Rolf Mantel and the Computability of General Equilibria: On the Origins of the Sonnenschein-Mantel-Debreu Theorem

In this brief paper we revise the original motivations of Rolf Mantel to pursue a proof of Sonnenschein´s conjecture. We contend that his work on computational models of general equilibrium lead him to seek an alternative to the usual fixed point theorems used in proofs of existence. Confronted with a paper of Uzawa and his own experience in programming a national planning system he found that the use of theorems like Brouwer´s and Kakutani´s was unavoidable. To check out whether Uzawa was right he sought to find out whether the only properties required of excess demand functions to ensure the existence of equilibria in competitive markets were continuity, homogeneity and Walras´ law. In 1974, he found that this was actually the case. We will see that this result and his interpretation were informed by Mantel´s interest in economic development and planning.Fil: Tohmé, Fernando

Local logics, non-monotonicity and defeasible argumentation

In this paper we present an embedding of abstract argumentation systems into the framework of Barwise and Seligman’s logic of information flow.We show that, taking P.M. Dung’s characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions of Barwise and Seligman’s logic of information flow.We show that, taking P.M. Dung’s characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions of Barwise and Seligman’s logic of information flow.We show that, taking P.M. Dung’s characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions of Barwise and Seligman’s logic of information flow.We show that, taking P.M. Dung’s characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions of Barwise and Seligman’s logic of information flow.We show that, taking P.M. Dung’s characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions of argument systems leads to a corresponding ordering of background conditions. The relations among extensions becomes a relation among partial orderings of background conditions. This introduces a conceptual innovation in Barwise and Seligman’s representation of commonsense reasoning.Fil: Bodanza, Gustavo Adrian. Universidad Nacional del Sur. Departamento de Humanidades; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; ArgentinaFil: Tohmé, Fernando Abel. Universidad Nacional del Sur. Departamento de Economía; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentin

Strategic economic growth with decreasing rates of time preference in a two-agent economy

This paper presents a two-agent economy, in which each agent has a consumption-dependent time preference. The optimal dynamic paths of accumulation will tend to one of many possible steady states, depending on the location of the initial capital level. The qualitative properties of this economic system have been analyzed elsewhere (Tohm´e and Dab´us, 2000). It has been shown that the interaction between the two agents may drag the poorest agent towards a higher steady state, getting her out of the potential poverty trap in which she could fall in isolation. We are interested now in studying specific functional forms of the joint production function, the utility functions and the psychological discount rates. The goal is to characterize both the individual and joint steady states in order to assess the advantages of interaction. Following the lead of (Dockner and Nishimura, 2004) we will obtain the subgame perfect equilibria of the economy seen as a two-person non-zero sum game. We will show that the non-linear convergence path towards the steady state examined by Tohm´e and Dab´us also obtains in a closed-loop solution.Fil: Larrosa, Juan Manuel Ceferino. Universidad Nacional del Sur. Departamento de Economía; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; ArgentinaFil: Tohmé, Fernando Abel. Universidad Nacional del Sur. Departamento de Economía; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentin

Asking infinite voters ‘Who is a J?’: Group Identification Problems in N

We analyze the problem of classifing individuals in a group N taking into account their opinions about which of them should belong to a specific subgroup N0 ⊆ N, in the case that |N| > ∞. We show that this problem is relevant in cases in which the group changes in time and/or is subject to uncertainty. The approach followed here to find the ensuing classification is by means of a Collective Identity Function (CIF) that maps the set of opinions into a subset of N. Kasher and Rubinstein (1997) characterized different CIFs axiomatically when |N| < ∞, in particular the Liberal and Oligarchic aggregators. We show that in the infinite setting the liberal result is still valid but the result no longer holds for the oligarchic case and give a characterization of all the aggregators satisfying the same axioms as the Oligarchic CIF. In our motivating examples, the solution obtained according to the alternative CIF is most cogent.Fil: Fioravanti, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaVIII Congreso Nacional de Estudiantes de Postgrado en EconomíaArgentinaUniversidad Nacional del Sur. Departamento de EconomíaInstituto de Investigaciones Económicas y Sociales del Su

Equilibrios en una sociedad de razonadores racionales

Un conjunto de agentes racionales en interacción constituye un marco apropiado para solucionar problemas de Inteligencia Artificial particularmente el problema del razonamiento. Sin embargo, al tener cada uno de los agentes objetivos propios, los que trata de satisfacer, aparece el problema de la resolución de conflictos entre agentes. Conviene determinar pues una noción de equilibrio que permita caracterizar situaciones en que las elecciones individuales provean resultados globalmente aceptables. Para derivar dicha noción se apelará a una formulación tomada de la Teoría Económica y se la analizará con herramientas de la Teoría de Juegos. Se muestra que dicha solución requiere que los agentes sigan un principio de elección al que denominamos cooperación condicional generalizada, que implica que los agentes operan con conocimiento común acera de las elecciones de los demás.Eje: 2do. Workshop sobre aspectos teóricos de la inteligencia artificialRed de Universidades con Carreras en Informática (RedUNCI

Equilibrios en una sociedad de razonadores racionales

Un conjunto de agentes racionales en interacción constituye un marco apropiado para solucionar problemas de Inteligencia Artificial particularmente el problema del razonamiento. Sin embargo, al tener cada uno de los agentes objetivos propios, los que trata de satisfacer, aparece el problema de la resolución de conflictos entre agentes. Conviene determinar pues una noción de equilibrio que permita caracterizar situaciones en que las elecciones individuales provean resultados globalmente aceptables. Para derivar dicha noción se apelará a una formulación tomada de la Teoría Económica y se la analizará con herramientas de la Teoría de Juegos. Se muestra que dicha solución requiere que los agentes sigan un principio de elección al que denominamos cooperación condicional generalizada, que implica que los agentes operan con conocimiento común acera de las elecciones de los demás.Eje: 2do. Workshop sobre aspectos teóricos de la inteligencia artificialRed de Universidades con Carreras en Informática (RedUNCI

Similarity as an extension of symmetry and its application to superrationality

In this paper we present a concept of similarity in games, on which to groundalternative solution concepts, some of which differ from the classical notions in the field. Inorder to do this we impose a constraint on players´ beliefs that amounts to a variant of thewell-known symmetry principle in classical bargaining theory. We show how this similarityrelation helps to identify different Nash equilibria in games, and how these "similar Nashequilibria" can be extended to non-symmetric games. While the notion is normative, it isnonetheless inspired by phenomena in which similarities between players lead to outcomesdetected in behavioral studies. We study the strategic properties of the concept of similarityand discuss its relationships with Hofstadter´ notion of superrationality.Fil: Senci, Carlos Maximiliano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; ArgentinaFil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin

Superrational types

We present a formal analysis of Douglas Hofstadter?s concept of superrationality. We start by defining superrationally justifiable actions, and study them in symmetric games. We then model the beliefs of the players, in a way that leads them to different choices than the usual assumption of rationality by restricting the range of conceivable choices. These beliefs are captured in the formal notion of type drawn from epistemic game theory. The theory of coalgebras is used to frame type spaces and to account for the existence of some of them. We find conditions that guarantee superrational outcomes.Fil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Viglizzo, Ignacio Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin

Equilibrios en una sociedad de razonadores racionales

Un conjunto de agentes racionales en interacción constituye un marco apropiado para solucionar problemas de Inteligencia Artificial particularmente el problema del razonamiento. Sin embargo, al tener cada uno de los agentes objetivos propios, los que trata de satisfacer, aparece el problema de la resolución de conflictos entre agentes. Conviene determinar pues una noción de equilibrio que permita caracterizar situaciones en que las elecciones individuales provean resultados globalmente aceptables. Para derivar dicha noción se apelará a una formulación tomada de la Teoría Económica y se la analizará con herramientas de la Teoría de Juegos. Se muestra que dicha solución requiere que los agentes sigan un principio de elección al que denominamos cooperación condicional generalizada, que implica que los agentes operan con conocimiento común acera de las elecciones de los demás.Eje: 2do. Workshop sobre aspectos teóricos de la inteligencia artificialRed de Universidades con Carreras en Informática (RedUNCI

Structural relations of symmetry among players in strategic games

The notions of symmetry and anonymity in strategic games have been formalized in different ways in the literature. We propose a combinatorial framework to analyze these notions, using group actions. Then, the same framework is used to define partial symmetries in payoff matrices. With this purpose, we introduce the notion of the role a player plays with respect to another one, and combinatorial relations between roles are studied. Building on them, we define relations directly between players, which provide yet another characterization of structural symmetries in the payoff matrices of strategic games.Fil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Economía; ArgentinaFil: Viglizzo, Ignacio Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin