On the diffuseness of incomplete information game
Wei He, Xiang Sun
TL;DR
This paper introduces the 'relative diffuseness' assumption to analyze incomplete information games, establishing conditions for pure strategy equilibria and proposing a stronger purification concept.
Contribution
It develops the 'relative diffuseness' framework and the 'undistinguishable purification' notion, advancing equilibrium existence theory in incomplete information games.
Findings
Pure strategy equilibria exist under the new assumption.
The 'undistinguishable purification' concept strengthens standard purification.
The framework clarifies the role of information diffuseness in game outcomes.
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.
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