Abstract
In some game-theoretic models, an agent is supposed to choose a subset of available items under a matroid constraint. If an agent always chooses a subset according to the standard greedy algorithm for matroids, then this choice rule fulfills the “substitutability," an essential property for the existence of equilibria in matching market models. In this paper, we introduce a notion of “matroidal choice functions" to capture the entire class of substitutable choice rules under a matroid constraint. For such functions, we provide two characterizations: one is by the behavior of an online greedy algorithm, and the other is by a local condition. We also show that matroidal choice functions extend choice rules defined by the maximization algorithm for valuated matroids and discrete concave functions.
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