Endogenous private information structures
Many models in the economics literature deal with strategic situations with privately informed agents. In those models the information structure is assumed to be exogenous and common knowledge. In many applications information gathering is one of the strategic options available to agents. We formally incorporate this option into the game and the information structure will arise endogenously. We ask whether models with exogenous information structures, and the results they provide, are robust with respect to this endogenization. We show that any Nash equilibrium of the game with information acquisition induces a Nash equilibrium in the corresponding game with an exogenous structure. The same is not always true when `Nash equilibrium' is replaced by `sequential equilibrium' but we provide sufficient conditions on the structure of the game for which this is true. Moreover, we characterize the (sequential) Nash equilibria of games with an exogenous information structure that can arise as a (sequential) Nash equilibrium of a game with endogenous information acquisition,
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