Fausto Cavalli

• Phd
• Researcher at Università degli Studi di Milano-Bicocca

We consider a simple evolutionary cobweb model with heterogeneous agents and propose a class of individuals aimed at addressing the limitations of perfectly rational agents and traditional fundamentalists. Fully rational expectations require complete knowledge of both the market structure and agents’ decisions. Conversely, traditional fundamentalis...

This study aims to provide a manageable symmetric two-players conflict model in which, defining measures for polarization and hostility, we investigate the effects of spillovers into the properties of the sets of equilibria, into the intensity of conflict, and into the endogenous changes in polarization and hostility. We show that, without spillove...

We propose a model with economic and environmental domains that interact with each other. The economic sphere is described by a Solow growth model, in which productivity is not exogenous but negatively affected by the stock of pollution that stems from the production process. A regulator can charge a tax on production, and the resources collected f...

We propose a model for exploring the feasibility and effectiveness of a green transition from dirty to clean technologies. It relies on an evolutionary framework for the technology selection that accounts for the environmental domain dynamics, in terms of pollution evolution. A regulator charges an environmental tax to the producers, and the agents...

We propose a model economy consisting of interdependent real, monetary and stock markets. The money market is influenced by the real one through a standard LM equation. Private expenditures depend on stock prices, which in turn are affected by interest rates and real profits, as these contribute to determine the participation level in the stock mar...

We study a financial market populated by heterogeneous agents, whose decisions are driven by “animal spirits”. Each agent may have either correct, optimistic or pessimistic beliefs about the fundamental value, which can change from time to time based on an evolutionary mechanism. The evolutionary selection of beliefs depends on a weighted evaluatio...

In this paper, we study a class of markets, among which we can mention agricultural and energy markets, characterized by seasonality, i.e., in which demand and/or supply conditions cyclically alternate with a precise and known periodicity. We propose a new theoretical framework based on a cobweb model with adaptive expectations, accordingly modifie...

In this paper we consider a nonlinear model for the real economy described by a multiplier–accelerator setup. The model comprises the government sector, which influences the output dynamics by means of the fiscal policy, and the money market, where the money supply depends upon the fluctuations in the economic activity. Through rigorous analytical...

We propose a modelling approach to study Cournotian oligopolies of boundedly rational firms which continuously update production decisions on the basis of information collected periodically. The model consists of a system of differential equations with piecewise constant arguments, which can be recast into a system of difference equations. Consider...

In the present paper, a model of a market consisting of real and financial interacting sectors is studied. Agents populating the stock market are assumed to be not able to observe the true underlying fundamental, and their beliefs are biased by either optimism or pessimism. Depending on the relevance they give to beliefs, they select the best perfo...

In the present paper a model of a market consisting of real and financial interacting sectors is studied. Agents populating the stock market are assumed to be not able to observe the true underlying fundamental, and their beliefs are biased by either optimism or pessimism. Depending on the relevance they give to beliefs, they select the best perfor...

We propose a financial market model with optimistic and pessimistic fundamentalists who, respectively, overestimate and underestimate the true fundamental value due to ambiguity in the stock market. We assume that agents form their beliefs about the fundamental value through an imitative process, considering the relative ability shown by optimists...

In the present paper, we investigate the dynamics of a model in which the real part of the economy, described within a multiplier-accelerator framework, interacts with a financial market with heterogeneous speculators, in order to study the channels through which the two sectors influence each other. Employing analytical and numerical tools, we inv...

We study a family of monopoly models for markets characterized by time-varying demand functions, in which a boundedly rational agent chooses output levels on the basis of a gradient adjustment mechanism. After presenting the model for a generic framework, we analytically study the case of cyclically alternating demand functions. We show that both t...

The purpose of this paper is to propose a symmetric two player general contest model in order to study the relationship between equilibria and crucial structural parameters of the model. In particular, given a general specification of the players’ set of possible entries, of the agents’ utility functions, and of the rules that presides over outcome...

In this work we study oligopoly models in which firms adopt decision mechanisms based on best response techniques with different rationality degrees. Firms are also assumed to face resource or financial constraints in adjusting their production levels, so that, from time to time, they can only increase or decrease their strategy by a bounded quanti...

We present a dynamic model for a boundedly rational monopolist who, in a partially known environment, follows a rule-of-thumb learning process. We assume that the production activity is continuously carried out and that the costly learning activity only occurs periodically at discrete time periods, so that the resulting dynamical model consists of...

In this paper, we investigate the dynamic properties of an overlapping generations' model with capital accumulation, in which agents work in both periods of life. We compare three different expectation mechanisms: perfect foresight, myopic foresight, and adaptive expectations, focusing, in particular, on this last one. We show that the steady...

In this work I present a cobweb model for markets characterized by two couples of demand and supply functions which cyclically alternate with period two, in a succession of peak and off-peak market phases. Starting from classical adaptive expectations, a new expectation formation mechanism is presented, to take into account such markets’ peculiar...

In this note, departing from the traditional static and fully rational economic agent setting, I study a dynamic model of a boundedly rational monopolist who, in a partially known environment, follows a rule of thumb learning process. Instead of considering the classical differential model with smooth argument, the proposed dynamic model consists o...

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 introduce and study a family of discrete-time dynamical systems to model binary choices based on the framework proposed by Schelling in 1973. The model we propose uses a gradient-like adjustment mechanism by means of a family of smooth maps and allows understanding and analytically studying the phenomena qualitatively described by Schelling. In...

In this paper we study some dynamical features of electricity markets modelling demand and supply by means of a nonlinear cobweb model. We consider a demand function periodically perturbed to take into account the real world seasonalities (daily, weekly and yearly) while supply function can include a stochastic term that is able to encompass possib...

We study a monopolistic market characterized by a constant elasticity demand function, in which the firm technology is described by a linear total cost function. The firm is assumed to be boundedly rational and to follow a gradient rule to adjust the production level in order to optimize its profit. We focus on what happens on varying the price ela...

In this paper, we propose and compare three heterogeneous Cournotian duopolies, in which players adopt best response mechanisms based on different degrees of rationality. The economic setting we assume is described by an isoelastic demand function with constant marginal costs. In particular, we study the effect of the rationality degree on stabilit...

We study complex phenomena arising from a simple optimal choice consumer model, starting from the classical framework in Benhabib and Day (Rev Econ Stud 48(3):459–471, 1981). We introduce elements of increasing complexity (dynamic adjustment processes, nonlinear social interdependence, agents heterogeneity, agents local interaction) and we investig...

We study a heterogeneous duopolistic Cournotian game, in which the firms, producing a homogeneous good, have reduced rationality and respectively adopt a “Local Monopolistic Approximation” (LMA) and a gradient-based approach with endogenous reactivity, in an economy characterized by isoelastic demand function and linear total costs. We give conditi...

In this paper we study oligopolies of generic size consisting of heterogeneous firms, which adopt best response adjustment mechanisms with either perfect foresight (rational firms) or static expectations (naive firms). Assuming an isoelastic demand function and possibly different marginal costs for the two groups of firms, we focus on the local sta...

We study heterogeneous Cournot oligopolies of variable sizes and compositions, in which the firms have different degrees of rationality, being either rational firms with perfect foresight or naive best response firms with static expectations. Each oligopoly can be described using its size and composition, that is, the fraction of firms that are rat...

We analyze a duopolistic Cournotian game with firms producing a homogeneous good, isoelastic demand function and linear total cost functions. In this economic setting, the traditional dynamic adjustment based on the classical best reply mechanism is very demanding in terms of rationality and information set. Therefore, in the competition we study,...

The purpose of this work is to provide a way to improve stability and convergence rate of a price adjustment mechanism that converges to a Walrasian equilibrium. We focus on a discrete tâtonnement based on a two-agent, two-good exchange economy, and we introduce memory, assuming that the auctioneer adjusts prices not only using the current excess d...

Diffusive relaxation systems provide a general framework to approximate nonlinear diffusion problems, also in the degenerate case (Aregba-Driollet et al. in Math. Comput. 73(245):63–94, 2004; Boscarino et al. in Implicit-explicit Runge-Kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit, 2011; Cavalli et al. in SIAM J....

We consider interface problems for second order elliptic partial differential equations with Dirichlet boundary conditions. It is well known that the finite element discretization may fail to produce solutions converging with optimal rates unless the mesh fits with the discontinuity interface. We introduce a method based on piecewise linear finite...

We present finite element approximations of relaxed systems for nonlinear diffusion problems, which can also tackle the cases of degenerate and strongly degenerate diffusion equations. Relaxation schemes take advantage of the replacement of the original partial differential equation (PDE) with a system of semilinear hyperbolic equations, with a sti...

In this work we introduce a new numerical approach for solving Cahn-Hilliard equation with Neumann boundary conditions involving recent mass transportation methods. The numerical scheme is based on an alternative formulation of the problem using the so called pseudo-inverse of the cumulative distribution function. We establish a stable fully discre...

Blood vessel networks form by spontaneous aggregation of individual cells migrating toward vascularization sites (vasculogenesis). A successful theoret- ical model of two dimensional experimental vasculogenesis has been recently proposed (1), showing the relevance of percolation concepts and of cell cross- talk (chemotactic autocrine loop) to the u...

In this work we present a family of relaxation schemes for nonlinear convec-tion diffusion problems, which can tackle also the cases of degenerate diffusion and of convection dominated regimes. The schemes proposed can achieve any order of ac-curacy, give non-oscillatory solutions even in the presence of singularities and their structure depends on...

We present a class of relaxed schemes for non linear convection diffusion problems, which can tackle also the cases of degenerate diffusion and of convection dominated regimes. These schemes can achieve any order of accuracy and they give non-oscillatory solutions even in the presence of singularities. Relaxation approximations to non-linear partia...

Vascular networks form by a self‐aggregation process of individual endothelial cells that differentiate at seemingly random sites in the embryo and collectively migrate toward each other forming a preliminary vascular plexus (vasculogenesis), followed by functional remodelling that gives rise to the final hierarchical system (angiogenesis). The stu...

The ability of eukaryotic cells to navigate along spatial gradients of extracellular guidance cues is crucial for embryonic development, tissue regeneration, and cancer progression. One proposed model for chemotaxis is a phosphoinositide-based phase separation process, which takes place at the plasma membrane upon chemoattractant stimulation and tr...

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...

In this work we compare two semidiscrete schemes for the solution of hyperbolic conservation laws, namely the relaxation and the Kurganov Tadmor central scheme. We are particularly interested in their behavior under small time steps, in view of future applications to convection diffusion problems. The schemes are tested on two benchmark problems, w...

Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto diffusive relaxed schemes for the numerical approximation of nonlinear reaction diffusion equations. High ord...

The application of Runge-Kutta schemes designed to enjoy a large region of absolute stability can significantly increase the efficiency of numerical methods for PDEs based on a method of lines approach. In this work we investigate the improvement in the efficiency of the time integration of relaxation schemes for degenerate diffusion problems, usin...

Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, and gas dynamics problems. The present paper focuses on diffusive relaxation schemes for the numerical approximation of nonlinear parabolic equations. These sc...

Cell migration plays a central role in a wide variety of biological phenomena. In the case of chemotaxis, cells (or an organism) move in response to a chemical gradient. Chemotaxis underlies many events during embryo development and in the adult body. An understanding of chemotaxis is not only gained through laboratory experiments but also through...

Many eukaryotic cell types share the ability to migrate directionally in response to external chemoattractant gradients. This ability is central in the development of complex organisms, and is the result of billion years of evolution. Cells exposed to shallow gradients in chemoattractant concentration respond with strongly asymmetric accumulation o...

Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses onto diffusive relaxation schemes for the numerical approximation of nonlinear parabolic equations. These sche...

Blood vessel networks form by spontaneous aggregation of individual cells migrating toward vascularization sites (vasculogenesis). A successful theoretical model of two-dimensional experimental vasculogenesis has been recently proposed, showing the relevance of percolation concepts and of cell cross-talk (chemotactic autocrine loop) to the understa...

Blood vessel networks form by spontaneous aggregation of individual cells migrating toward vascularization sites (vasculogenesis). A successful theoretical model of two dimensional experimental vasculogenesis has been recently proposed, showing the relevance of percolation concepts and of cell cross-talk (chemotactic autocrine loop) to the understa...

It has been shown that the equation of diffusion, linear and nonlinear, can be obtained in a suitable scaling limit by a two-velocity model of the Boltzmann equation [7] . Several numerical approximations were introduced in order to discretize the corresponding multiscale hyperbolic systems [8, 1, 4]. In the present work we consider relaxed approxi...