Interim Partially Correlated Rationalizability

In game theory, there is a basic methodological dichotomy between Harsanyi's "game-theoretic" view and Aumann's "Bayesian decision-theoretic" view of the world. We follow the game-theoretic view, propose and study interim partially correlated rationalizability for games with incomplete information. We argue that the distinction between this solution concept and the interim correlated rationalizability studied by Dekel, Fudenberg and Morris (2007) is fundamental, in that the latter implicitly follows Aumann's Bayesian view. Our main result shows that two types provide the same prediction in interim partially correlated rationalizability if and only if they have the same infinite hierarchy of beliefs over conditional beliefs. We also establish an equivalence result between this solution concept and the Bayesian solution--a notion of correlated equilibrium proposed by Forges (1993).Games with incomplete information, Rationalizability, Common knowledge, Hierarchies of beliefs.

Interim Rationalizability

This paper proposes the solution concept of interim rationalizability, and shows that all type spaces that have the same hierarchies of beliefs have the same set of interim rationalizable outcomes. This solution concept characterizes common knowledge of rationality in the universal type space.

Using Bayesian Programming for Multisensor Multi-Target Tracking in Automative Applications

A prerequisite to the design of future Advanced Driver Assistance Systems for cars is a sensing system providing all the information required for high-level driving assistance tasks. Carsense is a European project whose purpose is to develop such a new sensing system. It will combine different sensors (laser, radar and video) and will rely on the fusion of the information coming from these sensors in order to achieve better accuracy, robustness and an increase of the information content. This paper demonstrates the interest of using probabilistic reasoning techniques to address this challenging multi-sensor data fusion problem. The approach used is called Bayesian Programming. It is a general approach based on an implementation of the Bayesian theory. It was introduced rst to design robot control programs but its scope of application is much broader and it can be used whenever one has to deal with problems involving uncertain or incomplete knowledge

Interim correlated rationalizability

This paper proposes the solution concept of interim correlated rationalizability, and shows that all types that have the same hierarchies of beliefs have the same set of interim-correlated-rationalizable outcomes. This solution concept characterizes common certainty of rationality in the universal type space.Rationalizability, incomplete information, common certainty, common knowledge, universal type space

Every hierarchy of beliefs is a type

When modeling game situations of incomplete information one usually considers the players' hierarchies of beliefs, a source of all sorts of complications. Hars\'anyi (1967-68)'s idea henceforth referred to as the "Hars\'anyi program" is that hierarchies of beliefs can be replaced by "types". The types constitute the "type space". In the purely measurable framework Heifetz and Samet (1998) formalize the concept of type spaces and prove the existence and the uniqueness of a universal type space. Meier (2001) shows that the purely measurable universal type space is complete, i.e., it is a consistent object. With the aim of adding the finishing touch to these results, we will prove in this paper that in the purely measurable framework every hierarchy of beliefs can be represented by a unique element of the complete universal type space.Comment: 19 page

Interdependent Preferences and Strategic Distinguishability

A universal type space of interdependent expected utility preference types is constructed from higher-order preference hierarchies describing (i) an agent's (unconditional) preferences over a lottery space; (ii) the agent's preference over Anscombe-Aumann acts conditional on the unconditional preferences; and so on. Two types are said to be strategically indistinguishable if they have an equilibrium action in common in any mechanism that they play. We show that two types are strategically indistinguishable if and only if they have the same preference hierarchy. We examine how this result extends to alternative solution concepts and strategic relations between types.Interdependent preferences, Higher-order preference hierarchy, Universal type space, Strategic distinguishability