We study dual reduction: a technique to reduce finite games in a way that selects among correlated equilibria. We show that the reduction process is independent of the utility functions chosen to represent the agents's preferences and that generic two-player games have a unique full dual reduction. Moreover, in full dual reductions, all strategies and strategy profiles which are never played in correlated equilibria are eliminated. The additional properties of dual reduction in several classes of games are studied and dual reduction is compared to other correlated equilibrium refinement's concepts. Finally, we review and connect the linear programming proofs of existence of correlated equilibria
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