This paper attempts to study market and noncooperative game models in the presence of indivisibilities from a unified point of view. For market models we examine the sum of consumers’ demand correspondences mapping an integral price space to an integral commodity space, whereas for noncooperative game models we investigate the product of players’ response correspondences mapping a discrete strategy profile space to itself. We show that, in several typical models, the sum and the product correspondences share an important property that they are ‘locally gross direction preserving’, on the standard triangulation of the convex hull of the domain. Moreover, we prove the existence of a Walrasian equilibrium and a Nash equilibrium in respective models through a discrete multivariate mean value theorem.

中文翻译：

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存在个别性时需求与反应对应关系的研究

本文试图从统一的角度研究在存在个体性的市场和非合作博弈模型。对于市场模型，我们检查了将整体价格空间映射到整体商品空间的消费者需求对应关系的总和，而对于非合作博弈模型，我们研究了将离散策略配置文件空间映射至自身的参与者响应对应关系的乘积。我们显示，在几个典型模型中，求和和乘积对应关系在域凸包的标准三角剖分上具有“局部总方向保留”的重要属性。此外，我们通过离散多元均值定理证明了各个模型中Walrasian均衡和Nash均衡的存在。