Totally balanced games arising from controlled programming problems
Totally balanced games arising from controlled programming problems
复制标题
由受控编程问题引起的完全平衡的游戏
作者：
P. Dubey;L. Shapley
特征函数形式的合作博弈是通过允许多个个体直接或通过委员会投票对一个（一般为非线性的）数学规划问题的约束进行部分控制而得到的。对定义编程问题和控制系统的函数施加条件，这些条件足以使游戏完全平衡。这保证了一个非空的核心，因此，一个稳定的分配的全部价值的规划问题之间的控制玩家。在线性情况下，核心与对偶问题的解密切相关。各种经济模型的应用，包括可转让的效用贸易经济的Shapley和Shubik和一个多托运人一种商品转运模型与凸成本函数和凹收入函数。放弃可转移效用的假设会导致一类受控的多目标或“帕累托规划”问题，这又会产生完全平衡的游戏。
A cooperative game in characteristic-function form is obtained by allowing a number of individuals to esercise partial control over the constraints of a (generally nonlinear) mathematical programming problem, either directly or through committee voting. Conditions are imposed on the functions defining the programming problem and the control system which suffice to make the game totally balanced. This assures a nonempty core and hence a stable allocation of the full value of the programming problem among the controlling palyers. In the linear case the core is closely related to the solutions of the dual problem. Applications are made to a variety of economic models, including the transferable utility trading economies of Shapley and Shubik and a multishipper one-commodity transshipment model with convex cost functions and concave revenue functions. Dropping the assumption of transferable utility leads to a class of controlled multiobjective or ‘Pareto programming’ problems, which again yield totally balanced games.