Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians

This paper is a sequel to ``Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey Hamiltonians at a quasi-periodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori.

Market rewards to patterns on increasing earnings: do cash flow patterns, accruals manipulation and real activities manipulation matter?

This study explores whether firms have differential price-earnings multiples associated with their means of achieving a sequential pattern of increasing positive earnings. Our main findings show that market participants assign higher price-earnings multiples to firms when their pattern of increasing earnings is supported by the same pattern of increasing cash flows. Market participants assign lower price-earnings multiples to firms suspect of having engaged in accrual-based earnings management, sales manipulation, and overproduction to achieve the earnings pattern. We find, however, that market participants do not penalize firms suspect of having achieved the earnings pattern through the opportunistic reduction of discretionary expenses.

Simulation methods with extended stability for stiff biochemical kinetics

Background: With increasing computer power, simulating the dynamics of complex systems in chemistry and biology is becoming increasingly routine. The modelling of individual reactions in (bio)chemical systems involves a large number of random events that can be simulated by the stochastic simulation algorithm (SSA). The key quantity is the step size, or waiting time, τ, whose value inversely depends on the size of the propensities of the different channel reactions and which needs to be re-evaluated after every firing event. Such a discrete event simulation may be extremely expensive, in particular for stiff systems where τ can be very short due to the fast kinetics of some of the channel reactions. Several alternative methods have been put forward to increase the integration step size. The so-called τ-leap approach takes a larger step size by allowing all the reactions to fire, from a Poisson or Binomial distribution, within that step. Although the expected value for the different species in the reactive system is maintained with respect to more precise methods, the variance at steady state can suffer from large errors as τ grows. Results: In this paper we extend Poisson τ-leap methods to a general class of Runge-Kutta (RK) τ-leap methods. We show that with the proper selection of the coefficients, the variance of the extended τ-leap can be well-behaved, leading to significantly larger step sizes.Conclusions: The benefit of adapting the extended method to the use of RK frameworks is clear in terms of speed of calculation, as the number of evaluations of the Poisson distribution is still one set per time step, as in the original τ-leap method. The approach paves the way to explore new multiscale methods to simulate (bio)chemical systems.

Computational Representation of Collaborative Learning Flow Patterns Using IMS Learning Design

The identification and integration of reusable and customizable CSCL (Computer Supported Collaborative Learning) may benefit from the capture of best practices in collaborative learning structuring. The authors have proposed CLFPs (Collaborative Learning Flow Patterns) as a way of collecting these best practices. To facilitate the process of CLFPs by software systems, the paper proposes to specify these patterns using IMS Learning Design (IMS-LD). Thus, teachers without technical knowledge can particularize and integrate CSCL tools. Nevertheless, the support of IMS-LD for describing collaborative learning activities has some deficiencies: the collaborative tools that can be defined in these activities are limited. Thus, this paper proposes and discusses an extension to IMS-LD that enables to specify several characteristics of the use of tools that mediate collaboration. In order to obtain a Unit of Learning based on a CLFP, a three stage process is also proposed. A CLFP-based Unit of Learning example is used to illustrate the process and the need of the proposed extension.

ILS-ESP An efficient, simple, and parameter-free algorithm for solving the permutation flow-shop problem

From a managerial point of view, the more effcient, simple, and parameter-free (ESP) an algorithm is, the more likely it will be used in practice for solving real-life problems. Following this principle, an ESP algorithm for solving the Permutation Flowshop Sequencing Problem (PFSP) is proposed in this article. Using an Iterated Local Search (ILS) framework, the so-called ILS-ESP algorithm is able to compete in performance with other well-known ILS-based approaches, which are considered among the most effcient algorithms for the PFSP. However, while other similar approaches still employ several parameters that can affect their performance if not properly chosen, our algorithm does not require any particular fine-tuning process since it uses basic "common sense" rules for the local search, perturbation, and acceptance criterion stages of the ILS metaheuristic. Our approach defines a new operator for the ILS perturbation process, a new acceptance criterion based on extremely simple and transparent rules, and a biased randomization process of the initial solution to randomly generate different alternative initial solutions of similar quality -which is attained by applying a biased randomization to a classical PFSP heuristic. This diversification of the initial solution aims at avoiding poorly designed starting points and, thus, allows the methodology to take advantage of current trends in parallel and distributed computing. A set of extensive tests, based on literature benchmarks, has been carried out in order to validate our algorithm and compare it against other approaches. These tests show that our parameter-free algorithm is able to compete with state-of-the-art metaheuristics for the PFSP. Also, the experiments show that, when using parallel computing, it is possible to improve the top ILS-based metaheuristic by just incorporating to it our biased randomization process with a high-quality pseudo-random number generator.

Non-Quasi-Competitiveness and Stability in Cournot's Model

This paper retakes previous work of the authors, about the relationship between non-quasi-competitiveness (the increase in price caused by an increase in the number of oligopolists) and stability of the equilibrium in the classical Cournot oligopoly model. Though it has been widely accepted in the literature that the loss of quasi-competitiveness is linked, in the long run as new firms entered the market, to instability of the model, the authors in their previous work put forward a model in which a situation of monopoly changed to duopoly losing quasi-competitiveness but maintaining the stability of the equilibrium. That model could not, at the time, be extended to any number of oligopolists. The present paper exhibits such an extension. An oligopoly model is shown in which the loss of quasi-competitiveness resists the presence in the market of as many firms as one wishes and where the successive Cournot's equilibrium points are unique and asymptotically stable. In this way, for the first time, the conjecture that non-quasi- competitiveness and instability were equivalent in the long run, is proved false.

Hot vs. cold: Sequential responses and preference stability in experimental games

In experiments with two-person sequential games we analyzewhether responses to favorable and unfavorable actions dependon the elicitation procedure. In our hot treatment thesecond player responds to the first player s observed actionwhile in our cold treatment we follow the strategy method and have the second player decide on a contingent action foreach and every possible first player move, without firstobserving this move. Our analysis centers on the degree towhich subjects deviate from the maximization of their pecuniaryrewards, as a response to others actions. Our results show nodifference in behavior between the two treatments. We also findevidence of the stability of subjects preferences with respectto their behavior over time and to the consistency of theirchoices as first and second mover.

Monetary policy rules and macroeconomic stability: Evidence and some theory

We estimate a forward-looking monetary policy reaction function for thepostwar United States economy, before and after Volcker's appointmentas Fed Chairman in 1979. Our results point to substantial differencesin the estimated rule across periods. In particular, interest ratepolicy in the Volcker-Greenspan period appears to have been much moresensitive to changes in expected inflation than in the pre-Volckerperiod. We then compare some of the implications of the estimated rulesfor the equilibrium properties of inflation and output, using a simplemacroeconomic model, and show that the Volcker-Greenspan rule is stabilizing.

Price increase and stability with new entries in Cournot markets

It is widely accepted in the literature about the classicalCournot oligopoly model that the loss of quasi competitiveness is linked,in the long run as new firms enter the market, to instability of the equilibrium. In this paper, though, we present a model in which a stableunique symmetric equilibrium is reached for any number of oligopolistsas industry price increases with each new entry. Consequently, the suspicion that non quasi competitiveness implies, in the long run, instabilityis proved false.

On the impact of fundamentals, liquidity and coordination on market stability

We develop a coordination game to model interactions betweenfundamentals and liquidity during unstable periods in financial markets.We then propose a flexible econometric framework for estimationof the model and analysis of its quantitative implications. The specificempirical application is carry trades in the yen dollar market, includingthe turmoil of 1998. We find a generally very deep market, withlow information disparities amongst agents. We observe occasionallyepisodes of market fragility, or turmoil with up by the escalator, downby the elevator patterns in prices. The key role of strategic behaviorin the econometric model is also confirmed.

Designing institutions for financial stability: Regulation and supervision by objective for the Euro area

In this paper, we discuss pros and cons ofdifferent models for financial market regulationand supervision and we present a proposal forthe re-organisation of regulatory and supervisoryagencies in the Euro Area. Our arguments areconsistent with both new theories and effectivebehaviour of financial intermediaries inindustrialized countries. Our proposed architecturefor financial market regulation is based on theassignment of different objectives or "finalities"to different authorities, both at the domesticand the European level. According to thisperspective, the three objectives of supervision- microeconomic stability, investor protectionand proper behaviour, efficiency and competition- should be assigned to three distinct Europeanauthorities, each one at the centre of a Europeansystem of financial regulators and supervisorsspecialized in overseeing the entire financialmarket with respect to a single regulatoryobjective and regardless of the subjective natureof the intermediaries. Each system should bestructured and organized similarly to the EuropeanSystem of Central Banks and work in connectionwith the central bank which would remain theinstitution responsible for price and macroeconomicstability. We suggest a plausible path to buildour 4-peak regulatory architecture in the Euro area.

Measuring the stability of histogram appearance when the anchor position is changed

Although the histogram is the most widely used density estimator, itis well--known that the appearance of a constructed histogram for a given binwidth can change markedly for different choices of anchor position. In thispaper we construct a stability index $G$ that assesses the potential changesin the appearance of histograms for a given data set and bin width as theanchor position changes. If a particular bin width choice leads to an unstableappearance, the arbitrary choice of any one anchor position is dangerous, anda different bin width should be considered. The index is based on the statisticalroughness of the histogram estimate. We show via Monte Carlo simulation thatdensities with more structure are more likely to lead to histograms withunstable appearance. In addition, ignoring the precision to which the datavalues are provided when choosing the bin width leads to instability. We provideseveral real data examples to illustrate the properties of $G$. Applicationsto other binned density estimators are also discussed.

On forward induction and evolutionary and strategic stability

We analyze which normal form solution concepts capture the notion offorward induction, as defined by van Damme (JET, 1989) in the classof generic two player normal form games preceded by an outsideoption. We find that none of the known strategic stability concepts(including Mertens stable sets and hyperstable sets) captures this form of forward induction. On the other hand, we show that the evolutionary concept of EES set (Swinkels, JET, 1992) is always consistent with forward induction.

Assessing an intuitive condition for stability under a range of traffic conditions via a generalised Lu-Kumar network

We argue the importance both of developing simple sufficientconditions for the stability of general multiclass queueing networks and also of assessing such conditions under a range of assumptions on the weight of the traffic flowing between service stations. To achieve the former, we review a peak-rate stability condition and extend its range of application and for the latter, we introduce a generalisation of the Lu-Kumar network on which the stability condition may be tested for a range of traffic configurations. The peak-rate condition is close to exact when the between-station traffic is light, but degrades as this traffic increases.