Menu theorems for bilateral contracting

This paper studies bilateral contracting where multiple principals negotiate contracts with multiple agents independently. It is shown that pure-strategy equilibrium allocations relative to any ad hoc set of feasible mechanisms are supported by pure-strategy perfect Bayesian equilibria relative to the set of menus. This paper also shows that all equilibrium allocations to any ad hoc set of feasible mechanisms are supported by correlated equilibria relative to the set of menus, where a state is a probability distribution function over payoff-relevant variables. Furthermore, all equilibrium allocations relative to the set of menus persist even if principals use more complex mechanisms.