Robust virtual implementation under common strong belief in rationality

Abstract

Bergemann and Morris (2009b) show that static mechanisms cannot robustly virtually implement non-constant social choice functions if preferences are sufficiently interdependent. Without any knowledge of how agents revise their beliefs this impossibility result extends to dynamic mechanisms. In contrast, we show that if the agents revise their beliefs according to the forward-induction logic embedded in strong rationalizability, admitting dynamic mechanisms leads to considerable gains. We show that all ex-post incentive compatible social choice functions are robustly virtually implementable in private consumption environments satisfying a weak sufficient condition, regardless of the level of preference interdependence. This result derives from the key insight that in such environments, in every belief-complete type space under common strong belief in rationality (Battigalli and Siniscalchi, 2002), dynamic mechanisms can distinguish all payoff type profiles by their strategic choices. Notably, dynamic mechanisms can robustly virtually implement the efficient allocation of an object in cases that static mechanisms cannot.

Interactive epistemology in simple dynamic games with a continuum of strategies

“…24 Artemov et al ( 2013) analyze robust virtual implementation with respect torationalizability in static mechanisms. Mueller (2016) applies strong rationalizability to dynamic mechanisms. Bergemann and Morris (2016 and references therein) apply to static mechanisms the solution concept without belief restrictions and call it "belief-free rationalizability."…”

Full Implementation and Belief Restrictions

“…In particular, Morris (2005, 2009a, b) study belief-free implementation in static settings, respectively in the partial, full, and virtual implementation sense. The belief-free approach has been extended to dynamic settings by Müller (2016) and Penta (2015). Penta (2015) considers dynamic mechanisms in environments in which agents may obtain information over time, and applies a dynamic version of rationalizability based on a backward induction logic (Penta 2011).…”

“…Penta (2015) considers dynamic mechanisms in environments in which agents may obtain information over time, and applies a dynamic version of rationalizability based on a backward induction logic (Penta 2011). Müller (2016) instead considers virtual implementation via dynamic mechanisms, in the same (static) belief-free environments as Bergemann and Morris (2009b), using a stronger version of rationalizability with forward induction. Thanks to the stronger assumptions on the belief revision policy, he shows that dynamic mechanisms weaken the conditions for virtual implementation.…”

Essays on mechanism design under non-Bayesian frameworks

“…Therefore, motivated by the Wilson doctrine(Wilson (1985)),Bergemann and Morris (2009, 2011) among others, relax the common knowledge assumption, and adopt a belief-free approach to study when and how a social choice function is fully implementable under all type spaces, which is the robust implementation problem.Most of the solution concepts studied under the interim implementation or robust implementation literature have been non-cooperative. For example,Postlewaite and Schmeidler (1986),Palfrey and Srivastava (1987, 1989), andJackson (1991) adopt the solution concept of Bayesian Nash equilibrium Bergemann and Morris (2009, 2011), Penta (2015,Müller (2016),. andOllár and Penta (2017) among others study rationalizable implementation or Bayesian Nash implementation under all type spaces.…”

“…Some other papers impose specific updating rules when Bayes' rule fails, e.g.,Penta (2015) andMüller (2016).…”