# Transportation Economics/Agents/Solution1

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## Problem[edit]

Two airlines (United, American) each offer 1 flight from New York to Los Angeles.

Price = $/pax, Payoff = $/flight.

Each plane carries 500 passengers.

Fixed cost is $50000 per flight, total demand at $200 is 500 passengers.

At $400, total demand is 250 passengers.

Passengers choose cheapest flight.

Payoff = Revenue - Cost

Work in pairs (4 minutes):

Formulate the Payoff Matrix for the Game

## Solution[edit]

' | ' | American |
' |

$200 | $400 | ||

United | $200 | [0,0] | [50000, -50000] |

$400 | [-50000, 50000] | [0,0] |

Equilibrium is [$200,$200]

SOLUTION: Maximin criterion

For a two-person, zero sum game it is rational for each player to choose the strategy that maximizes the minimum payoff, and the pair of strategies and payoffs such that each player maximizes her minimum payoff is the “solution to the game."