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A Class of Team Problems with Discrete Action Spaces: Optimality Conditions Based on Multimodularity

In this paper we discuss a class of team problems with discrete action spaces. We introduce multimodularity into team theory as a natural alternative to convexity in continuous spaces. The main result relates coordinatewise-optimal (cw-optimal) points to the optimal team decision for a class of team problems. The method is based on a characterization of coordinatewise minima of multimodular functions.