A study on the demand and response correspondences in the presence of indivisibilities

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.