A linear two-level programming problem

A stackleberg game in which a first player can affect the resources available to a second player is defined. For given first move the second player will maximize a linear program, subject to the resources available. The first player attempts to maximize his own linear objective function which contains variables under the control of the second player. Even though all functions are linear, it is shown that local optima can exist. An implicit search is described which uses necessary conditions for a better solution, to limit the extent of the search.