An extension of the Antoci-Dei-Galeotti evolutionary model for environment protection through financial instruments.

This work moves from a recent paper by Antoci, Dei and Galeotti [1] where a dynamic model is proposed to describe an innovative method to improve environmental quality based on the exchange of financial activities, promoted by a Public Administration, between firms and tourists in a given region. We extend their analysis in two directions: we first perform a global analysis of the basins of attraction to check the stability extents of the coexisting stable attractors of the model, and we show that some undesirable and sub-optimal stable equilibria always exist, whose basins may be quite intermingled with those of the optimal equilibrium; then we introduce a structural change of the model by assuming that the Public Administration, besides its action as an intermediary between visitors and polluting firms, also performs a direct action for the pollution control. We show how the cost of this direct action of the Public Administration can be balanced by proper taxes and we prove that undesired equilibria can be ruled out by a suitable balance of financial instruments and direct actions of Public Administration for environmental remediation.Environmental economics, evolutionary dynamics, replicator equations, multistability, basins of attraction.

Bifurcation Curves in Discontinuous Maps

Several discrete-time dynamic models are ultimately expressed in the form of iterated piecewise linear functions, in one or two-dimensional spaces. In this paper we study a one-dimensional map made up of three linear pieces which are separated by two discontinuity points, motivated by a dynamic model arising in social sciences. Starting from the bifurcation structure associated with one-dimensional maps with only one discontinuity point, we show how this is modied by the introduction of a second discontinuity point, and we give the analytic expressions of the bifurcation curves of the principal tongues (or tongues of first degree), for the family of maps considered, that depends on five parameters.iterated piecewise linear functions, discrete-time dynamic models, bifurcation curves.

MONETARY AND FISCAL POLICY IN A NONLINEAR MODEL OF PUBLIC DEBT

none3noIn this paper we study the dynamic relationship between the public debt ratio and the real interest rate. Specifically, by means of a macroeconomic model of simultaneous difference equations - one for the debt ratio and the other for the real interest rate - we focus on the role of monetary policy, fiscal policy and risk premium in affecting the stability of the debt ratio and the existence of steady states, if any. We show that, in a dynamic framework, fiscal rules may not be enough to control the pattern of the debt ratio, and the adoption of a monetary policy, in the form of an interest rate rule, is necessary to control the pattern of the debt ratio for assuring its sustainability over time. Notably, the creation or disappearance of steady states, or peri- odic (stable) cycles, can generate scenarios of multistability. While we obtain clear evidence that an active monetary policy has a stabilizing effect on both the real interest rate and the debt ratio, we also find that, in some scenarios, fiscal policy is not sufficient to avoid explosive patterns of the debt ratio.openGermana Giombini; Gian Italo Bischi; Giuseppe TravagliniGiombini, Germana; Bischi, GIAN ITALO; Travaglini, Giusepp

MULTISPECIES EXPLOITATION WITH EVOLUTIONARY SWITCHING OF HARVESTING STRATEGIES

none3noIn this paper, we propose a bioeconomic model which describes a fishery in which each of two noninteracting species is harvested by a given group of fishers during a defined time period. Then the Fishing Regulatory Authority allows each fisher to reconsider the harvesting decision at fixed (discrete) periods of time. The model derives from an Italian fisheries management experience in the Northern Adriatic Sea, where this kind of self-adjusting fishing policy has been proposed to regulate harvesting of two shellfish species. The proposed dynamic model assumes the form of a hybrid system, as the natural growth functions of the two species (in continuous time) are coupled with a discrete time adaptive system that regulates how agents switch from one harvesting strategy to the other period by period according to an evolutionary mechanism based on profit comparison. In order to obtain some insights into the basic mechanisms of the system, some relevant benchmark cases are analyzed before tackling (mainly numerically) the complete hybrid model. Our results suggest that, for proper sets of parameters, this kind of myopic and adaptive self-regulation may ensure a virtuous trade-off between profit maximization and resource conservation, driven by cost externalities and market pressure.openG.I. Bischi; F. Lamantia; D. RadiBischi, GIAN ITALO; F., Lamantia; D., Rad

A prey-predator fishery model with endogenous switching of harvesting strategy

We propose a dynamic model to describe a fishery where both preys and predators are harvested by a population of fishermen who are allowed to catch only one of the two species at a time. According to the strategy currently employed by each agent, i.e. the harvested variety, at each time period the population of fishermen is partitioned into two groups, and an evolutionary mechanism regulates how agents dynamically switch from one strategy to the other in order to improve their profits. Among the various dynamic models proposed, the most realistic is a hybrid system formed by two ordinary differential equations, describing the dynamics of the interacting species under fishing pressure, and an impulsive variable that evolves in a discrete time scale, in order to describe the changes of the fraction of fishermen that harvest a given stock. The aim of the paper is to analyze the economic consequences of this kind of self-regulating fishery, as well as its biological sustainability, in comparison with other regulatory policies. Our analytic and numerical results give evidence that in some cases this kind of myopic, evolutionary self-regulation might ensure a satisfactory trade-off between profit maximization and resource conservation

looking ahead part iii

In the past decades, manufacturing firms have increasingly off-shored main activities along their value chain to emerging economies in order to take advantage of lower costs. More recently, however, the trend of re-shoring has gained increasing attention. We argue that more research is needed to fully understand firms' motives for bringing their activities back home. Furthermore, multinational firms need to evaluate their activities along environmental, social and governance dimensions. Research on corporate social responsibility strategies of multinational enterprises and their global value chains is still scarce, however

Oligopoly Games with Local Monopolistic Approximation

We propose a repeated oligopoly game where quantity setting firms have incomplete knowledge of the demand function of the market in which they operate. At each time step they solve a profit maximization problem by using a subjective approximation of the demand function based on a local estimate its partial derivative, computed at the current values of prices and outputs, obtained through market experiments. At each time step they extrapolate such local approximation by assuming a linear demand function and ignoring the effects of the competitors outputs. Despite a so rough approximation, that we call "Local Monopolistic Approximation" (LMA), the repeated game may converge to a Nash equilibrium of the true oligopoly game, i.e. the game played under the assumption of full information. An explicit form of the dynamical system that describes the time evolution of oligopoly games with LMA is given for arbitrary differentiable demand functions, provided that the cost functions are linear or quadratic. Sufficient conditions for the local stability of Nash Equilibria are given. In the particular case of an isoelastic demand function, we show that the repeatead game based on LMA always converges to a Nash equilibrium, both with linear and quadratic cost functions. This stability result is compared with "best reply" dynamics, obtained under the assumption of isoelastic demand (fully known by the players) and linear costs.Oligopoly games, bounded rationality, subjective demand, Nash equilibrium, dynamical systems, stability