An answer to a question of herings et al.

One answers to an open question of Herings et al. (2008), by proving that their fixed point theorem for discontinuous functions works for mappings defined on convex compact subset of a Euclidean space, and not only polytopes. This rests on a fixed point result of ToussaintNash equilibrium, fixed point, discontinuity

On the orientability of the asset equilibrium manifold

This paper addresses partly an open question raised in the Handbook of Mathematical Economics about the orientability of the pseudo-equilibrium manifold in the basic two-period General Equilibrium with Incomplete markets (GEI) model. For a broad class of explicit asset structures, it is proved that the asset equilibrium space is an orientable manifold if S-J is even, where S is the number of states of nature and J the number of assets. This implies, under the same conditions, the orientability of the pseudo-equilibrium manifold. By a standard homotopy argument, it also entails the index theorem for S-J even. A particular case is Momi's result, i.e the index theorem for generic endowments and real asset structures if S-J is even.incomplete markets, equilibria manifold, orientability, index theorem

An answer to a question of herings et al

One answers to an open question of Herings et al. (2008), by proving that their fixed point theorem for discontinuous functions works for mappings defined on convex compact subset of $\R^n$, and not only polytopes. This fixed point theorem can be applied to the problem of Nash equilibrium existence in discontinuous games.fixed point theorem; discontinuity; nash equilibrium

Emergent processes as generation of discontinuities

In this article we analyse the problem of emergence in its diachronic dimension. In other words, we intend to deal with the generation of novelties in natural processes. Our approach aims at integrating some insights coming from Whitehead’s Philosophy of the Process with the epistemological framework developed by the “autopoietic” tradition. Our thesis is that the emergence of new entities and rules of interaction (new “fields of relatedness”) requires the development of discontinuous models of change. From this standpoint natural evolution can be conceived as a succession of emergences — each one realizing a novel “extended” present, described by distinct models — rather than as a single and continuous dynamics. This theoretical and epistemological framework is particularly suitable to the investigation of the origin of life, an emblematic example of this kind of processes

Systems, Autopoietic

Definition The authors’ definition of the autopoietic system has evolved through the years. One of them states that an autopoietic system is organized (defined as a unity) as a network of processes of production (transformation and destruction) of components that produces the components which: (1) through their interactions and transformations regenerate and realize the network of processes (relations) that produced them; and (2) constitute it (the machine) as a concrete unity in the space in which they exist by specifying the topological domain of its realization as such a network (Varela 1979, p. 13). Nearly the same formula was earlier used to define an autopoietic machine (Maturana and Varela 1973/1980, 1984/1987, p. 135

On the existence of approximated equilibria in discontinuous economies

In this paper, we prove an existence theorem for approximated equilibria in a class of discontinuous economies. The existence result is a direct consequence of a discontinuous extension of Brouwer's fixed point Theorem (1912), and is a refinement of several classical results in the standard General Equilibrium with Incomplete markets (GEI) model (e.g., Bottazzi (1995), Duffie and Shafer (1985), Husseini et al. (1990), Geanakoplos and Shafer (1990), Magill and Shafer (1991)). As a by-product, we get the first existence proof of an approximated equilibrium in the GEI model, without perturbing the asset structure nor the endowments. Our main theorem rests on a new topological structure result for the asset equilibrium space and may be of interest by itself.general equilibrium, incomplete markets, approximated equilibrium

Hitchin Systems at Low Genera

The paper gives a quick account of the simplest cases of the Hitchin integrable systems and of the Knizhnik-Zamolodchikov-Bernard connection at genus 0, 1 and 2. In particular, we construct the action-angle variables of the genus 2 Hitchin system with group SL(2) by exploiting its relation to the classical Neumann integrable systems.Comment: 20 pages, late

On the orientability of the asset equilibrium manifold.

This paper addresses partly an open question raised in the Handbook of Mathematical Economics about the orientability of the pseudo-equilibrium manifold in the basic two-period General Equilibrium with Incomplete Markets (GEI) model. For a broad class of explicit asset structures, it is proved that the asset equilibrium space is an orientable manifold if S − J is even. This implies, under the same conditions, the orientability of the pseudo-equilibrium manifold. By a standard homotopy argument, it also entails the index theorem for S − J even. A particular case is Momi's result, i.e. the index theorem for generic endowments and real asset structures if S − J is even.General equilibrium; Incomplete markets; Index theorem; Orientability;