Mechanism Design without Rational Expectations

Is incentive compatibility still necessary for implementation if we relax the rational expectations assumption?

This paper proposes a generalized model of implementation that does not assume agents hold rational expectations and characterizes the class of solution concepts requiring Bayesian Incentive Compatibility (BIC) for full implementation. Surprisingly, for a broad class of solution concepts, full implementation of functions still requires BIC even if rational expectations do not hold. This finding implies that some classical results, such as the impossibility of efficient bilateral trade (Myerson & Satterthwaite, 1983), hold for a broader range of non-equilibrium solution concepts, confirming their relevance even in boundedly rational setups.

The Revelation Principle without Rational Expectations

The revelation principle states that it is without loss of generality to restrict attention to direct mechanisms and, consequently, that incentive compatibility is necessary for implementation. This paper extends the discussion beyond Bayesian Nash Equilibrium by providing sufficient conditions on the solution concept that ensure any implementable social choice function can be implemented via a direct mechanism. These conditions do not generally imply incentive compatibility is necessary for implementation, as the class of solution concepts requiring incentive compatibility for implementation is characterized via a logically independent condition.

Mechanism Design with Opportunity Constraints

Traditional mechanism design assumes the planner has almost complete freedom in choosing an implementing mechanism. The paper generalizes the model by requiring the implementing mechanism to satisfy some exogenously imposed constraints on the lotteries in each agent’s opportunity set. We show the revelation principle is still valid for a class of these restrictions, and we discuss applications of this framework to mechanism design in network environments.

Selected Work in Progress