Gian-Italo Bischi

Università degli Studi di Urbino "Carlo Bo" | UNIURB · DESP - Department of Economics, Society, Politics

This paper formulates and analyzes a two-stage oligopoly game where firms can invest in cost-reducing R&D activity with the possibility of sharing R&D results with partner firms as well as gaining knowledge for free through spillovers. Firms are arranged within networks (or districts) inside which they can cooperate by bilateral agreements for shar...

Within a classical discrete-time Cournot oligopoly model with linear demand and quadratic cost functions, minimum and maximum production constraints are imposed in order to explore their effects on the dynamic of the system. Due to the presence of such constraints, the dynamic model assumes the form of a continuous piecewise linear map of the plane...

We propose an oligopoly game where quantity setting firms have incomplete information about the demand function. At each time step they solve a profit maximization problem assuming a linear demand function and ignoring the effects of the competitors’ outputs. Despite such a rough approximation, that we call “Local Monopolistic Approximation” (LMA),...

The aim of this paper is to study the effects of the Covid-19 pandemic suppression policies (i.e. containment measures or lockdowns) on labor supply, capital accumulation, and so the economic growth. We merge an epidemic SIS population model and a Solow’s type growth model, i.e. we propose a fusion between economics and epidemiology. We show the cr...

This paper proposes dynamic oligopolistic models to describe heterogenous banks that compete in the loan market. Two boundedly rational banks adopt an adaptive behavior to increase their profits under different assumptions of limited information and bounded computational ability, in the presence of a share of credits that might not be reimbursed (i...

We propose an oligopoly model where players can choose between two kinds of behaviors, denoted as cooperative and aggressive, respectively. Each cooperative agent chooses the quantity to produce in order to maximize her own profit as well as the profits of other agents (at least partially), whereas an aggressive player decides the quantity to produ...

Why is populism emerging now in Europe? Why is it present in USA and Latin America? What model of political choice may explain these facts? Our paper addresses these questions by building an evolutionary game with two groups of players that decide whether to support a populist party by weighting demand for redistribution and demand for tough policy...

This paper deals with the issue of communication and dissemination of scientific knowledge outside the circle of specialists. In particular, in the occasion of the 700th anniversary of the death of Dante Alighieri, we will focus on the program for the popularization of knowledge outlined by Dante in the Convivio and De Vulgari Eloquentia, as well a...

In this paper, we propose a unitary formulation for evolutionary oligopoly models with memory. In particular, we consider behavioral rules that are stationary at the Nash equilibria so that we can study the stability of the oligopolistic model with memory with generic strategies for determining quantities. Although the introduction of memory does n...

We consider a learning mechanism where expected values of an economic variable in discrete time are computed in the form of a weighted average that exponentially discounts older data. Also adaptive expectations can be expressed as weighted sums of infinitely many past states, with exponentially decreasing weights, but these are not averages since t...

Social Dynamics aims at providing a unifying view on the evolution of social systems, including social conflicts and dilemmas, interactions between populations and the environment, financial markets and the broader macroeconomy, by looking at the interplay between individual behavior at the micro-level and collective behaviors at the macro-level. T...

This book focuses on the latest advances in nonlinear dynamic modeling in economics and finance, mainly—but not solely—based on the description of strategic interaction by using concepts and methods from dynamic and evolutionary game theory. The respective chapters cover a range of theoretical issues and examples concerning how the qualitative theo...

In this paper, the location patterns of Multinational Enterprises are modeled by an evolutionary two-country model in which producing in a developed economy offers strong cost-reducing externalities of within-country spillovers and opting for a developing economy entails cheap labor but also extra operational costs due to the undersupply of public...

A dynamic adjustment mechanism, based on replicator dynamics in discrete time, is used to study the time evolution of a population of players facing a binary choice game with social influence, characterized by payoff curves that intersect at two interior points, also denoted as thresholds. So, besides the boundary equilibria where all players make...

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 ac...

We introduce an evolutionary two-country model to characterize long run location patterns of the manufacturing activities of competing multinational enterprises. Firms located in country 1 can decide to offshore their manufacturing activities to country 2. The profitability of production in a country depends on several factors: unitary costs of pro...

This book is open access under a CC BY-NC 4.0 license. This collected volume represents the final outcome of the COST Action IS1104 “The EU in the new complex geography of economic systems: models, tools and policy evaluation”. Visualizing the EU as a complex and multi-layered network, the book is organized in three parts, each of them dealing wi...

We propose a simple dynamic adjustment mechanism, equivalent to the standard replicator dynamics in discrete time, to study the time evolution of a population of players facing a binary choice game, and apply this mechanism to minority games in order to investigate the effects of memory on the stability of the unique Nash equilibrium. Two different...

The paper gives an elementary introduction to the concept of bifurcation in the context of dynamical systems, providing a historical background as well as examples of applications in real life.

In the Cournot duopoly game with unimodal piecewise-linear reaction functions (tent maps) proposed by Rand (J Math Econ, 5:173–184, 1978) to show the occurrence of robust chaotic dynamics, a maximum production constraint is imposed in order to explore its effects on the long run dynamics. The presence of such constraint causes the replacement of ch...

This paper provides a survey of some recent results and examples concerning the use of the method of critical curves in the study of chaos synchronization in discrete dynamical systems with an invariant one-dimensional submanifold. Some examples of two-dimensional discrete dynamical systems, which exhibit synchronization of chaoti1c trajectories wi...

This chapter gives a general and friendly overview to the qualitative theory of continuous and discrete dynamical systems, as well as some applications to simple dynamic economic models, and is concluded by a section on basic principles and results of optimal control in continuous time, with some simple applications. The chapter aims to introduce s...

In this paper we provide an overview of some recent dynamic models of commercial fisheries. Our starting points are the papers by Okuguchi (Keio Econ Stud 35:9–17, 1998) and Okuguchi and Szidarovszky (Seoul J Econ 11(3):321–330, 1998) and Szidarovszky and Okuguchi (Seoul J Econ 13:471–476, 2000) on oligopoly competition in international fisheries,...

The book presents the lectures delivered during a short course held at Urbino University in summer 2015 on qualitative theory of dynamical systems, included in the activities of the COST Action IS1104 “The EU in the new economic complex geography: models, tools and policy evaluation”. It provides a basic introduction to dynamical systems and optima...

We analyze the recurrence x n+1 = f (zn), where zn is a weighted power mean of x 0 ,. .. , xn, which has been proposed to model a class of non-linear forward-looking economic models with bounded rationality. Under suitable hypotheses on weights, we prove the convergence of the sequence xn. Then, to simulate a fading memory, we consider exponentiall...

We consider a discrete time version of the model proposed by Lamantia and Radi (2015) to describe a fishery where a population regulated by a logistic growth function is exploited by a pool of agents that can choose, at each time period, between two different harvesting strategies according to a profit-driven evolutionary selection rule. The result...

In this paper we consider a nonlinear discrete-time dynamic model proposed by Farris et al. (2005) as a market share attraction model with two firms that decide marketing efforts over time according to best reply strategies with naïve expectations. The model also considers an adaptive adjustment toward best reply, a form of inertia or anchoring att...

In this paper we analyze a dynamic game of Cournot competition with heterogeneous firms choosing between two different adaptive behavioral rules in deciding output strategies. The underling oligopoly structure is standard: using a constant returns to scale technology, N firms produce homogeneous goods, which are sold in a market characterized by co...

The aim of this chapter is two-fold. It first provides a (non exhaustive) overview of the literature concerning oligopoly models where firms produce homogeneous goods and share R&D cost-reducing results through bilateral agreements and/or involuntary spillovers of knowledge. These models are expressed by the formalism of networks (i.e. theory of gr...

The concept of the 'postmodern consumer' plays a central role in the debate, started in the early 80s, about economic, social and cultural changes in developed countries in the years following the end of the second world war. These changes were interpreted as a passage from modern to postmodern society. According to this literature, postmodern cond...

Gian Italo Bischi interviews Giuseppe Mussardo, a theoretical physicist and author of several documentary films on important figures in the history of science. The interview sheds light on the importance of the documentary and fiction in popular science, and the kind of work that goes into creating this kind of scientific communication. Also includ...

Interview given during the annual meeting of AMASES (Italian Association for Mathematics Applied to Economics and Finance) in Lecce (Italy), September 2007.

The theory of dynamical systems has been one of the most developed mathematical areas in the last 50 years with a wide spectrum of applications ranging from physics to biology to economics. During the last decades, economic theory in particular has witnessed an important shift in methodology. The classical approach that describes economic outcomes...

In this paper, we propose a bioeconomic model which describes a fishery in which each of two non-interacting 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 Ital...

In this paper we propose a discrete-time dynamic model for study- ing the time evolution of fish stocks in an aquatic environment divided into two adjacent patches. Each area is characterized by a dierent fishing policy: an imposed constant fishing eort in a patch and oligopolistic competition in the other one, where fishermen are free to decide th...

In this paper, we propose a fishery model with a discontinuous on–off harvesting policy, based on a very simple and well known rule: stop fishing when the resource is too scarce, i.e. whenever fish biomass is lower than a given threshold. The dynamics of the one-dimensional continuous time model, represented by a discontinuous piecewise-smooth ordi...

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 gro...

The essays in this special volume survey some of the most recent advances in the global analysis of dynamic models for economics, finance and the social sciences. They deal in particular with a range of topics from mathematical methods as well as numerous applications including recent developments on asset pricing, heterogeneous beliefs, global bif...

In Bischi and Lamantia [4] a two-stage oligopoly game has been proposed to describe networks of firms that invest in cost-reducing R&D activity with the possibility of sharing R&D results with partner firms as well as gaining knowledge for free through spillovers, and an adaptive dynamic mechanism is proposed to describe how firms repeatedly update...

This work moves from a recent paper by Antoci et al. (2009) where a dynamic model is proposed to describe an innovative method for improving 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 perf...

In this paper, we run through an example of oligopoly, recently introduced in the literature, where firms operate under constraints. The dynamical system describing firms' choices over time assumes the form of a piecewise-smooth map because of such constraints. By carrying on a leading example, we show possible routes to complexity in the model, ma...

We investigate the properties of recurrence of the type , known as Lyness iterations from [Lyness, 1942, 1945, 1961] and recently analyzed by several authors in the case a > 0, see e.g. [Kocic et al., 1993; Csornyei & Laczkovich, 2000]. We reconsider Lyness recurrences at the light of some recent results on iterated maps with denominator, given in...

Long-run analyses usually stress the leading role of aggregate supply. As a result, aggregate demand is supposed to adjust in order to accommodate supply changes. In a medium-run perspective, however, both aggregate demand and supply forces must be taken ...

De Finetti’s commitment to mathematics education was always concrete and vigorous, as shown by his publications of treatises, textbooks, educational papers, and articles for non-specialists, as well by intense organisational activities.

In this paper we study a class of dynamic promotional competition models, in which firms compete for market share by expending marketing effort. We investigate two main issues. First, we answer the question if it is possible to give a global characterization of the stability of the steady state effort allocation. We show that by using the concept o...

In this chapter we propose an oligopoly model where firms invest in cost reducing R&D for producing homogeneous goods that are sold in a market. In particular, we assume that R&D efforts build up a "stock of knowledge", which, in turn, reduces marginal costs of production. Moreover, though all firms are competitors in the marketplace, they can deci...

Starting from a seminal paper of Thomas Schelling (1969) we formalize a twodimensional discrete time dynamical system to study segregation. The simple adaptive mechanism we propose may lead to the segregation of two different populations whose members are characterized by a limited tolerance about the presence of individuals of the other group. We...

We consider a three-dimensional discrete dynamical system that describes an application to economics of a generalization of the Lotka–Volterra prey–predator model. The dynamic model proposed is used to describe the interactions among industrial clusters (or districts), following a suggestion given by [23]. After studying some local and global prope...

In the previous chapter we analyzed concave oligopolies where the best response functions were monotonic and therefore the local and global analysis of the corresponding dynamic processes were relatively simple. The examples discussed there have allowed the reader to become familiar with the major concepts and methods that we shall use in the rest...

The previous chapters have introduced and analyzed the classical Cournot model under a number of assumptions. In this chapter we discuss some important modifications and extensions. We first introduce market share attraction games where the dynamics are driven by a generalization of the gradient adjustment process introduced in Chaps. 1 and 1. We c...

In the previous chapter we have seen that except in very special cases oligopoly models have nonlinear features and therefore can generally exhibit a vast array of dynamical behavior ranging from simple to complicated. Under special conditions however the uniqueness of the equilibrium can be guaranteed, simple conditions can be derived for the loca...

The previous chapters have already dealt with the behavior of boundedly rational firms in an oligopoly. Although the firms know the true demand relationship, we have assumed that they do not know their competitors’ quantity choices. Instead they form expectations about these quantities and they base their own decisions on these beliefs. In particul...

In this chapter we present a unified approach for modelling the diffusion of alternative choices within a population of individuals in the presence of social externalities, starting from two particular discrete-time dynamic models – Galam’s model of rumors spreading [10] and a formalization of Schelling’s binary choices [7]. We describe some peculi...

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 bi...

Two different ways to model the diffusion of alternative choices within a population of individuals in the presence of social externalities are known in the literature. While Galam’s model of rumors spreading considers a majority rule for interactions in several groups, Schelling considers individuals interacting in one large group, with payoff fun...

The book focuses on the dynamics of nonlinear oligopoly models. It discusses the classical Cournot model with a large variety of demand and cost functions that illustrate the many different types of possible best response functions and it shows the existence of unique and multiple equilibria. Particular emphasis is placed on the influence of nonneg...

Over the last two decades there has been a great deal of research into nonlinear dynamic models in economics, finance and the social sciences. This book contains twenty papers that range over very recent applications in these areas. Topics covered include structural change and economic growth, disequilibrium dynamics and economic policy as well as...

In this chapter we will introduce the classical Cournot model, which is also known as the single-product quantity setting oligopoly model without product differentiation. In the first section of the chapter the Cournot model will be discussed as an N-firm static game and the best responses of the firms and the equilibria will be determined in a ser...

In Chap. 1 we introduced the classical Cournot model and after setting up the general framework we focused on a number of specific examples involving combinations of linear and hyperbolic price functions and linear and quadratic cost functions, also taking careful account of capacity constraints. These examples illustrated the variety of reaction f...

Starting from a family of discontinuous piece-wise linear one-dimensional maps, recently introduced as a dynamic model in social sciences, we propose a geometric method for finding the analytic expression of the bifurcation curves, in the space of the parameters, that bound the regions characterized by the existence of stable periodic cycles of any...

A discrete-time dynamical system is proposed to model a class of binary choice games with externalities as those described by Schelling (197320. Schelling , T. C. ( 1973 ). Hockey helmets, concealed weapons, and daylight saving . Journal of Conflict Resolution , 17 ( 3 ), 381 – 428 . [CrossRef], [Web of Science ®]View all references, 197821. Sche...

In this paper we propose a discrete-time dynamic model for studying the time evolution of fish stocks in an aquatic environment divided into two adjacent patches, one characterized by an imposed constant fishing effort and another one where fishermen are free to decide the quantity to harvest according to oligopolistic competition taking into accou...

Binary choice games with externalities, as those described by Schelling (1973, 1978), have been recently modelled as discrete dynamical systems (Bischi and Merlone, 2009). In this paper we discuss the dynamic behavior in the case in which agents are impulsive; that is; they decide to switch their choices even when the difference between payoffs is...

In this article, single product Cournot oligopolies are considered, where the demand and cost functions are linear. While cost functions are completely known by all firms, they only partially know the demand function, as they misspecify the slope. At any stage of the repeated oligopoly game firms update the slope of their subjective demand function...

for, on the one hand, very encouraging suggestions and, on the other hand, extensive critical remarks on an earlier version of this paper. Corresponding author.

This note shows that the assumptions about the abatement technology modify the impact of the environmental taxation on the long-run growth driven by human capital accumulation � la Lucas (1988), when lifetime is finite. Whereas no impact of the environmental policy on long-run growth is found when pollution originates from final output and abatemen...

In this paper we analyze a recurrence , where is a weighted power mean of ,…., . Such an iteration scheme has been proposed to model a class of non-linear forward-looking economic models ( the state today is affected by tomorrow’ s expectation ) under bounded rationality; the agents employ a recursive learning rule to update beliefs using weighted...

Two-dimensional (Z 1 –Z 3 –Z 1) maps are such that the plane is divided into three unbounded open regions: a region Z 3 , whose points generate three real rank-one preimages, bordered by two regions Z 1 , whose points generate only one real rank-one preimage. This paper is essentially devoted to the study of the structures, and the global bifurcati...