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On the diffuseness of incomplete information game |
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| Affiliation: | 1. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076, Singapore;2. Economics and Management School, Wuhan University, Wuhan, 430072, China;1. Department of Economics and Management, University of Pisa, Italy;2. CNRS, CMAP - Ecole Polytechnique, France;1. Paris School of Economics - University Paris 1, CES, 106 bd de l’Hopital, 75013, Paris, France;2. University of La Rochelle (MIA), Avenue Michel Crepeau, 47042, La Rochelle, France;3. University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands |
| Abstract: | We introduce the “relative diffuseness” assumption to characterize the differences between payoff-relevant and strategy-relevant diffuseness of information. Based on this assumption, the existence of pure strategy equilibria in games with incomplete information and general action spaces can be obtained. Moreover, we introduce a new notion of “undistinguishable purification” which strengthens the standard purification concept, and its existence follows from the relative diffuseness assumption. |
| Keywords: | Game with incomplete information Pure strategy equilibrium Relative diffuseness Undistinguishable purification |
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