Uniformity and games decomposition

Abstract : We introduce the classes of uniform and non-interactive games. We study appropriate projection operators over the space of finite games in order to propose a novel canonical direct-sum decomposition of an arbitrary game into three components, which we refer to as the uniform with zero-constant, the non-interactive total-sum zero and the constant components. We prove orthogonality between the components with respect to a natural extension of the standard inner product and we further provide explicit expressions for the closet uniform and non-interactive games to a given game. The, we characterize the set of its approximate equilibria in terms of the uniformly mixed and dominant strategies equilibria profiles of its closet uniform and non-interactive games respectively.
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Submitted on : Wednesday, May 3, 2017 - 10:07:43 AM
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Joseph Abdou, Nikolaos Pnevmatikos, Marco Scarsini. Uniformity and games decomposition. 2017. ⟨halshs-01147442v2⟩

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