While payoff-based learning models are almost exclusively devised for finite action games, where players can test every action, it is harder to design such learning processes for continuous games. We construct a stochastic learning rule, designed for games with continuous action sets, which requires no sophistication from the players and is simple to implement: players update their actions according to variations in own payoff between current and previous action. We then analyze its behavior in several classes of continuous games and show that convergence to a stable Nash equilibrium is guaranteed in all games with strategic complements as well as in concave games, while convergence to Nash occurs in all locally ordinal potential games as soon as Nash equilibria are isolated.
Although it is widely acknowledged that non-cognitive skills matter for adult outcomes, little is known about the role played by family environment in the formation of these skills. We use a longitudinal survey of children born in the UK in 2000–2001, the Millennium Cohort Study by the Centre for Longitudinal Studies, to estimate the effect of family size on socio-emotional skills, measured by the Strengths and Difficulties Questionnaire. To account for the endogeneity of fertility decisions, we use a well-known instrumental approach that exploits parents’ preference for children’s gender diversity. We show that the birth of a third child negatively affects the socio-emotional skills of the first two children in a persistent manner. However, we show that this negative effect is entirely driven by girls. We provide evidence that this gender effect is partly driven by an unequal response of parents’ time investment in favour of boys and, to a lesser extent, by an unequal demand for household chores.
Two traditional theorems of welfare economics posit a trade-off between a government redistribution targets and efficiency. We propose a third ‘claim’ of welfare economics, stating that in closed economies the actual efficiency costs associated with redistribution are small. We then examine the claim in the current phase of ‘hyper-globalization’. On the one hand, a race-to-the-bottom in taxation restricts the capacity to tax high-earners and the associated brain drain may affect a country’s long-run growth. On the other hand, demand for social insurance should be particularly high in an open economy, especially with advancing digitalization. Xenophobic sentiments may, however, offset this demand. We also discuss the impact of globalization on wage equalization and productive efficiency. We conclude against the idea that the welfare state is intrinsically unable to carry out its redistributive function in an era of globalization. However, its strategies and tools of intervention must be rethought.
We investigate empirically, and explain theoretically, how the relative wages of skilled and unskilled workers vary with their relative supplies in open economies. Our results combine the insights of simple labour market and trade models. In countries that trade, relative wages respond inversely to variation in skill supplies, but the response decreases with the degree of openness to trade and is small in very open countries. To reconcile our results with standard estimates of the elasticity of substitution between skilled and unskilled workers, we allow also for the influence of directed technical change and income elasticity of demand for skill-intensive goods.
To what extent do childhood experiences continue to affect adult wellbeing over the life course? Previous work on this link has been carried out either at one particular adult age or for some average over adulthood. We here use two British birth-cohort datasets (the 1958 NCDS and the 1970 BCS) to map out the time profile of the effect of childhood experiences on adult outcomes, including life satisfaction. We find that the effects of many aspects of childhood do not fade away over time but are rather remarkably stable. In both birth-cohorts, child non-cognitive skills are the strongest predictors of adult life satisfaction at all ages. Of these, emotional health is the strongest. Childhood cognitive performance is more important than good conduct in explaining adult life satisfaction in the earlier NCDS cohort, whereas this ranking is inverted in the more recent BCS.
The purpose of this paper is twofold. First, we examine convergence properties of an inexact proximal point method with a quasi distance as a regularization term in order to find a critical point (in the sense of Toland) of a DC function (difference of two convex functions). Global convergence of the sequence and some convergence rates are obtained with additional assumptions. Second, as an application and its inspiration, we study in a dynamic setting, the very important and difficult problem of the limit of the firm and the time it takes to reach it (maturation time), when increasing returns matter in the short run. Both the formalization of the critical size of the firm in term of a recent variational rationality approach of human dynamics and the speed of convergence results are new in Behavioral Sciences.
This study compares GDP per capita levels and growth rates across 17 advanced economies over the period 1890–2013 using an accounting breakdown and runs Phillips and Sul (Econometrica 75(6):1771–1855, 2007) convergence tests. An overall convergence process has been at work among advanced economies, mainly after WWII, driven mostly by capital intensity and then TFP, while trends in hours worked and employment rates are disparate. However, this convergence process came to a halt during technology shocks, during the two world wars and since the 1990s, with the convergence of advanced economies stopping far from the level of US GDP per capita.
The marketing-mix of price–quality and advertising–quality relationship is well studied. Less understood is the price–advertising–quality relationship. This article fills the gap, investigating the interplay between price, advertising, and quality in an optimal control model. Our results generalize the condition of Dorfman–Steiner in a dynamic context. Also, they point to the impact of greater product quality on the dynamic policies of pricing and advertising. Furthermore, a phase diagram analysis shows that quality develops monotonically in time and converges to a unique steady state. We also show that quality investment could either decrease or increase over time but this depends on its effectiveness. Our results spot the profitable opportunities of a firm managing a more complex marketing-mix.
In this paper we investigate if government balanced-budget rules together with endogenous taxation may lead to aggregate instability in an endogenous growth framework. After highlighting the differences with the exogenous growth framework, we prove that under counter-cyclical consumption taxes, while there exists a unique balanced growth path, sunspot equilibria based on self-fulfilling expectations occur through a form of global indeterminacy. In addition, we argue that this result is empirically plausible for a large set of OECD countries and that it may also emerge with endogenous income taxes.
We consider an economy with three cities producing different outputs. Two cities produce intermediate goods, a type 1 city producing an intermediate “agricultural” good with capital and labor only, and a type 2 city producing an intermediate “industrial” good with capital, labor, and human capital. A type 3 city produces the final good which is obtained from the two intermediate goods and labor. The asymmetric introduction of human capital allows us to prove that the three cities experience, at equilibrium, heterogeneous endogenous growth rates which are proportional to the growth rate of human capital. We show that the “industrial” type 2 city is characterized by the larger growth rate while the “agricultural” type 1 city experiences the lower growth rate, and thus the type 3 city is characterized by a growth rate which is a convex combination of the two former growth rates. This implies that the relative size in terms of output of the “agricultural” city decreases over time. This property allows us to recover the empirical fact that most non-agricultural production occurs in growing metropolitan areas. But, simultaneously, as we prove that total labor employed in each city is proportional to the total population, the relative population size distribution of cities is constant over time, as shown in empirical studies.