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A mechanism can be simplified by restricting its message space. If the restricted message spaces satisfy a certain "outcome closure property," then the simplification is "tight": for every _≥0 any Nash equilibrium of the simplified mechanism is also an Nash equilibrium of the unrestricted mechanism. Prominent auction and matching mechanisms are tight simplifications of mechanisms studied in economic theory and often incorporate price-adjustment features that facilitate simplification. The generalized second price auction used for sponsored-search advertising is a tight simplification of a series of second-price auctions that eliminates the lowest revenue equilibrium outcomes and leaves intact only higher revenue equilibria.