Final answer:
The statement "Both airlines would be better off than in the Nash equilibrium if both set a high price" is true.
Step-by-step explanation:
In a Nash equilibrium, each firm chooses their best strategy given the strategies all other firms are following. In the context of a duopoly or oligopoly, like the airline industry example provided, if both firms commit to setting high prices, they could potentially share a monopoly-like profit. However, this situation is unstable because each firm has an incentive to undercut the other to gain market share, which leads back to the Nash equilibrium where firms earn less profit due to competitive pricing.
Individual firms in an oligopoly might employ predatory pricing, as the large incumbent airline did, which is a strategic move where prices are reduced to eliminate competition. In the case provided, the large firm might temporarily lower prices to push the small start-up out of the market. Once the competition is gone, the incumbent can raise prices again and enjoy higher profits.
The tendency of firms in an oligopoly to follow price cuts but not price increases creates a situation akin to the prisoner's dilemma. Cooperation between firms to set higher prices could yield better profits for both. However, the trust issue and the potential for higher immediate gains by deviating from the cooperative agreement often result in both firms settling for lower profits at the Nash equilibrium where neither firm wants to unilaterally set high prices due to the fear of being undercut by the competition.