Reciprocal contracting

This paper models competing mechanism games as extensive-form games where the extensive form is incompletely understood by a modeler, typically because the modeler doesn't see all the messages that are being exchanged and doesn't understand all the contracts that can be enforced. For this reason, the revelation principle can't be used to characterize supportable outcomes. The paper provides a relatively weak restriction, referred to as regularity, on the unknown part the competing mechanism game. This condition makes it possible to characterize the set of supportable equilibrium outcomes of the unknown part of the game using information about the part of the game the modeler does understand. In addition, the paper provides a canonical game called the reciprocal contracting game which supports as an equilibrium every equilibrium outcome of any regular competing mechanism game that embeds the known part of the game. As a consequence, the reciprocal contracting game can be used as a stand-in for the true game.