Question

We listen to the following conversation between the presidents of two airlines: American Airlines and Braniff Airways. The companies can charge expensive or cheap. If one charges 300, its profit is low if the other also charges 300 and high if the other charges 600 . If it charges 600 and the other 300 , it will earn very low, and it will have medium profit if the other also charges 600 . What is the Nash equilibrium of this game?

Two athletes with the same ability compete for a prize of 10,000 . Both are considering taking a dangerous but performance-enhancing drug. If one takes the drug and the other doesn't, the one who takes the drug will win the prize. If no one gets high, they will tie and split the prize. Taking drugs brings health risks that are equivalent to a loss of X dollars. For what value of X is getting high the Nash equilibrium?

Answer 1

The Nash equilibrium for the airline pricing scenario is both airlines pricing at 600, and for the athletes, the equilibrium occurs when X < $5,000. Oligopoly price competition typically involves silent cooperation by matching price cuts but not increasing prices.

Step-by-step explanation:

Nash Equilibrium in Airline Pricing

Regarding the conversation between the presidents of American Airlines and Braniff Airways, the Nash equilibrium would occur when both airlines choose a pricing strategy that leaves them with no incentive to unilaterally deviate from it. Considering the profits described, both airlines charging 600 would be the Nash equilibrium; any deviation would result in a lower profit for the deviating airline.

Nash Equilibrium with Performance-Enhancing Drugs

For the athletes considering taking a performance-enhancing drug, given the prize of $10,000, if taking the drug guarantees winning the prize, the Nash equilibrium occurs when the cost of health risks, X, is less than the gain from winning, which is $10,000 for a single athlete. Therefore, taking the drug is a Nash equilibrium when X < $5,000, as an athlete’s expected gain, after splitting the prize if neither takes drugs, would be $5,000.

Oligopoly and Price Competition

In an oligopolistic market, firms may opt for a pricing strategy where they match price cuts but not price increases, as noted in the provided scenario of airline companies. This acts as a form of silent cooperation, allowing them to effectively manage output and profits similar to a monopoly without a formal agreement. This is because unilateral price increases result in a significant loss of sales, while price cuts are matched, creating minimal incentive for change.