Economist Bill Samuelson suggests a problem centering around three air carriers competing for passengers on a given city-pair route. Namely, the fare that can be charged on the route is fixed at $225, while the size of the market is fixed at 2,000 passengers per day. There are three competing airlines: A, B, and C. Each airline gets passengers in proportion to its share of total flights. For example, if all three airlines offered the same number of flights, then they would each get one-third of the passengers. If Airline A offered six flights and B and C each offered three, then A would get 50 percent of the market, while B and C would get 25 percent each. Each plane holds a maximum of 300 passengers. Each plane trip costs $20,000, whether the plane is full or not.

a. Confirm firm A’s profit equals $450,000[a/(a + b + c)] –

$20,000a, where

a, b, and c represent the number of flights by firms A, B, and C, respectively.

b. Confirm to yourself that the table below gives the profits to A as a function of its flights and its competitors’ flights per day.

c. Consider a strategy for any one of the firms to be a policy of flying a certain number of flights per day. Is there a dominant strategy for A—that is, a number of flights that gives higher profits no matter what the competitors do?