. If Airbus makes more planes while Boeing keeps output low those numbers reverse. Finally, If both produce more planes they get $16 billion profit each. Arrange these into a payoff matrix and explain why the Nash equilibrium is likely to occur.

Answer 1

Payoff Matrix:

		Boeing
		High Price	Low Price
Airbus	High Price	$20 billion, $20 billion	$12 billion , $24 billion
Low price	$24 billon , $12 billion	$16 billion, $16 billion

Note: First entry in the each cell is the profit of Airbus

Second entry in the each cell is the profit of Boeing.

Low output implies high price

More output implies low prices.

The nash equilibrium of this game is to choose "Low price, Low Price".

In that case the profit of Airbus would be $16 billion and profit of Boeing would be $16 billion

The nash equilibrium occurs becasue there is no incentive to deviate from their strategy of "Low Price"

For example: If Airbus decides to deviate from "Low price" to "High price" in order to get a profit of $20 billion, then in response Boeing will choose " Low price" to maximize his profit. At last Airbus would end with $12 billion.

Hence, there is no incentive for Airbus to deviate from "Low Price"

Similarly, it is applied on Boeing.