Rationalizability and Minimal Complexity in Dynamic Games

This paper presents a formal epistemic framework for dynamic games in which players, during the course of the game, may revise their beliefs about the opponents'' utility functions. We impose three key conditions upon the players'' beliefs: (a) throughout the game, every move by the opponent should be interpreted as being part of a rational strategy, (b) the belief about the opponents'' relative ranking of two strategies should not be revised unless one is certain that the opponent has decided not to choose one of these strategies, and (c) the players'' initial beliefs about the opponents'' utility functions should agree on a given profile u of utility functions. Types that, throughout the game, respect common belief about these three events, are called persistently rationalizable for the profile u of utility functions. It is shown that persistent rationalizability implies the backward induction procedure in generic games with perfect information. We next focus on persistently rationalizable types for u that hold a theory about the opponents of ``minimal complexity'''', resulting in the concept of minimal rationalizability. For two-player simultaneous move games, minimal rationalizability is equivalent to the concept of Nash equilibrium strategy. In every outside option game, as defined by van Damme (1989), minimal rationalizability uniquely selects the forward induction outcome.microeconomics ;

Proper Rationalizability and Belief Revision in Dynamic Games

In this paper we develop an epistemic model for dynamic games in which players may revise their beliefs about the opponents'' preferences (including the opponents'' utility functions) as the game proceeds. Within this framework, we propose a rationalizability concept that is based upon the following three principles: (1) at every instance of the game, a player should believe that his opponents are carrying out optimal strategies, (2) a player should only revise his belief about an opponent''s relative ranking of two strategies if he is certain that the opponent has decided not to choose one of these strategies, and (3) the players'' initial beliefs about the opponents'' utility functions should agree on a given profile u of utility functions. Common belief about these events leads to the concept of persistent rationalizability for the profile u of utility functions. It is shown that for a given profile u of utility functions, every properly rationalizable strategy for ``types with non-increasing type supports'''' is a persistently rationalizable strategy for u. This result implies that persistently rationalizable strategies always exist for all game trees and all profiles of utility functions.mathematical economics;

An Epistemic Characterisation of Extensive Form Rationalisability

We use an extensive form, universal type space to provide the following epistemic characterisation of extensive form rationalisability. Say that player i strongly believes event E if i is certain of E conditional on each of her information sets consistent with E. Our main contribution is to show that a strategy profile s is extensive form rationalisable if and only if there is a state in which s is played and (0) everybody is rational, (1) everybody strongly believes (0), (2) everybody strongly believes (0) & (1), (3) everybody strongly believes (0) & (1) & (2), .... This result also allows us to provide sufficient epistemic conditions for the backward induction outcome and to relate extensive form rationalisability and conditional common certainty of rationality.Rationalisability, Extensive Form Games

Datalog± Ontology Consolidation

Knowledge bases in the form of ontologies are receiving increasing attention as they allow to clearly represent both the available knowledge, which includes the knowledge in itself and the constraints imposed to it by the domain or the users. In particular, Datalog ± ontologies are attractive because of their property of decidability and the possibility of dealing with the massive amounts of data in real world environments; however, as it is the case with many other ontological languages, their application in collaborative environments often lead to inconsistency related issues. In this paper we introduce the notion of incoherence regarding Datalog± ontologies, in terms of satisfiability of sets of constraints, and show how under specific conditions incoherence leads to inconsistent Datalog ± ontologies. The main contribution of this work is a novel approach to restore both consistency and coherence in Datalog± ontologies. The proposed approach is based on kernel contraction and restoration is performed by the application of incision functions that select formulas to delete. Nevertheless, instead of working over minimal incoherent/inconsistent sets encountered in the ontologies, our operators produce incisions over non-minimal structures called clusters. We present a construction for consolidation operators, along with the properties expected to be satisfied by them. Finally, we establish the relation between the construction and the properties by means of a representation theorem. Although this proposal is presented for Datalog± ontologies consolidation, these operators can be applied to other types of ontological languages, such as Description Logics, making them apt to be used in collaborative environments like the Semantic Web.Fil: Deagustini, Cristhian Ariel David. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Martinez, Maria Vanina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Falappa, Marcelo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Simari, Guillermo Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; Argentin

Rational Requirements and the Primacy of Pressure

There are at least two threads in our thought and talk about rationality, both practical and theoretical. In one sense, to be rational is to respond correctly to the reasons one has. Call this substantive rationality. In another sense, to be rational is to be coherent, or to have the right structural relations hold between one’s mental states, independently of whether those attitudes are justified. Call this structural rationality. According to the standard view, structural rationality is associated with a distinctive set of requirements that mandate or prohibit certain combinations of attitudes, and it’s in virtue of violating these requirements that incoherent agents are irrational. I think the standard view is mistaken. The goal of this paper is to explain why, and to motivate an alternative account: rather than corresponding to a set of law-like requirements, structural rationality should be seen as corresponding to a distinctive kind of pro tanto rational pressure—i.e. something that comes in degrees, having both magnitude and direction. Something similar is standardly assumed to be true of substantive rationality. On the resulting picture, each dimension of rational evaluation is associated with a distinct kind of rational pressure—substantive rationality with (what I call) justificatory pressure and structural rationality with attitudinal pressure. The former is generated by one’s reasons while the latter is generated by one’s attitudes. Requirements turn out to be at best a footnote in the theory of rationality

A Cognitive Model for Conversation

International audienceThis paper describes a symbolic model of rational action and decision making to support analysing dialogue. The model approximates principles of behaviour from game theory, and its proof theory makes Gricean principles of cooperativity derivable when the agents’ preferences align