Simplified mechanisms with an application to sponsored-search auctions

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 ε⩾0, any ε-Nash equilibrium of the simplified mechanism is also an ε-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.