Question

Airbus and Boeing - A and B hereafter - are two major players in the market for aircrafts. B is deciding whether to enter a new market. If B stays Out, B receives 0 and A bags $100 million in profit. If B enters, i.e., if B stays In, A can either start a Price war or Accommodate. If A chooses Accommodate, each receives $30 million. Else, if A chooses Price war, each loses $10 million (i.e., think of this as −10). Now consider the normal-form game where payoffs are as stated above but A and B are moving simultaneously. Draw the payoff matrix with A being the row player and B is the column player and find all Nash equilibria (in both pure and mixed strategies).

Answer 1

In the given scenario, Airbus and Boeing are deciding whether to enter a new market. If Boeing chooses to stay out, Airbus will earn $100 million in profit. If Boeing enters, Airbus can either choose to accommodate or start a price war. There are two pure Nash equilibria in this game. The first one is where both companies choose to cooperate and accommodate, earning $30 million each. The second one is where both companies choose to defect and start a price war, resulting in both of them losing $10 million each.

Step-by-step explanation:

In the given scenario, Airbus and Boeing are deciding whether to enter a new market. If Boeing chooses to stay out, Airbus will earn $100 million in profit. If Boeing enters, Airbus can either choose to accommodate or start a price war. If Airbus chooses to accommodate, both companies receive $30 million each. If Airbus chooses to start a price war, both companies will lose $10 million each.

The payoff matrix for this game can be represented as:

A/BCooperateDefectCooperate$30/$30-$10/$-10Defect$1,000/$1,500$0/$100

There are two pure Nash equilibria in this game. The first one is where both companies choose to cooperate and accommodate, earning $30 million each. The second one is where both companies choose to defect and start a price war, resulting in both of them losing $10 million each.

In addition to the pure Nash equilibria, there can also be mixed Nash equilibria in which companies choose strategies randomly to optimize their payoff. These equilibria can be found by solving for the probability distribution of strategies that maximizes each player's expected payoff.