Secretary problems and incentives via linear programming

In the classical secretary problem an employer would like to choose the best candidate among n competing candidates that arrive in a random order. Our main contribution is a new linear programming technique that we introduce as a tool for obtaining and analyzing mechanisms for the secretary problem and its variants. The linear program is formulated using judiciously chosen variables and constraints and we show a one-to-one correspondence between mechanisms for the secretary problem and feasible solutions to the linear program.