Continuous implementation with payoff knowledge
Abstract
For full text, see https://ink.library.smu.edu.sg/soe_research/2672. Published in Journal of Economic Theory DOI: https://doi.org/10.1016/j.jet.2023.105624. The robust mechanism design literature assumes players’ knowledge about a fixed payoff environment and investigates the global robustness of optimal mechanisms to large changes in the information structure. Acknowledging the global robustness as a demanding requirement, we propose continuous implementation as a local robustness of optimal mechanisms to small changes in the information structure. Keeping the assumption of the payoff knowledge, we say that a social choice function is continuously implementable if there exists a mechanism which yields the outcome close to the desired one for all types close to the planner’s initial model. We show that when a generic correlation condition is imposed on the class of interdependent-value environments, any (interim) incentive compatible social choice function is continuouslyimplementable with arbitrarily small transfers imposed on and off the equilibrium. This exhibits a stark contrast with Bergemann and Morris (2005) who show that their global robustness amounts to ex post incentive compatibility as well as Oury and Tercieux (2012) who show that continuous implementation without payoff knowledge generates a substantial restriction, tightly connected to full implementation in rationalizablestrategies.