A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

We introduce and study a class of infinite-horizon nonzero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove “fixation”, i.e. that players will adopt a constant strategy after a finite time. The resulting dynamics is related to zerotemperature Glauber dynamics on random graphs of possibly infinite volume.

Monopolistic competition and different wage setting systems

In this paper we match the static disequilibrium unemployment model without frictions in the labor market and monopolistic competition with an infinite horizon model of growth. We compare the wages set at the firm, sector and national (centralized) levels, their unemployment rates and growth of the economic variables, for the Cobb-Douglas production function, in order to see under wich conditions the inverse U hypothesis between unemployment and centralization of wage bargain is confirmed. We also analyze, in the three wage setting systems, the effect of an increase in the monopoly power on employment and growth.

Social capital, government expenditures, and growth

Countries with greater social capital have higher economic growth. We show that socialcapital is also highly positively correlated across countries with government expenditureon education. We develop an infinite-horizon model of public spending and endogenousstochastic growth that explains both facts through frictions in political agency whenvoters have imperfect information. In our model, the government provides servicesthat yield immediate utility, and investment that raises future productivity. Voters aremore likely to observe public services, so politicians have electoral incentives to underprovidepublic investment. Social capital increases voters' awareness of all governmentactivity. As a consequence, both politicians' incentives and their selection improve.In the dynamic equilibrium, both the amount and the efficiency of public investmentincrease, permanently raising the growth rate.

Can we identify Walrasian allocations?

[eng] We consider a discrete time, pure exchange infinite horizon economy with two or more consumers and at least one concumption good per period. Within the framework of decentralized mechanisms, we show that for a given consumption trade at any period of time, say at time one, the consumers will need, in general, an infinite dimensional (informational) space to identigy such a trade as an intemporal Walrasian one. However, we show and characterize a set of enviroments where the Walrasian trades at each period of time can be achieved as the equilibrium trades of a sequence of decentralized competitive mechanisms, using only both current prices and quantities to coordinate decisions.

Can we identify Walrasian allocations?

[eng] We consider a discrete time, pure exchange infinite horizon economy with two or more consumers and at least one concumption good per period. Within the framework of decentralized mechanisms, we show that for a given consumption trade at any period of time, say at time one, the consumers will need, in general, an infinite dimensional (informational) space to identigy such a trade as an intemporal Walrasian one. However, we show and characterize a set of enviroments where the Walrasian trades at each period of time can be achieved as the equilibrium trades of a sequence of decentralized competitive mechanisms, using only both current prices and quantities to coordinate decisions.

D-String on near horizon geometries and infinite conformal symmetry

We show that the symmetries of effective D-string actions in constant dilaton backgrounds are directly related to homothetic motions of the background metric. In the presence of such motions, there are infinitely many nonlinearly realized rigid symmetries forming a loop (or looplike) algebra. Near horizon (antideSitter) D3 and D1+D5 backgrounds are discussed in detail and shown to provide 2D interacting field theories with infinite conformal symmetry.

Infinite index subgroups and finiteness properties of intersections of geometrically finite groups

We explore which types of finiteness properties are possible for intersections of geometrically finite groups of isometries in negatively curved symmetric rank one spaces. Our main tool is a twist construction which takes as input a geometrically finite group containing a normal subgroup of infinite index with given finiteness properties and infinite Abelian quotient, and produces a pair of geometrically finite groups whose intersection is isomorphic to the normal subgroup.

Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

On a size-structured two-phase population model with infinite states-at-birth

In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an “active” phase when individuals grow, reproduce and die and a second “resting” phase when individuals only grow. Transition between these two phases depends on individuals’ size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant state space. Then we investigate, in the framework of the spectral theory of linear operators, the asymptotic behavior of solutions of the model. We prove that the associated semigroup has, under biologically plausible assumptions, the property of asynchronous exponential growth.

Inversion of analytic characteristic functions and infinite convolutions of exponential and Laplace densities

This paper shows that certain quotients of entire functions are characteristic functions. Under some conditions, we provide expressions for the densities of such characteristic functions which turn out to be generalized Dirichlet series which in turn can be expressed as an infinite linear combination of exponential or Laplace densities. We apply these results to several examples.

Nash equilibrium strategies in discrete-time finite-horizon dynamic games with risk-and effort-averse players

The objective of this paper is to re-examine the risk-and effort attitude in the context of strategic dynamic interactions stated as a discrete-time finite-horizon Nash game. The analysis is based on the assumption that players are endogenously risk-and effort-averse. Each player is characterized by distinct risk-and effort-aversion types that are unknown to his opponent. The goal of the game is the optimal risk-and effort-sharing between the players. It generally depends on the individual strategies adopted and, implicitly, on the the players' types or characteristics.

An algorithm for semi-infinite polynomial optimization

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2010 Horizon Report: Iberoamerican Edition

The series of Horizon Reports is the most tangible outcome of the New Media Consortium's Horizon Project, a qualitative research endeavour launched in 2002 which identifies and describes the emergingtechnologies with the greatest potential to have an impact on teaching, learning, research and creative expression in the global education field. This volume,the 2010 Horizon Report: Iberoamerican Edition, focuses on research in countries of the iberoamerican region (including the whole of Latin America, Spainand Portugal) and in the field of higher education. The 2010 Horizon Report: Iberoamerican Edition is the first to offer this regional contextualization and hasbeen produced by the NMC and the eLearn Center of the Universitat Oberta de Catalunya (UOC).

Relatório Horizon : edição Ibero-americana 2010

La sèrie d'informes Horizon és el resultat més tangible del Projecte Horizon del New Media Consortium, un esforç de recerca qualitativa iniciat el 2002, que identifica i descriu les tecnologies emergents amb més potencial d'impacte en l'ensenyament, l'aprenentatge, la recerca i la expressió creativa en l'àmbit educatiu global. Aquest volum, l'Informe Horizon 2010: Edició Iberoamericana, se centra en la investigació en els països de la regió Iberoamericana (incloent-hi tota Llatinoamèrica, Espanya i Portugal) i en l'àmbit de l'educació superior. L'Informe Horizon 2010: Edició Iberoamericana és el primer que ofereix aquesta contextualització regional i ha estat produït per l'NMC i el eLearn Center de la Universitat Oberta de Catalunya.

Informe Horizon : edición iberoamericana 2010

La serie de Informes Horizon es el resultado más tangible del Proyecto Horizon del New Media Consortium, un esfuerzo de investigación cualitativa iniciado en 2002, que identifica y describe las tecnologías emergentes con mayor potencial de impacto en la enseñanza, el aprendizaje, la investigación y la expresión creativa en el ámbito educativo global. Este volumen, elInforme Horizon 2010: Edición Iberoamericana, centra la investigación en los países de la región Iberoamericana (incluyendo a toda Latinoamérica, España y Portugal) y en el ámbito de la educación superior. ElInforme Horizon 2010: Edición Iberoamericana es el primero que ofrece esta contextualización regional y ha sido producido por el NMC y el eLearn Center de laUniversitat Oberta de Catalunya.