Necessary conditions for the linear three level programming problem

The multilevel programming problem (MLPP) conceptually extends the basic Stackelberg game to p players and can thus be used as a model for a variety of hierarchical systems in which sequential planning is the norm. This paper first develops the rational reaction sets for each of the players and then states the geometric properties of the linear MLPP. Next, first order necessary conditions are derived and the problem recast as a standard nonlinear program. A cutting plane algorithm employing a vertex search procedure at each iteration is proposed to solve the linear 3-level case. An example is given to highlight the results.