Uniformity and games decomposition

Joseph M. Abdou (1, 2) , Nikolaos Pnevmatikos (1) , Marco Scarsini (3)

1 CES - Centre d'économie de la Sorbonne
2 PSE - Paris School of Economics
3 Engineering and System Design Pillar

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.

Mots clés: decomposition of games; projection operator; uniformly mixed strategy

Domaines: Economies et finances

Joseph M. Abdou, Nikolaos Pnevmatikos, Marco Scarsini. Uniformity and games decomposition. 2017. ⟨halshs-01147442v2⟩