Uniformity and games decomposition
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...
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Published in | IDEAS Working Paper Series from RePEc |
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Main Authors | , , |
Format | Paper |
Language | English |
Published |
St. Louis
Federal Reserve Bank of St. Louis
01.01.2017
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Online Access | Get full text |
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Summary: | 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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