Global Nash convergence of Foster and Young's regret testing

We construct an uncoupled randomized strategy of repeated play such that, if every player follows such a strategy, then the joint mixed strategy profiles converge, almost surely, to a Nash equilibrium of the one-shot game. The procedure requires very little in terms of players' information about the game. In fact, players' actions are based only on their own past payoffs and, in a variant of the strategy, players need not even know that their payoffs are determined through other players' actions. The procedure works for general finite games and is based on appropriate modifications of a simple stochastic learningrule introduced by Foster and Young.

A note on the convergence to competitive equilibria in economies with moral hazard

We examine the conditions under which competitive equilibria can beobtained as the limit, when the number of strategic traders getslarge, of Nash equilibria in economies with asymmetric informationon agents' effort and possibly imperfect observability of agents'trades. Convergence always occur when either effort is publiclyobserved (no matter what is the information available tointermediaries on agents' trades); or effort is private informationbut agents' trades are perfectly observed; or no information at allis available on agents' trades. On the other hand, when eachintermediary can observe its trades with an agent, but not theagent's trades with other intermediaries, the (Nash) equilibriawith strategic intermediaries do not converge to any of thecompetitive equilibria, for an open set of economies. The source ofthe difficulties for convergence is the combination of asymmetricinformation and the restrictions on the observability of tradeswhich prevent the formation of exclusive contractual relationshipsand generate barriers to entry in the markets for contracts.

Stochastic uncoupled dynamics and Nash equilibrium

In this paper we consider dynamic processes, in repeated games, that are subject to the natural informational restriction of uncoupledness. We study the almost sure convergence to Nash equilibria, and present a number of possibility and impossibility results. Basically, we show that if in addition to random moves some recall is introduced, then successful search procedures that are uncoupled can be devised. In particular, to get almost sure convergence to pure Nash equilibria when these exist, it su±ces to recall the last two periods of play.

A comment on "Rational learning lead to nash equilibrium" by professors Ehud Kalai and Ehud Lehrer

Kalai and Lebrer (93a, b) have recently show that for the case of infinitely repeated games, a coordination assumption on beliefs and optimal strategies ensures convergence to Nash equilibrium. In this paper, we show that for the case of repeated games with long (but finite) horizon, their condition does not imply approximate Nash equilibrium play. Recently Kalai and Lehrer (93a, b) proved that a coordination assumption on beliefs and optimal strategies, ensures that pIayers of an infinitely repeated game eventually pIay 'E-close" to an E-Nash equilibrium. Their coordination assumption requires that if players believes that certain set of outcomes have positive probability then it must be the case that this set of outcomes have, in fact, positive probability. This coordination assumption is called absolute continuity. For the case of finitely repeated games, the absolute continuity assumption is a quite innocuous assumption that just ensures that pIayers' can revise their priors by Bayes' Law. However, for the case of infinitely repeated games, the absolute continuity assumption is a stronger requirement because it also refers to events that can never be observed in finite time.

From tropics to tundra: Global convergence in plant functioning

Despite striking differences in climate, soils, and evolutionary history among diverse biomes ranging from tropical and temperate forests to alpine tundra and desert, we found similar interspecific relationships among leaf structure and function and plant growth in all biomes. Our results thus demonstrate convergent evolution and global generality in plant functioning, despite the enormous diversity of plant species and biomes. For 280 plant species from two global data sets, we found that potential carbon gain (photosynthesis) and carbon loss (respiration) increase in similar proportion with decreasing leaf life-span, increasing leaf nitrogen concentration, and increasing leaf surface area-to-mass ratio. Productivity of individual plants and of leaves in vegetation canopies also changes in constant proportion to leaf life-span and surface area-to-mass ratio. These global plant functional relationships have significant implications for global scale modeling of vegetation–atmosphere CO2 exchange.

A note on the coincidence between Stackelberg and Nash equilibria in a differential game between government and firms

[cat] A Navas i Marín Solano es va demostrar la coincidència entre els equilibris de Nash i de Stackelberg per a una versi´o modificada del joc diferencial proposat por Lancaster (1973). Amb l’objectiu d’obtenir una solució interior, es van imposar restriccions importants sobre el valors dels paràmetres del model. En aquest treball estenem aquest resultat, en el límit en que la taxa de descompte és igual a zero, eliminant les restriccions i considerant totes les solucions possibles.

A note on the coincidence between Stackelberg and Nash equilibria in a differential game between government and firms

[cat] A Navas i Marín Solano es va demostrar la coincidència entre els equilibris de Nash i de Stackelberg per a una versi´o modificada del joc diferencial proposat por Lancaster (1973). Amb l’objectiu d’obtenir una solució interior, es van imposar restriccions importants sobre el valors dels paràmetres del model. En aquest treball estenem aquest resultat, en el límit en que la taxa de descompte és igual a zero, eliminant les restriccions i considerant totes les solucions possibles.

Spike-based decision learning of nash equilibria in two-player games

Humans and animals face decision tasks in an uncertain multi-agent environment where an agent's strategy may change in time due to the co-adaptation of others strategies. The neuronal substrate and the computational algorithms underlying such adaptive decision making, however, is largely unknown. We propose a population coding model of spiking neurons with a policy gradient procedure that successfully acquires optimal strategies for classical game-theoretical tasks. The suggested population reinforcement learning reproduces data from human behavioral experiments for the blackjack and the inspector game. It performs optimally according to a pure (deterministic) and mixed (stochastic) Nash equilibrium, respectively. In contrast, temporal-difference(TD)-learning, covariance-learning, and basic reinforcement learning fail to perform optimally for the stochastic strategy. Spike-based population reinforcement learning, shown to follow the stochastic reward gradient, is therefore a viable candidate to explain automated decision learning of a Nash equilibrium in two-player games.

Convergence to the European Energy Policy in European countries: case studies and comparison

Purpose – Our paper aims at analyzing how different European countries cope with the European Energy Policy, which proposes a set of measures (free energy market, smart meters, energy certificates) to improve energy utilization and management in Europe. Design/methodology/approach – The paper first reports the general vision, regulations and goals set up by Europe to implement the European Energy Policy. Later on, it performs an analysis of how some European countries are coping with the goals, with financial, legal, economical and regulatory measures. Finally, the paper draws a comparison between the countries to present a view on how Europe is responding to the emerging energy emergency of the modern world. Findings – Our analysis on different use cases (countries) showed that European countries are converging to a common energy policy, even though some countries appear to be later than others In particular, Southern European countries were slowed down by the world financial and economical crisis. Still, it appears that contingency plans were put into action, and Europe as a whole is proceeding steadily towards the common vision. Research limitations/implications – European countries are applying yet more cuts to financing green technologies, and it is not possible to predict clearly how each country will evolve its support to the European energy policy. Practical implications – Different countries applied the concepts and measures in different ways. The implementation of the European energy policy has to cope with the resulting plethora of regulations, and a company proposing enhancement regarding energy management still has to possess robust knowledge of the single country, before being able to export experience and know-how between European countries. Originality/Value – Even though a few surveys on energy measures in Europe are already part of the state-of-the-art, organic analysis diagonal to the different topics of the European Energy Policy is missing. Moreover, this paper highlights how European countries are converging on a common view, and provides some details on the differences between the countries, thus facilitating parties interesting into cross-country export of experience and technology for energy management.

Gerogescu-Roegen versus Solow/Stiglitz and the convergence to the Cobb-Douglas

The value of the elasticity of substitution of capital for resources is a crucial element in the debate over whether continual growth is possible. It is generally held that the elasticity has to be at least one to permit continual growth and that there is no way of estimating this outside the range of the data. This paper presents a model in which the elasticity is determined endogenously and may converge to one. It is concluded that the general opinion is wrong: that the possibility of continual growth does not depend on the exogenously given value of the elasticity and that the value of the elasticity outside the range of the data can be studied by econometric methods.

The Global Dimension to Fiscal Sustainability

This paper examines the issue of fiscal sustainability in emerging market countries and industrial countries. We highlight the importance of the time series properties of the primary surplus and debt, and find evidence of a positive long run relationship. Consequently we emphasise, that especially for emerging markets, it is important to recognise the implications of global capital market shocks for fiscal sustainability, a relationship which has hitherto been ignored in the empirical literature. Using a factor model we demonstrate that the relationship between deficit and debt is conditional upon a global factor and we suggest that this global factor is related to world-wide liquidity. We also demonstrate that this acts as a constraint on emerging market economies’ fiscal policy.

Scale-dependent adaptive evolution and morphological convergence to climatic niche in Californian eriogonoids (Polygonaceae)

Aim Macroevolutionary patterns and processes change substantially depending on levels of taxonomic and ecological organization, and the resolution of environmental and spatial variability. In comparative methods, the resolution of environmental and spatial variability often defines the number of selective regimes used to test whether phenotypic characteristics are adaptively correlated with the environment. Here, we examine how investigator choice of the number of selective regimes, determined by varying the resolution of among-species variability in the species climatic niche (hereafter called ecological scale'), influences trait morphological diversification among Eriogonoideae species. We assess whether adaptive or neutral processes drive the evolution of several morphological traits in these species. Location South-western North America. Methods We applied a phylogenetic framework of three evolutionary models to four morphological traits and the climatic niches of Eriogonoideae (in the buckwheat family, Polygonaceae). We tested whether morphological traits evolve in relation to climate by adaptive or neutral process, and whether the resulting patterns of morphological variability are conserved or convergent across the clade. We inspected adaptive models of evolution under different levels of resolution of among-species variability of the climatic niche. Results We show that morphological traits and climate niches of Eriogonoideae species are not phylogenetically conserved. Further, adaptive evolution of phenotypic traits is specific to climatic niche occupancy across this clade. Finally, the likely evolutionary process and the level of detectable niche conservatism change depending on the resolution of environmental variability of the climatic niche. Main conclusions Our study demonstrates the need to consider both the resolution of environmental variability and alternative evolutionary models to understand the morphological diversification that accompanies divergent adaptive evolution of lineages to climatic conditions.

New Findings in a Global Approach to Dissect the Whole Phenotype of PLA2G6 Gene Mutations.

Mutations in PLA2G6 gene have variable phenotypic outcome including infantile neuroaxonal dystrophy, atypical neuroaxonal dystrophy, idiopathic neurodegeneration with brain iron accumulation and Karak syndrome. The cause of this phenotypic variation is so far unknown which impairs both genetic diagnosis and appropriate family counseling. We report detailed clinical, electrophysiological, neuroimaging, histologic, biochemical and genetic characterization of 11 patients, from 6 consanguineous families, who were followed for a period of up to 17 years. Cerebellar atrophy was constant and the earliest feature of the disease preceding brain iron accumulation, leading to the provisional diagnosis of a recessive progressive ataxia in these patients. Ultrastructural characterization of patients' muscle biopsies revealed focal accumulation of granular and membranous material possibly resulting from defective membrane homeostasis caused by disrupted PLA2G6 function. Enzyme studies in one of these muscle biopsies provided evidence for a relatively low mitochondrial content, which is compatible with the structural mitochondrial alterations seen by electron microscopy. Genetic characterization of 11 patients led to the identification of six underlying PLA2G6 gene mutations, five of which are novel. Importantly, by combining clinical and genetic data we have observed that while the phenotype of neurodegeneration associated with PLA2G6 mutations is variable in this cohort of patients belonging to the same ethnic background, it is partially influenced by the genotype, considering the age at onset and the functional disability criteria. Molecular testing for PLA2G6 mutations is, therefore, indicated in childhood-onset ataxia syndromes, if neuroimaging shows cerebellar atrophy with or without evidence of iron accumulation.