Siyang Xiong

Uniform Topologies on Types

We study the robustness of interim correlated rationalizability to perturbations of higher-order beliefs. We introduce a new metric topology on the universal type space, called uniform weak topology, under which two types are close if they have similar first-order beliefs, attach similar probabilities to other players having similar first-order beliefs, and so on, where the degree of similarity is uniform over the levels of the belief hierarchy. This topology generalizes the now classic notion of proximity to common knowledge based on common p-beliefs (Monderer and Samet (1989)). We show that convergence in the uniform weak topology implies convergence in the uniform strategic topology (Dekel, Fudenberg, and Morris (2006)). Moreover, when the limit is a finite type, uniform-weak convergence is also a necessary condition for convergence in the strategic topology. Finally, we show that the set of finite types is nowhere dense under the uniform strategic topology. Thus, our results shed light on the connection between similarity of beliefs and similarity of behaviors in games.

GENERICITY AND ROBUSTNESS OF FULL SURPLUS EXTRACTION

We study whether priors that admit full surplus extraction (FSE) are generic, an issue that becomes a gauge to evaluate the validity of the current mechanism design paradigm. We consider the space of priors on the universal type space, and thereby relax the assumption of a fixed finite number of types made by Cremer and McLean (1988). We show that FSE priors are topologically generic, contrary to the result of Heifetz and Neeman (2006) that FSE is generically impossible, both geometrically and measure-theoretically. Instead of using the BDP approach or convex combinations of priors adopted in Heifetz and Neeman (2006), we prove our genericity results by showing a robustness property of Cremer�McLean mechanisms.

Core equivalence theorem with production

In production economies, the extent to which non-equilibria are blocked depends on the allocation of control rights among shareholders, because a blocking coalitions resources are affected by the firms it jointly owns with outsiders. We formulate a notion of blocking that takes such interdependency problem into account, and we prove an analog of the Debreu-Scarf theorem for replica production economies. Our theorem differs from theirs in using an additional assumption, which we argue is indispensable and is driven by the interdependency problem.

The genericity of beliefs-determine-preferences models revisited☆

Barelli [P. Barelli, On the genericity of full surplus extraction in mechanism design, J. Econ. Theory 144 (2009) 1320-1332] defines beliefs-determine-preferences (BDP) models and argues that BDP models are nongeneric in a topological sense. In this note, we point out some difficulties in Barelli[modifier letter apostrophe]s approach. Furthermore, we follow the idea of Heifetz and Neeman [A. Heifetz, Z. Neeman, On the generic (im)possibility of full surplus extraction, Econometrica 74 (2006) 213-233] to propose a more relevant notion of BDP* model. We prove that BDP* models are generic, which is opposite to Barelli[modifier letter apostrophe]s conclusion.

The e-mail game phenomenon

The e-mail game in Rubinstein (1989) shows that types with arbitrarily close higher-order beliefs may differ substantially in strategic behaviors. We define a notion called strategic discontinuity in arbitrary incomplete-information scenarios to generalize this e-mail game phenomenon. We show that almost all types involved in economic analysis — types in finite or common-prior models — display strategic discontinuity in simple games.

Agreeing to agree with uncountable information structures

Given the regularity condition on posteriors proposed in Lehrer and Samet (2011), we show that Lehrer and Sametʼs (2011) characterization of agreeing to agree in countable-information models cannot be extended to uncountable-information models. This answers an open question raised in Lehrer and Samet (2011).