“Assignment messages” are messages that parameterize substitutable preferences using a particular linear program. An “assignment exchange” is a simplified Walrasian exchange in which participants are restricted to report only assignment messages. Any pure Nash or e-Nash equilibrium of...

A simplified mechanism is a direct mechanism modified by restricting the set of reports or bids. An example is the auction used to place ads on Internet search pages, in which each advertiser bids a single price to determine the allocation of eight or more ad positions on a page. If a simplified...

A mechanism can be simplified by restricting its message space. If the restricted message space satisfies a certain “outcome closure property,” then the simplification is “tight”: for every S=0 any Nash equilibrium of the simplified mechanism is also an Nash equilibrium of the...