Abstract
The definition of a correlated equilibrium takes as given the information possessed by the players. Some correlated equilibria rely on information acquisition decisions that are difficult to rationalize. We study the correlated equilibria which can arise when agents choose their information and information acquisition costs are (ordinally) symmetric. The set of correlated equilibria which are attainable in this sense is much smaller than the full set of correlated equilibria. In two-player games, the only attainable correlated equilibria are randomizations over pure strategy Nash equilibria. More generally, cyclic monotonicity is necessary and sufficient for a correlated equilibrium distribution to be attainable.
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