Question
Boeing and Airbus are the world’s only major producers of large, wide-bodied aircrafts. But with the cost of fuel increasing and changing demand in the airline industry, the need for smaller regional jets has increased. Suppose that both firms must decide whether they will produce a smaller plane. We will assume that Boeing has a slight cost advantage over Airbus in both large and small planes, as shown in the following payoff matrix (in millions of U. S. dollars). Assume that each producer chooses to either produce only large, only small, or no planes at all.
Explanation / Answer
a ) Nash equilibrium: the best strategy adopted, given the opponents strategy, and neither have an incentive to deviate from the strategy. Nash equilibria: If Boeing decides to produce small planes as it is its dominant strategy , than the Airbus chooses large plains and the nash equilibrium exists at payoff 150 (B) and 100 (Airbus). and if airbus moves first, than the dominat strategy for air bus is small planes, and if it chooses small planes than Boieng will choose large palins, where Boeing receives 115 and Airbus receives 125 as payoff. So, there is no single nash equilibria existing. b) Yes, there are multiple Nash equilibria exixting between these frims, and it depends on the first mover. If Boeing decides first and chooses to produce small planes as it is its dominant strategy , than the Airbus chooses large plains and the nash equilibrium exists at payoff 150 (B) and 100 (Airbus). and if airbus decides to moves first, than the dominat strategy for air bus is small planes, and if it chooses small planes than Boieng will choose large palins, where Boeing receives 115 and Airbus receives 125 as payoff. Subsidy: If the EU wants to give subsidy to Airbus for producing small plane: For small plane production, Airbus pay off is 125 or 0 or 125 based on Boieng strategy, to incduce Airbus to produce small planes without making it to consider the Boieng strategy, than a profit of 15 shold ne given as subsidy. So the new pay off for Airbus if it produces small plane is 140 or 15 or 140. Thus Airbus will produce as it receives 15 as pay off even if boieng produces small planes, but looking at the subsidy , boieng might decide to concentrate on large plains. Now the pay off will be 140 for air bus by producing small planes and 115 for Boieng for producing large plains. Yes EU gains the market for small planes. and if airbus decides to moves first, than the dominat strategy for air bus is small planes, and if it chooses small planes than Boieng will choose large palins, where Boeing receives 115 and Airbus receives 125 as payoff. Subsidy: If the EU wants to give subsidy to Airbus for producing small plane: For small plane production, Airbus pay off is 125 or 0 or 125 based on Boieng strategy, to incduce Airbus to produce small planes without making it to consider the Boieng strategy, than a profit of 15 shold ne given as subsidy. So the new pay off for Airbus if it produces small plane is 140 or 15 or 140. Thus Airbus will produce as it receives 15 as pay off even if boieng produces small planes, but looking at the subsidy , boieng might decide to concentrate on large plains. Now the pay off will be 140 for air bus by producing small planes and 115 for Boieng for producing large plains. Yes EU gains the market for small planes.