Mechanism Design without Rational Expectations

Non-equilibrium models of strategic interaction often offer sharply different predictions from equilibrium ones. In the context of mechanism design, does this mean that dropping the rational expectations assumption allows the social planner to fully implement a larger class of social choice functions? The answer to this question turns out to be mainly negative. This paper proposes a generalized model of full implementation that does not assume rational expectations and characterizes the class of solution concepts such that Bayesian Incentive Compatibility is necessary for implementation of social choice functions. Surprisingly, dropping the rational expectations assumption and moving to non-equilibrium models does not deliver significantly more permissive results for a large class of models of strategic behavior. A key implication of this finding is that some classical results (such as Myerson and Satterthwaite’s impossibility of efficient bilateral trade) hold for a wide range of non-equilibrium solution concepts, confirming their relevance even in bounded rationality setups.

Paper presentations: Brown University Brown Bag Seminar (2021, 2022), Boston College Brown Bag Seminar (2022, 2023), 12th Conference on Economic Design, 16th SSCW Meeting, University of Bologna (2022), SING17, 33rd Stony Brook International Conference, 1st NSEF Worskhop, 12th Lisbon Meetings in Game Theory and Applications, 34th Stony Brook International Conference, SMYE2023 (scheduled).

The Revelation Principle without Rational Expectations
Draft coming soon!

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.

Work in Progress

Revelation Principle and Opportunity Constraints
Draft coming soon!

In traditional mechanism design, it is assumed the planner has almost complete freedom in choosing the implementing mechanism. The paper generalizes the model by requiring the implementing mechanism to also satisfy some exogenously imposed constraints on the outcomes in each agent’s opportunity set. I discuss applications of this framework to mechanism design in network environments and to one-sided matching with priorities.