Abstract

This paper considers a model of a hierarchical system of the Principal–agent type, in which the Principal manages the set of agent’s choices. The model of such a system is a hierarchical two-player game with forbidden situations. In this game, the Principal chooses some subset of a fixed set, whereas the agent chooses his control from this subset. The agent’s payoff explicitly depends on his own choice only, whereas the Principal’s payoff depends both on the agent’s control and on its own choice. The dependence of the Principal’s payoff on his choice is assumed to be monotonic with respect to the inclusion relation on the set of his strategies. The problems formulated below are to calculate the Principal’s maximum guaranteed result, under the assumption of the agent’s benevolence and without this assumption. A new definition of the Principal’s maximum guaranteed result in the game with a benevolent agent is proposed, which remains correct also in the case when the agent’s payoff achieves no maximum for some of the Principal’s strategies. The equivalence of this definition to the classical Stackelberg’s definition is proved for the cases in which the latter is correct. In the general case, the problems formulated below require calculating the maximin with bound constraints on complex infinite-dimensional spaces. Some methods for simplifying these problems are suggested. In the case of a finite basic set, algorithms for solving the problem in a polynomial time with respect to the number of elements in this set are developed. In the case of infinite basic set, the problem is reduced to a sequence of ordinary optimization problems. The methods proposed below can be used to construct and investigate many applications-relevant models of this type.

中文翻译：

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管理活动约束的模型

摘要

本文考虑了委托人-代理人类型的分层系统模型，其中委托人管理着代理人的选择集。这种系统的模型是带有禁止情况的分级两人游戏。在此游戏中，委托人选择固定集的某个子集，而代理从该子集中选择其控制权。代理人的收益明确地仅取决于他自己的选择，而委托人的收益既取决于代理人的控制，也取决于其自己的选择。就委托人的策略集上的包含关系而言，假定委托人的收益对他的选择的依赖是单调的。下面提出的问题是在代理的仁慈假设下并且没有此假设的情况下计算委托人的最大保证结果。提出了对具有仁慈代理的博弈中委托人的最大保证结果的新定义，在代理的某些策略的代理人的收益没有达到最大的情况下，该定义也仍然是正确的。在后者正确的情况下，证明了该定义与经典Stackelberg定义的等效性。在一般情况下，下面提出的问题需要在复杂的无穷维空间上计算具有约束的极大值。建议了一些简化这些问题的方法。在有限基本集的情况下，开发了用于在多项式时间内针对该集合中的元素数量解决问题的算法。在无限基本集的情况下，该问题被简化为一系列普通优化问题。