Anna Agliari - Academia.edu (original) (raw)

Papers by Anna Agliari

Research paper thumbnail of Appearance of closed invariant curves in a piecewise Cournot model with advertising

Chaos, Solitons & Fractals

Research paper thumbnail of A duopoly Cournot model with delayed expectations

We consider a Cournot duopoly with isoelastic demand function and constant marginal costs (see [2... more We consider a Cournot duopoly with isoelastic demand function and constant marginal costs (see [2]). As it is well known, in this case the reaction of the competitors are functions de…ned on R+ and depend on the expected production of the opponent: q i = Ri q (e) j , i 6= j. To close the model we assume that both producers have naive expectations but one of them reacts with delay to the move of its competitor, that is q 1;t = q2;t 1 and q (e) 2;t = q1;t 2. In this way we obtain a discrete two dimensional time-delayed sistem, that can be described by a 3D mapM such that its third iterate has separate components. As proved in [1], the attractors of M as well as their stability properties can be obtained by the analysis of a one dimensional map (one of the components of third iterate of M). This allows us to show that the introduction of delayed espectations enriches the dynamics of the model and many stable cycles may coexist. In our analysis we …rst characterize the basins of attract...

Research paper thumbnail of Endogenous cycles from income diversity, capital ownership, and differential savings

Chaos, Solitons & Fractals, 2020

Endogenous cycles in standard growth models with capital accumulation of the Solow or the OLG typ... more Endogenous cycles in standard growth models with capital accumulation of the Solow or the OLG type occur only when there is some degree of heterogeneity among consumers, differential savings, income diversity, or market specialization. Otherwise, without income effects or distribution effects long run steady states are mostly asymptotically stable predicting stable balanced growth for many of the commonly accepted growth models under most aggregative concave neoclassical production functions. This paper provides an attempt to exhibit a full richness of bifurcation scenarios for endogenously generated cycles using minimal extensions concerning preferences, technologies, and ownership of capital by extending the models of Kaldor, Pasinetti, and others to allow for ownership of capital among OLG consumers of workers and capitalists. It is shown that, under a sufficiently low but constant elasticity of substitution, the interaction of the nonlinear income distribution with heterogeneous logarithmic intertemporal preferences of consumers causes a variety of local bifurcation scenarios (Neimark-Sacker, fold, period doubling), multi-stability, as well as a rich variety of complex global dynamic features, such as homoclinic tangles, periodicity regions originating from Arnold tongues, closed curve attractors, and complex basins. The paper provides a detailed numerical analysis under a CES production scenario of several global bifurcations arising from heterogeneity which does not exist under the specific ownership restrictions imposed in the original Kaldor/Pasinetti models.

Research paper thumbnail of Chaotic dynamics in a three-dimensional map with separate third iterate: The case of Cournot duopoly with delayed expectations

Chaos, Solitons & Fractals, 2018

We consider a Cournot duopoly with isoelastic demand function and constant marginal costs. We ass... more We consider a Cournot duopoly with isoelastic demand function and constant marginal costs. We assume that both producers have naive expectations but one of them reacts with delay to the move of its competitors, due to a "less efficient" production process of a competitor with respect to its opponent. The model is described by a 3D map having the so-called "cube separate property", that is its third iterate has separate components. We show that many cycles may coexist and, through global analysis, we characterize their basins of attraction. We also study the chaotic dynamics generated by the model, showing that the attracting set is either a parallelepiped or the union of coexisting parallelepipeds. We also prove that such attracting sets coexist with chaotic surfaces, having the shape of generalized cylinders, and with different chaotic curves.

Research paper thumbnail of Boom-bust dynamics in a stock market participation model with heterogeneous traders

Journal of Economic Dynamics and Control, 2018

The boundedly rational heterogeneous agent literature can be considered to have properly started ... more The boundedly rational heterogeneous agent literature can be considered to have properly started with a number of contributions in the early 90s, with the impressive contribution by Carl Chiarella who, amongst his huge field of research, developed several milestone models of heterogeneous interacting agents that are able to generate a number of dynamic outcomes compatible with the empirical evidence. In this paper, we propose a stock market model in which participation depends upon an attractiveness measure related to the market activity and the fundamental value of the market. A market maker adjusts the stock price with respect to the current endogenous excess market demand which, in turn, depends on the demands of the different types of agents populating the economy. Market participants are also allowed to switch between different strategies. Analytical and numerical results confirm how the participation mechanism amplifies the occurrence of endogenous booms and busts, in line with empirical and experimental evidence.

Research paper thumbnail of Bifurcation structures of a cobweb model with memory and competing technologies

Communications in Nonlinear Science and Numerical Simulation, 2017

In this paper we study a simple model based on the cobweb demand-supply framework with costly inn... more In this paper we study a simple model based on the cobweb demand-supply framework with costly innovators and free imitators. The evolutionary selection between technologies depends on a performance measure which is related to the degree of memory. The resulting dynamics is described by a two-dimensional map. The map has a fixed point which may lose stability either via supercritical Neimark-Sacker bifurcation or flip bifurcation and several multistability situations exist. We describe some sequences of global bifurcations involving attracting and repelling closed invariant curves. These bifurcations, characterized by the creation of homoclinic connections or homoclinic tangles, are described through several numerical simulations. Particular bifurcation phenomena are also observed when the parameters are selected inside a periodicity region.

Research paper thumbnail of Inflation Targeting, Recursive Inattentiveness, and Heterogeneous Beliefs

Journal of Money, Credit and Banking, 2017

In this paper we consider a scenario in which the monetary authority provides an explicit inflati... more In this paper we consider a scenario in which the monetary authority provides an explicit inflation target in order to anchor private sector expectations and align them with policy objectives. In this context, a biased perception of the target may arise due to imperfect information flows and idiosyncrasies in information processing lead to heterogenous beliefs about the target. We allow private sector expectations to be revised over time as new information becomes available and the direction of change is determined by the distance between agents' beliefs and actual realizations of macro variables. The recursive choice between alternative predictors is modeled as an optimization problem under rational inattention. Within this framework we investigate whether a simple interest rate rule can steer the economy toward the targeted equilibrium. Our findings suggest that standard policy advices, i.e., ensure determinacy under rational expectations, may not be sufficient to reach the target. Instead, a sound monetary policy should be fine-tuned to ensure that the signal sent by realizations of macro variables can correct biased agents' beliefs.

Research paper thumbnail of Dynamic effects of memory in a cobweb model with competing technologies

Physica A: Statistical Mechanics and its Applications, 2017

We analyze a simple model based on the cobweb demand-supply framework with costly innovators and ... more We analyze a simple model based on the cobweb demand-supply framework with costly innovators and free imitators and study the endogenous dynamics of price and firms' fractions in a homogeneous good market. The evolutionary selection between technologies depends on a performance measure in which a memory parameter is introduced. The resulting dynamics is then described by a two-dimensional map. In addition to the locally stabilizing effect due to the presence of memory, we show the existence of a double stability threshold which entails for different dynamic scenarios occurring when the memory parameter takes extreme values (i.e. when consideration of the last profit realization prevails or it is too much neglected). The eventuality of different coexisting attractors as well as the structure of the basins of attraction that characterizes the path dependance property of the model with memory is shown. In particular, through global analysis we also illustrate particular bifurcations sequences that may increase the complexity of the related basins of attraction.

Research paper thumbnail of Multistability and global dynamics in complementary good market model

Research paper thumbnail of Nonlinear dynamics of a Cournot duopoly game with differentiated products

Applied Mathematics and Computation, 2016

Two typical instances of market structure are perfect competition and monopoly. Halfway between t... more Two typical instances of market structure are perfect competition and monopoly. Halfway between them, when the market is supplied by only few firms, oligopolistic competition takes place (see Cournot, 1838). Few sellers are assumed to sell a homogenous good in the same market. As market price is assumed dependent on the total quantity sold by competitors, the market structure turns out to be more complicated than monopoly. The optimal decision of each competitor becomes dependent, not only on repercussions on the demand side, but also on the expected reverberations of the other competitors on any of its own moves. While Cournot considered a duopoly with a single homogeneous product, the economic literature also offered duopoly models with (horizontal) differentiated products (see, e.g., Dixit, 1979, Singh and Vives, 1984 and Fanti and Gori, 2012) which allow goods and services to be substitutes or complements, in models with a standard linear demand structure. The paper investigates the dynamics of a Cournot duopoly game with differentiated goods in which boundedly rational firms apply a gradient adjustment mechanism to update their quantity in each period. As in Ahmed et al. (2015), the nonlinear demand functions are derived from an underlying CES utility function. The present analysis reveals that a higher degree of product differentiation may destabilize the Nash equilibrium. We provide analytical conditions for the stability of the market equilibrium and we show, through local and global analysis, that a cascade of flip bifurcations and a Neimark-Sacker bifurcation may lead to periodic cycles, attractor coexistence and ultimately, chaotic motions. Since a higher degree of product differentiation tends to reduce competition, an implication of our findings is that a stronger competition could help in stabilizing the unique Nash equilibrium.

Research paper thumbnail of Path dependent coordination of expectations in asset pricing experiments: A behavioral explanation

Journal of Economic Behavior & Organization, 2016

In the learning-to-forecast laboratory experiments in Hommes et al. (2005), three different types... more In the learning-to-forecast laboratory experiments in Hommes et al. (2005), three different types of aggregate asset price behavior have been observed: monotonic convergence to the stable fundamental steady state, dampened price oscillations and permanent price oscillations. We present a simple behavioral 2-type heuristics switching model explaining individual as well as aggregate behavior in the experiment. Based on relative performance, agents switch between a simple trend-following and an anchor and adjustment heuristic that differ in how much weight is given to the long run average price level. The nonlinear switching model exhibits path dependence through coexistence of a locally stable fundamental steady state and a stable (quasi-)periodic orbit, created via a so-called Chenciner bifurcation. Depending on initial states, agents coordinate individual expectations either on a stable fundamental steady state path or on almost self-fulfilling persistent price fluctuations around the fundamental steady state.

Research paper thumbnail of UvA-DARE ( Digital Academic Repository ) Path dependent coordination of expectations in asset pricing experiments : a behavioral

In the learning-to-forecast laboratory experiments in Hommes et al. (2005), three different types... more In the learning-to-forecast laboratory experiments in Hommes et al. (2005), three different types of aggregate asset price behavior have been observed: monotonic convergence to the stable fundamental steady state, dampened price oscillations and permanent price oscillations. We present a simple behavioral 2-type heuristics switching model explaining individual as well as aggregate behavior in the experiment. Based on relative performance, agents switch between a simple trend-following and an anchor and adjustment heuristic that differ in how much weight is given to the long run average price level. The nonlinear switching model exhibits path dependence through co-existence of a locally stable fundamental steady state and a stable (quasi-)periodic orbit, created via a so-called Chenciner bifurcation. Depending on initial states, agents coordinate individual expectations either on a stable fundamental steady state path or on almost self-fulfilling persistent price fluctuations around ...

Research paper thumbnail of Variable priority dispatching rules: An analytical approach

International Journal of Production Economics, 1995

Scheduling techniques and dispatching rules are widely studied because of their strategic role in... more Scheduling techniques and dispatching rules are widely studied because of their strategic role in achieving optimal management of manufacturing systems. In the case of flexible and CIM-orientated plants, it is essential to evaluate the effects of different dispatching rules to foresee the system performance. The Authors proposed an analytical technique, based on the Markov Chain Theory, enabling the analysis of the behaviour of some common-practice dispatching rules. The results obtained in the previous studies suggested the application of the analytical method to a dispatching rule observing a variable priority criterion. This research aims to show the possibility of extending the method to the investigation of such dispatching rules, offering some of the results that this kind of approach may lead to. The rule satisfies production requirements, but inconveniences are to be planned for, as detailed later;

Research paper thumbnail of Dispatching rules and flexible environments: the influence on buffer behaviour

International Journal of Production Research, 1992

ABSTRACT Frequent production requirements are linked to effective and profitable strategies for t... more ABSTRACT Frequent production requirements are linked to effective and profitable strategies for the management of queues, e.g. input buffers of machining centres and selection of rough workpieces from central storage. As a matter of fact, management policy performances must be evaluated by focusing not only on induced queue lengths or customer waiting times, but also on the future composition of the queues themselves, this being a consequence of the dispatching rule adopted. The question acquires further importance when flexible environments and buffer capacity constraints are considered. The aim of the present study is to illustrate an analytical procedure, based on the Markov chains theory, able to forecast the composition of buffers starting from any initial configuration. Attention is given to the buffer behaviour during the transient period and the steady state: results are offered for sequential and prioritized dispatching of items, together with application examples derived from common industrial situations. In the final sections, the possible extension of the procedure is considered and outlined with regard to particular management rules, thus introducing a further development of the present research.

Research paper thumbnail of Periodic Orbits and Their Bifurcations in 3D Maps with a Separate Third Iterate

Global Analysis of Dynamic Models in Economics and Finance, 2012

Research paper thumbnail of Global dynamics in a non-linear model of the equity ratio

Chaos, Solitons & Fractals, 2000

A model for ®rms' ®nancial conditions is proposed, which ultimately reduces to a two-dimensional ... more A model for ®rms' ®nancial conditions is proposed, which ultimately reduces to a two-dimensional non-invertible map in the variables mean and variance of the equity ratio. The possible dynamics of the model and the global behaviour are investigated. We describe the mechanism of bifurcations leading to fractalization of the basins and/or fractalization of their boundaries, showing how a locally stable attractor may be almost globally unstable. Multistability is also investigated. Two, three or four co-existing attractors have been found and we describe the mechanism of bifurcations leading their basins to become chaotically intermingled, and thus to unpredictability of the asymptotic state in a wide region. The knowledge of such regimes, besides those associated with simple dynamics, may be of help for the operators. While the use of the technical tools we propose to study the global dynamics and bifurcations may be of help for further investigations. Ó

Research paper thumbnail of GLOBAL BIFURCATIONS OF BASINS IN A TRIOPOLY GAME

International Journal of Bifurcation and Chaos, 2002

A Cournot model based on bounded inverse demand function and constant marginal production costs i... more A Cournot model based on bounded inverse demand function and constant marginal production costs is studied. The case of three producers is considered and the adjustment process reduces to a three-dimensional noninvertible map in the output of competitors. The analysis of the dynamical behavior of the map is performed by the "critical curve method", extended to the critical surfaces in 3D. By this method, we explain the different bifurcations in the basins of attraction and in the attracting sets. In particular, given the economic application, feasible trajectories are focused, starting from the simple situation of two identical producers and extending the results to the generic case.

Research paper thumbnail of Credit market imperfection, financial market globalization, and catastrophic transition

Mathematics and Computers in Simulation, 2015

Research paper thumbnail of Agglomeration Dynamics and First Nature Asymmetries

Mathematics and Computers in Simulation, 2014

ABSTRACT The standard Footloose Capital (FC) model, as well as the discrete time version, assumes... more ABSTRACT The standard Footloose Capital (FC) model, as well as the discrete time version, assumes that all capital units are internationally mobile between two regions. In this paper, we assume that in one of the two regions some of the blueprints/capital units may be immobile because their utilization requires some locally specific natural resource (first nature advantage). Mobile blueprints, instead, can be utilized in both regions. We focus on this asymmetric distribution of immobile firms / capital units, labeled first nature firms. The central question of our paper is how the existence of first nature asymmetry affects agglomerative processes framed in discrete time. This modification of the FC model leads to a one dimensional piecewise smooth map for which we show analytically that border collision bifurcations are pervasive and (even asymmetric) multistability is possible.

Research paper thumbnail of Borrowing constraints and complex dynamics in an OLG framework

Journal of Economic Behavior & Organization, 2009

In this paper we model an OLG economy à la Kiyotaki and Moore whose novel feature is the role of ... more In this paper we model an OLG economy à la Kiyotaki and Moore whose novel feature is the role of money as a store of value and of bequest as a source of funds to be “invested” in landholding. The dynamics generated by the model are generally characterized by ...

Research paper thumbnail of Appearance of closed invariant curves in a piecewise Cournot model with advertising

Chaos, Solitons & Fractals

Research paper thumbnail of A duopoly Cournot model with delayed expectations

We consider a Cournot duopoly with isoelastic demand function and constant marginal costs (see [2... more We consider a Cournot duopoly with isoelastic demand function and constant marginal costs (see [2]). As it is well known, in this case the reaction of the competitors are functions de…ned on R+ and depend on the expected production of the opponent: q i = Ri q (e) j , i 6= j. To close the model we assume that both producers have naive expectations but one of them reacts with delay to the move of its competitor, that is q 1;t = q2;t 1 and q (e) 2;t = q1;t 2. In this way we obtain a discrete two dimensional time-delayed sistem, that can be described by a 3D mapM such that its third iterate has separate components. As proved in [1], the attractors of M as well as their stability properties can be obtained by the analysis of a one dimensional map (one of the components of third iterate of M). This allows us to show that the introduction of delayed espectations enriches the dynamics of the model and many stable cycles may coexist. In our analysis we …rst characterize the basins of attract...

Research paper thumbnail of Endogenous cycles from income diversity, capital ownership, and differential savings

Chaos, Solitons & Fractals, 2020

Endogenous cycles in standard growth models with capital accumulation of the Solow or the OLG typ... more Endogenous cycles in standard growth models with capital accumulation of the Solow or the OLG type occur only when there is some degree of heterogeneity among consumers, differential savings, income diversity, or market specialization. Otherwise, without income effects or distribution effects long run steady states are mostly asymptotically stable predicting stable balanced growth for many of the commonly accepted growth models under most aggregative concave neoclassical production functions. This paper provides an attempt to exhibit a full richness of bifurcation scenarios for endogenously generated cycles using minimal extensions concerning preferences, technologies, and ownership of capital by extending the models of Kaldor, Pasinetti, and others to allow for ownership of capital among OLG consumers of workers and capitalists. It is shown that, under a sufficiently low but constant elasticity of substitution, the interaction of the nonlinear income distribution with heterogeneous logarithmic intertemporal preferences of consumers causes a variety of local bifurcation scenarios (Neimark-Sacker, fold, period doubling), multi-stability, as well as a rich variety of complex global dynamic features, such as homoclinic tangles, periodicity regions originating from Arnold tongues, closed curve attractors, and complex basins. The paper provides a detailed numerical analysis under a CES production scenario of several global bifurcations arising from heterogeneity which does not exist under the specific ownership restrictions imposed in the original Kaldor/Pasinetti models.

Research paper thumbnail of Chaotic dynamics in a three-dimensional map with separate third iterate: The case of Cournot duopoly with delayed expectations

Chaos, Solitons & Fractals, 2018

We consider a Cournot duopoly with isoelastic demand function and constant marginal costs. We ass... more We consider a Cournot duopoly with isoelastic demand function and constant marginal costs. We assume that both producers have naive expectations but one of them reacts with delay to the move of its competitors, due to a "less efficient" production process of a competitor with respect to its opponent. The model is described by a 3D map having the so-called "cube separate property", that is its third iterate has separate components. We show that many cycles may coexist and, through global analysis, we characterize their basins of attraction. We also study the chaotic dynamics generated by the model, showing that the attracting set is either a parallelepiped or the union of coexisting parallelepipeds. We also prove that such attracting sets coexist with chaotic surfaces, having the shape of generalized cylinders, and with different chaotic curves.

Research paper thumbnail of Boom-bust dynamics in a stock market participation model with heterogeneous traders

Journal of Economic Dynamics and Control, 2018

The boundedly rational heterogeneous agent literature can be considered to have properly started ... more The boundedly rational heterogeneous agent literature can be considered to have properly started with a number of contributions in the early 90s, with the impressive contribution by Carl Chiarella who, amongst his huge field of research, developed several milestone models of heterogeneous interacting agents that are able to generate a number of dynamic outcomes compatible with the empirical evidence. In this paper, we propose a stock market model in which participation depends upon an attractiveness measure related to the market activity and the fundamental value of the market. A market maker adjusts the stock price with respect to the current endogenous excess market demand which, in turn, depends on the demands of the different types of agents populating the economy. Market participants are also allowed to switch between different strategies. Analytical and numerical results confirm how the participation mechanism amplifies the occurrence of endogenous booms and busts, in line with empirical and experimental evidence.

Research paper thumbnail of Bifurcation structures of a cobweb model with memory and competing technologies

Communications in Nonlinear Science and Numerical Simulation, 2017

In this paper we study a simple model based on the cobweb demand-supply framework with costly inn... more In this paper we study a simple model based on the cobweb demand-supply framework with costly innovators and free imitators. The evolutionary selection between technologies depends on a performance measure which is related to the degree of memory. The resulting dynamics is described by a two-dimensional map. The map has a fixed point which may lose stability either via supercritical Neimark-Sacker bifurcation or flip bifurcation and several multistability situations exist. We describe some sequences of global bifurcations involving attracting and repelling closed invariant curves. These bifurcations, characterized by the creation of homoclinic connections or homoclinic tangles, are described through several numerical simulations. Particular bifurcation phenomena are also observed when the parameters are selected inside a periodicity region.

Research paper thumbnail of Inflation Targeting, Recursive Inattentiveness, and Heterogeneous Beliefs

Journal of Money, Credit and Banking, 2017

In this paper we consider a scenario in which the monetary authority provides an explicit inflati... more In this paper we consider a scenario in which the monetary authority provides an explicit inflation target in order to anchor private sector expectations and align them with policy objectives. In this context, a biased perception of the target may arise due to imperfect information flows and idiosyncrasies in information processing lead to heterogenous beliefs about the target. We allow private sector expectations to be revised over time as new information becomes available and the direction of change is determined by the distance between agents' beliefs and actual realizations of macro variables. The recursive choice between alternative predictors is modeled as an optimization problem under rational inattention. Within this framework we investigate whether a simple interest rate rule can steer the economy toward the targeted equilibrium. Our findings suggest that standard policy advices, i.e., ensure determinacy under rational expectations, may not be sufficient to reach the target. Instead, a sound monetary policy should be fine-tuned to ensure that the signal sent by realizations of macro variables can correct biased agents' beliefs.

Research paper thumbnail of Dynamic effects of memory in a cobweb model with competing technologies

Physica A: Statistical Mechanics and its Applications, 2017

We analyze a simple model based on the cobweb demand-supply framework with costly innovators and ... more We analyze a simple model based on the cobweb demand-supply framework with costly innovators and free imitators and study the endogenous dynamics of price and firms' fractions in a homogeneous good market. The evolutionary selection between technologies depends on a performance measure in which a memory parameter is introduced. The resulting dynamics is then described by a two-dimensional map. In addition to the locally stabilizing effect due to the presence of memory, we show the existence of a double stability threshold which entails for different dynamic scenarios occurring when the memory parameter takes extreme values (i.e. when consideration of the last profit realization prevails or it is too much neglected). The eventuality of different coexisting attractors as well as the structure of the basins of attraction that characterizes the path dependance property of the model with memory is shown. In particular, through global analysis we also illustrate particular bifurcations sequences that may increase the complexity of the related basins of attraction.

Research paper thumbnail of Multistability and global dynamics in complementary good market model

Research paper thumbnail of Nonlinear dynamics of a Cournot duopoly game with differentiated products

Applied Mathematics and Computation, 2016

Two typical instances of market structure are perfect competition and monopoly. Halfway between t... more Two typical instances of market structure are perfect competition and monopoly. Halfway between them, when the market is supplied by only few firms, oligopolistic competition takes place (see Cournot, 1838). Few sellers are assumed to sell a homogenous good in the same market. As market price is assumed dependent on the total quantity sold by competitors, the market structure turns out to be more complicated than monopoly. The optimal decision of each competitor becomes dependent, not only on repercussions on the demand side, but also on the expected reverberations of the other competitors on any of its own moves. While Cournot considered a duopoly with a single homogeneous product, the economic literature also offered duopoly models with (horizontal) differentiated products (see, e.g., Dixit, 1979, Singh and Vives, 1984 and Fanti and Gori, 2012) which allow goods and services to be substitutes or complements, in models with a standard linear demand structure. The paper investigates the dynamics of a Cournot duopoly game with differentiated goods in which boundedly rational firms apply a gradient adjustment mechanism to update their quantity in each period. As in Ahmed et al. (2015), the nonlinear demand functions are derived from an underlying CES utility function. The present analysis reveals that a higher degree of product differentiation may destabilize the Nash equilibrium. We provide analytical conditions for the stability of the market equilibrium and we show, through local and global analysis, that a cascade of flip bifurcations and a Neimark-Sacker bifurcation may lead to periodic cycles, attractor coexistence and ultimately, chaotic motions. Since a higher degree of product differentiation tends to reduce competition, an implication of our findings is that a stronger competition could help in stabilizing the unique Nash equilibrium.

Research paper thumbnail of Path dependent coordination of expectations in asset pricing experiments: A behavioral explanation

Journal of Economic Behavior & Organization, 2016

In the learning-to-forecast laboratory experiments in Hommes et al. (2005), three different types... more In the learning-to-forecast laboratory experiments in Hommes et al. (2005), three different types of aggregate asset price behavior have been observed: monotonic convergence to the stable fundamental steady state, dampened price oscillations and permanent price oscillations. We present a simple behavioral 2-type heuristics switching model explaining individual as well as aggregate behavior in the experiment. Based on relative performance, agents switch between a simple trend-following and an anchor and adjustment heuristic that differ in how much weight is given to the long run average price level. The nonlinear switching model exhibits path dependence through coexistence of a locally stable fundamental steady state and a stable (quasi-)periodic orbit, created via a so-called Chenciner bifurcation. Depending on initial states, agents coordinate individual expectations either on a stable fundamental steady state path or on almost self-fulfilling persistent price fluctuations around the fundamental steady state.

Research paper thumbnail of UvA-DARE ( Digital Academic Repository ) Path dependent coordination of expectations in asset pricing experiments : a behavioral

In the learning-to-forecast laboratory experiments in Hommes et al. (2005), three different types... more In the learning-to-forecast laboratory experiments in Hommes et al. (2005), three different types of aggregate asset price behavior have been observed: monotonic convergence to the stable fundamental steady state, dampened price oscillations and permanent price oscillations. We present a simple behavioral 2-type heuristics switching model explaining individual as well as aggregate behavior in the experiment. Based on relative performance, agents switch between a simple trend-following and an anchor and adjustment heuristic that differ in how much weight is given to the long run average price level. The nonlinear switching model exhibits path dependence through co-existence of a locally stable fundamental steady state and a stable (quasi-)periodic orbit, created via a so-called Chenciner bifurcation. Depending on initial states, agents coordinate individual expectations either on a stable fundamental steady state path or on almost self-fulfilling persistent price fluctuations around ...

Research paper thumbnail of Variable priority dispatching rules: An analytical approach

International Journal of Production Economics, 1995

Scheduling techniques and dispatching rules are widely studied because of their strategic role in... more Scheduling techniques and dispatching rules are widely studied because of their strategic role in achieving optimal management of manufacturing systems. In the case of flexible and CIM-orientated plants, it is essential to evaluate the effects of different dispatching rules to foresee the system performance. The Authors proposed an analytical technique, based on the Markov Chain Theory, enabling the analysis of the behaviour of some common-practice dispatching rules. The results obtained in the previous studies suggested the application of the analytical method to a dispatching rule observing a variable priority criterion. This research aims to show the possibility of extending the method to the investigation of such dispatching rules, offering some of the results that this kind of approach may lead to. The rule satisfies production requirements, but inconveniences are to be planned for, as detailed later;

Research paper thumbnail of Dispatching rules and flexible environments: the influence on buffer behaviour

International Journal of Production Research, 1992

ABSTRACT Frequent production requirements are linked to effective and profitable strategies for t... more ABSTRACT Frequent production requirements are linked to effective and profitable strategies for the management of queues, e.g. input buffers of machining centres and selection of rough workpieces from central storage. As a matter of fact, management policy performances must be evaluated by focusing not only on induced queue lengths or customer waiting times, but also on the future composition of the queues themselves, this being a consequence of the dispatching rule adopted. The question acquires further importance when flexible environments and buffer capacity constraints are considered. The aim of the present study is to illustrate an analytical procedure, based on the Markov chains theory, able to forecast the composition of buffers starting from any initial configuration. Attention is given to the buffer behaviour during the transient period and the steady state: results are offered for sequential and prioritized dispatching of items, together with application examples derived from common industrial situations. In the final sections, the possible extension of the procedure is considered and outlined with regard to particular management rules, thus introducing a further development of the present research.

Research paper thumbnail of Periodic Orbits and Their Bifurcations in 3D Maps with a Separate Third Iterate

Global Analysis of Dynamic Models in Economics and Finance, 2012

Research paper thumbnail of Global dynamics in a non-linear model of the equity ratio

Chaos, Solitons & Fractals, 2000

A model for ®rms' ®nancial conditions is proposed, which ultimately reduces to a two-dimensional ... more A model for ®rms' ®nancial conditions is proposed, which ultimately reduces to a two-dimensional non-invertible map in the variables mean and variance of the equity ratio. The possible dynamics of the model and the global behaviour are investigated. We describe the mechanism of bifurcations leading to fractalization of the basins and/or fractalization of their boundaries, showing how a locally stable attractor may be almost globally unstable. Multistability is also investigated. Two, three or four co-existing attractors have been found and we describe the mechanism of bifurcations leading their basins to become chaotically intermingled, and thus to unpredictability of the asymptotic state in a wide region. The knowledge of such regimes, besides those associated with simple dynamics, may be of help for the operators. While the use of the technical tools we propose to study the global dynamics and bifurcations may be of help for further investigations. Ó

Research paper thumbnail of GLOBAL BIFURCATIONS OF BASINS IN A TRIOPOLY GAME

International Journal of Bifurcation and Chaos, 2002

A Cournot model based on bounded inverse demand function and constant marginal production costs i... more A Cournot model based on bounded inverse demand function and constant marginal production costs is studied. The case of three producers is considered and the adjustment process reduces to a three-dimensional noninvertible map in the output of competitors. The analysis of the dynamical behavior of the map is performed by the "critical curve method", extended to the critical surfaces in 3D. By this method, we explain the different bifurcations in the basins of attraction and in the attracting sets. In particular, given the economic application, feasible trajectories are focused, starting from the simple situation of two identical producers and extending the results to the generic case.

Research paper thumbnail of Credit market imperfection, financial market globalization, and catastrophic transition

Mathematics and Computers in Simulation, 2015

Research paper thumbnail of Agglomeration Dynamics and First Nature Asymmetries

Mathematics and Computers in Simulation, 2014

ABSTRACT The standard Footloose Capital (FC) model, as well as the discrete time version, assumes... more ABSTRACT The standard Footloose Capital (FC) model, as well as the discrete time version, assumes that all capital units are internationally mobile between two regions. In this paper, we assume that in one of the two regions some of the blueprints/capital units may be immobile because their utilization requires some locally specific natural resource (first nature advantage). Mobile blueprints, instead, can be utilized in both regions. We focus on this asymmetric distribution of immobile firms / capital units, labeled first nature firms. The central question of our paper is how the existence of first nature asymmetry affects agglomerative processes framed in discrete time. This modification of the FC model leads to a one dimensional piecewise smooth map for which we show analytically that border collision bifurcations are pervasive and (even asymmetric) multistability is possible.

Research paper thumbnail of Borrowing constraints and complex dynamics in an OLG framework

Journal of Economic Behavior & Organization, 2009

In this paper we model an OLG economy à la Kiyotaki and Moore whose novel feature is the role of ... more In this paper we model an OLG economy à la Kiyotaki and Moore whose novel feature is the role of money as a store of value and of bequest as a source of funds to be “invested” in landholding. The dynamics generated by the model are generally characterized by ...