Martin Meier

A canonical model for interactive unawareness

Heifetz, Meier and Schipper (2006) introduced a generalized state-space model that allows for non-trivial unawareness among several individuals and strong properties of knowledge. We show that this generalized state-space model arises naturally if states consist of maximally consistent sets of formulas in an appropriate logical formulation.

Finitely additive beliefs and universal type spaces

In this paper we examine the existence of a universal (to be precise: terminal) type space when beliefs are described by finitely additive probability measures. We find that in the category of all type spaces that satisfy certain measurability conditions (-measurability, for some fixed regular cardinal ), there is a universal type space (i.e. a terminal object, that is a type space to which every type space can be mapped in a unique beliefs-preserving way (the morphisms of our category, the so-called type morphisms)), while, by an probabilistic adaption of the elegant sober-drunk example of Heifetz and Samet (1998a), we show that if all subsets of the spaces are required to be measurable there is no universal type space.

On the nonexistence of universal information structures

This paper extends the nonexistence result of Heifetz and Samet (Games Econ. Behav. 22 (1998) 260 273). They have shown that there exists no universal knowledge space to which every knowledge space can be mapped in a knowledge-preserving manner. We show that an analogous nonexistence result holds in the more general context of information structures. These structures can be viewed as generalizations of knowledge spaces that describe non-probabilistic beliefs. (c) 2003 Elsevier Inc. All rights reserved.

Universal knowledge-belief structures

In this paper, we provide a notion of structure preserving maps (i.e. knowledge–belief morphisms) between knowledge–belief spaces. Then we show that—under the condition that the knowledge operators of the players in a knowledge–belief space operate only on measurable subsets of the space—there is a unique (up to isomorphism) universal knowledge–belief space to which every knowledge–belief space can be mapped by a unique knowledge–belief morphism.

A New Strategy for Robbins' Problem of Optimal Stopping

In this article we study the expected rank problem under full information. Our approach uses the planar Poisson approach from Gnedin (2007) to derive the expected rank of a stopping rule that is one of the simplest non-trivial examples combining rank dependent rules with threshold rules. This rule attains an expected rank lower than the best upper bounds obtained in the literature so far, in particular we obtain an expected rank of 2.32614.

Speculative trade under unawareness: the infinite case

We prove a “no-speculative-trade” theorem under unawareness for the infinite case. This generalizes the result for the finite case by Heifetz et al. (Games Econ Behav 77:100–121, 2013).