A model of managing business constraints

A model of hierarchical system of the Center–agent type is considered, in which the Center manages the set of agent’s choices. A model of such a system is a hierarchical two-person game with forbidden situations. In this game, the Center selects some subset of the fixed set, while the agent selects his control from this subset. The agent’s payoff explicitly depends only on his own choice, while the Center’s payoff depends both on the agent’s control and on its own choice. The dependence of the Center's payoff on its choice is assumed to be monotonic with respect to relation of inclusion on the set of its strategies. The tasks are set of calculating the maximum guaranteed result of the Center under the assumption of the benevolence of the agent and without such an assumption. A new definition is proposed of the maximum guaranteed result of the Center in the game with a benevolent agent, staying correct also in the case when the maximum of agent’s payoff is not reached for some of Center’s strategies. The equivalence of this definition to the classical definition of Stackelberg is proved in cases when the latter is correct. In general case, the problems posed assume the calculation of maximin with connected constraints on complex infinite-dimensional spaces. Methods are proposed that significantly simplify these problems. For the case of a finite basic set, algorithms are proposed that allow solving the problem in a polynomial time with respect to the number of elements of this set. For the case of an infinite basic set, the problem is reduced to solving a sequence of ordinary optimization problems. The methods proposed allow to build and explore many meaningful models of such type.