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We extend the dynamic Cournot duopoly framework with emission charges on output by Mamada and Perrings (Econ Anal Policy 66:370–380, 2020), which encompassed homogeneous products in its original formulation, to the more general case of differentiated goods, in order to highlight the richness in its static and dynamic outcomes. Each firm is taxed proportionally to its own emission only and charge functions are quadratic. Moreover, due to an adjustment capacity constraint, firms partially modify their output level toward the best response. Like in Mamada and Perrings (Econ Anal Policy 66:370–380, 2020), the only steady state coincides with the Nash equilibrium, and it will be considered admissible when it guarantees the positivity of the marginal emission charge. We find that the full efficacy of the environmental policy, which applies to an equilibrium that is globally asymptotically stable anytime it is admissible, is achieved in the case of independent goods, as well as with a low good interdependence degree in absolute value, independently of being substitutes or complements. When goods are substitutes and their interdependence degree is high, the considered environmental policy is still able to reduce pollution at the equilibrium, but the latter is stable just when the policy intensity degree is large enough. When instead goods are complements and their interdependence degree is high in absolute value, the considered environmental policy produces detrimental effects on the pollution level and the unique equilibrium is always unstable, when admissible. This highlights that, from the static viewpoint, even in the absence of free riding possibilities, the choice of the mechanism to implement has to be carefully pondered, according to the features of the considered economy.

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 modified to be consistent with market’s seasonality. The model, consisting in a second-order non-autonomous difference equation, is investigated with the aim of understanding how the periodical nature of the market together with the agents’ expectation formation mechanism affects the resulting dynamics. We analytically prove the emergence of dynamical scenarios that are missing in the classic cobweb model for non-seasonal markets, such as quasi-periodic dynamics and an ambiguous role on stability of the expectation weight. Finally, we discuss their economic rationale with the help of numerical simulations. In such a peculiar economic framework, agents’ learning plays a key role to explain the dynamical properties of economic observables.

We consider the overlapping generation model formulated in Dioikitopoulos (J Econ Dyn Control 93:260–276, 2018). Its innovative approach involves endogenous adaptations of the deficit/surplus to debt and income levels through an empirically estimated fiscal policy rule. We improve the analysis of the model in order to tackle the issue of debt sustainability. In detail, we derive the analytic expressions of stationary states of the model as well as necessary and sufficient existence conditions.Moreover, our mathematical analysis sheds new light on the role of fiscal parameters and policy prescriptions. As a result, low deficit levels can be associated with the presence of steady-state configurations, which is a prerequisite for sustainable economic patterns to be achieved.

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 evaluation of the general market sentiment perceived by the agents and on a profitability measure of the existent strategies. As the relevance given to the sentiment index increases, a herding phenomenon in agent behavior may occur and animal spirits can drive the market toward polarized economic regimes, which coexist and are characterized by persistent high or low levels of optimism and pessimism. This conduct is detectable from agents polarized shares and beliefs, which in turn influence the price level. Such polarized regimes can consist in stable steady states or can be characterized by endogenous dynamics, generating persistent alternating waves of optimism and pessimism, as well as return distributions displaying the typical features of financial time series, such as fat tails, excess volatility and multifractality. Moreover, we show that if the sentiment has no or low relevance on belief selection, those stylized facts are abated or are missing from the simulated time series.

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 market. An evolutionary mechanism regulates agents’ participation in the stock market on the basis of a fitness measure that depends on the comparison between the stock return and the interest rate. Relying on analytical investigations complemented by numerical simulations, we study the economically relevant static and dynamic properties of the equilibrium, identifying the possible sources of instabilities and the channels through which they spread across markets. We aim at understanding what micro- and macro-factors affect the dynamics and, at the same time, how the dynamics of asset prices, which are ultimately influenced by the money market, behave over the business cycle. Starting from isolated markets, we show the effect of increasing the market interdependence on the national income, the stock price and the share of agents that participate in the stock market at the equilibrium. Moreover, we investigate the stabilizing/destabilizing role of market integration and the possible emergence of out-of-equilibrium dynamics.

We present a cobweb model to explain price adjustment in a competitive market with homogeneous firms based on assumptions from Prospect Theory. Price changes are evaluated with respect to a psychological reference price which enters directly into the demand function. Accordingly, firms face a downward-sloping demand curve that is kinked at the consumers’ reference price. Differently from the traditional cobweb model, the economy is described by a discontinuous map. Without assuming specific non-linearities and keeping the essential underlying mechanics of the model intact, we find that the implementation of several features from Prospect Theory into our simple cobweb model may significantly influence the market dynamics. Behavioral parameters play an important role for the market stability by reducing fluctuations and by directly affecting consumers’ demand as well as production decisions.

Imitation-based behaviors are considered in economics with significant contributions in reference to homogeneous populations where players are characterized by the same decisional processes (see for example [42,48]). However, the presence of imitation behaviors is detected in experimental oligopolies coexisting with rational-like rules. This motivates us to consider an heterogeneous population where best responders and imitators coexist and compete in a deterministic oligopoly framework. The model we formulate is characterized by two stationary states, specifically the Cournot–Nash equilibrium and a further production level at which best responders are inactive and imitators produce at the marked clearing price. The heterogeneities among players give to the model a nonlinear structure, influence the stability properties of the Cournot–Nash equilibrium and give rise to complex dynamic scenarios. We found that the imitators’ relative fraction have an ambiguous role in determining the stability properties of the Cournot–Nash equilibrium and, provided intermediate values of the population size, its variations may cause the occurrence of both flip and Neimark–Sacker bifurcations. Chaotic dynamics and coexistent attractors, characterized by not connected basins, may also be observed. We finally note that certain dynamic regimes, described by the model, are provided by analogous features as those characterizing experimental outcomes and several experiments can be reproduced with different parameters’ sets.

We analyze a class of congestion games where agents use resources to send a finite amount of goods from an initial location to a terminal one. The resources are costly and costs are load dependent. In this context we concentrate on the heterogeneity because we not only assume that agents have limited computational capability but also they differ in the quantities they must send and the reactivity. We introduce an appropriate dynamical system, which has the steady state exactly at the unique Nash equilibrium of the static congestion game, and we investigate the dynamical behavior of the game. We provide a closed form characterization on the unique Nash equilibrium in the underlying static congestion game and we prove that the equilibrium crucially depends on the aggregate congestion. Not only do we provide a local stability condition in terms of the agents’ reactivity and the nonlinearity of the cost functions but also we study the role of the heterogeneity in this context. We show analytically that heterogeneity can be destabilizing with a cascade of flip-bifurcation leading to periodic cycles and finally to chaos but also that mastering the degree of heterogeneity can be used to tame and control complex dynamics; moreover in relation to the reactivity levels their product must roughly small. However if both reactivity levels are near but outside the stability region then it is sufficient to act on just one to restore stability. Finally, if both levels are far form the stability region acting on one will not restore stability.

The dynamics of a pure exchange overlapping generations model with endogenous money growth rule is investigated. We consider a nonlinear monetary policy rule which, in each period, bounds the money growth rate so that money is determined by the deviation of the inflation rate from its target. More precisely, we introduce such a mechanism through a sigmoidal money adjustment mechanism characterized by the presence of two asymptotes that bound the money variation, and thus the dynamics. It is shown that, depending on the timing of the monetary policy and the degree of reaction of the Central Bank, the target equilibrium may be destabilized via different types of bifurcations. Multistability and coexistence of attractors may also occur and the study of the basins of attraction allows us to analyze the global dynamic properties of the economy under scrutiny. We find that active monetary policy rules may be relevant for their stabilizing properties, but they also may open the door to equilibrium cycles of any periodicity and even chaos.

This paper considers a pure exchange overlapping generations model in which the money-growth rate is endogenous and follows a feedback rule. Different specifications for the monetary policy rule are analyzed, namely a so-called current, forward, or backward-looking feedback rule, depending on whether the monetary authority uses the actual, expected, or last observed values of the inflation rate to set the monetary policy. We study how the responsiveness of the policy rule with respect to inflation affects the determinacy of the monetary equilibrium. A policy rule is called aggressive (moderate) if it responds strongly (moderately) to inflation deviations from the target. We show how aggressive feedback rules, depending on the considered timing, can reinforce mechanisms that lead to indeterminacy or may lead the inflation rate to fluctuate around the monetary equilibrium at which monetary policy is aggressive. Aleaning against the windpolicy seems to be more desirable from an equilibrium determinacy point of view. On the contrary, aleaning with the windpolicy could not be the recommended policy for the Central Bank.

Starting from a Muthian cobweb model, we extend the profit-based evolutionary setting in Hommes and Wagener (2010) by assuming that, in addition to pessimistic, optimistic and unbiased fundamentalists, the market is populated by rational producers, which correctly anticipate the next period price. Thanks to their introduction, we find that, differently from the framework in Hommes and Wagener (2010), the map governing the dynamics is no more monotonically decreasing. Hence, if on the one hand adding rational agents enlarges the local stability region of the steady state, on the other hand their consideration opens the door to complex dynamic outcomes, characterized by chaotic attractors and rich multistability phenomena, that we investigate along the paper.

Starting from a Muthian cobweb model, we extend the profit-based evolutionary setting in Hommes and Wagener (2010) populated by pessimistic, optimistic and unbiased fundamentalists, by assuming that agents face heterogeneous information costs, inversely proportional to the entity of their bias. Hommes and Wagener (2010) proved that, when the unique steady state of their model is globally eductively stable in the sense of Guesnerie (2002), the equilibrium under evolutionary learning may be just locally, but not globally, stable, due to the presence of a period-two cycle. Thanks to the introduction of information costs, we find that the equilibrium, when globally eductively stable, may be not even locally stable under evolutionary learning. More precisely, we analyze our setting by measuring the influence of agents’ heterogeneity through the parameter describing the degree of optimism and pessimism. According to the considered parameter configuration, the unique steady state, which coincides with the fundamental, may be (locally or globally) stable for every value of the bias, like in Hommes and Wagener (2010), or it may be stable just for suitably small and for suitably large values of the bias. Hence, increasing beliefs’ heterogeneity can be stabilizing when information costs are taken into account. We give an interpretation of such counterintuitive result in terms of profits, on which the share updating rule is based.

We consider a Minskyan type model of a closed economy with autonomous public expenditure formulated in a discrete time framework, where an endogenous debt adjustment process is considered and where income variations account for real world physical and social constraints. The model is characterized by a unique nontrivial fixed point matching the economic equilibrium. We study its stability properties in terms of the constant factor that fixes the firms’ desired debt level at a certain proportion of the current income. The stability loss of the fixed point is associated with either a subcritical flip or a supercritical Neimark–Sacker bifurcation. The latter implies occurrence of self-sustained oscillations interpreted as business cycles. We present three possible dynamic scenarios right after the Neimark–Sacker bifurcation: in a generic case and in two resonant cases. We also describe modifications of the attractor when propensity of firms to get into debt grows. In addition, we highlight that the increase of instabilities and complexities of dynamic outcomes is paired with the rise of the so called financial fragility indicator, which is a measure of fragility of the financial structure of the economy.

Starting from a Muthian cobweb model, we here extend the profit-based evolutionary settings in Hommes and Wagener (2010) and in Naimzada and Pireddu (2020a) by assuming that unbiased fundamentalists and several groups of biased fundamentalists face information costs that are inversely proportional to their bias. Like in those works, we deal with the case in which the model is globally eductively stable, being globally stable under naive expectations. Similarly to Naimzada and Pireddu (2020a), we find that the stability of the unique steady state, which coincides with the fundamental, holds either for every value of the bias, like in Hommes and Wagener (2010), or just for suitably small and large values of the bias. On the other hand, introducing into the economy new couples of symmetrically biased groups of fundamentalists with a sufficiently high bias, multiple coexisting locally stable period-two cycles emerge. While in Hommes and Wagener (2010) such phenomenon occurs only when the steady state is locally stable, we observe the coexistence of multiple locally stable period-two cycles also when the equilibrium is unstable, thanks to information costs. Moreover, we show that the relative position of the newly arisen period-two cycles may not coincide with and without information costs.

We propose a discrete-time exchange economy evolutionary model with two groups of agents. In our setting the definition of equilibrium depends also on agents’ population shares, which affect the market clearing conditions. We prove that, despite such difference with the classical Walrasian framework, for all economies and population shares there exists at least one equilibrium, and we show that for all population shares, generically in the set of the economies, equilibria are finite and regular. We then introduce the dynamic law governing the evolution of the population shares, and we investigate the existence and the stability of the resulting stationary equilibria. We assume that the reproduction level of a group is related to its attractiveness degree, which depends on the social visibility level, determined by the consumption choices of the agents in that group. The attractiveness of a group is described via a generic bell-shaped map, increasing for low visibility levels, but decreasing when the visibility of the group exceeds a given threshold value, due to a congestion effect. The model is able to reproduce the recurrent dynamic behavior typical of the fashion cycle, presenting booms and busts in the agents’ consumption choices, and in the groups’ attractiveness and population shares.

In the present note we prove the first fundamental theorem of welfare economics, according to which all equilibrium allocations are Pareto optimal, for the standard pure exchange model with shares. In this context the social interaction among agents enters the definition of equilibrium only through the market clearing conditions, but it does not affect the agents’ maximization problem. We show that the first fundamental theorem of welfare holds true also when introducing stationary equilibria in relation to a share updating mechanism.

We extend the exchange economy evolutionary discrete-time model with heterogeneous agents introduced in ‘Fashion cycle dynamics in a model with endogenous discrete evolution of heterogeneous preferences’, by A. Naimzada and M. Pireddu, appeared in Chaos: An Interdisciplinary Journal of Nonlinear Science 28, 055907 (2018), by considering generic bell-shaped attractiveness functions for the two groups of agents, increasing for low visibility levels, but decreasing when the visibility of the group exceeds a given threshold value, due to a congestion effect. The reproduction level of a group is related to its attractiveness degree, which depends on its social visibility level, determined by the consumption choices of the agents in that group. We investigate the asymptotic heterogeneity among agents, finding that the global dynamics may differ according to the chosen functional form for the attractiveness. Nonetheless, the model is still able to reproduce the recurrent dynamic behaviour typical of the fashion cycle.

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 tools combined with numerical simulations, we investigate the stability conditions of the unique steady state and the emergence of different kinds of endogenous dynamics, which are the results of the action of the fiscal and the monetary policy through their reactivity degrees. Such policies, if properly tuned, can lead the economy toward the desired full employment target but, on the other hand, can also generate endogenous fluctuations in the pace of the economic activity, associated with the occurrence of closed invariant curves and multistability phenomena.

We consider the competition among quantity setting players in a linear evolutionary environment. To set their outputs, players adopt, alternatively, the best response rule having perfect foresight or an imitative rule. Players are allowed to change their behavior through an evolutionary mechanism according to which the rule with better performance will attract more followers. The relevant stationary state of the model describes a scenario where players produce at the Cournot-Nash level. Due to the presence of imitative behavior, we find that the number of players and implementation costs, needed to the best response exploitation, have an ambiguous role in determining the stability properties of the equilibrium and double stability thresholds can be observed. Differently, the role of the intensity of choice, representing the evolutionary propensity to switch to the most profitable rule, has a destabilizing role, in line with the common occurrence in evolutionary models. The global analysis of the model reveals that increasing values of the intensity of choice parameter determine increasing dynamic complexities for the internal attractor representing a population where both decision mechanisms coexist.

In the rank of behavioral rules, imitation-based heuristics have received special attention in economics (see Vega-Redondo, 1997; Schlag, 1998). In particular, imitative behavior explains the evidence from experimental oligopolies where the Cournot–Nash equilibrium does not emerge as unique outcome and outputs are placed, for the most part, on fairly competitive levels (see e.g. Apesteguia et al., 2006 and Oechssler et al., 2016). Here, we derive a dynamic model of a linear Cournot oligopoly with a deterministic structure where rational agents having perfect foresight and imitators are present. The Cournot–Nash equilibrium is a stationary state of our models together with a further production level that can be interpreted as the competitive equilibrium in case only imitators are present. We found that the heterogeneities among players influence the stability properties of the Cournot–Nash equilibrium and the arising dynamical scenarios are characterized by similar features as those from experimental outcomes.

We propose a discrete-time exchange economy evolutionary model, in which two groups of agents are possibly characterized by heterogeneous preference structures. With respect to the classical Walrasian framework, in our setting the definition of equilibrium, in addition to utility functions and endowments, depends also on population shares, which affect the market clearing conditions. We prove that, despite such difference with the standard framework, for every economy and for each population shares there exists at least one equilibrium and we show that, for all population shares, generically in the set of the economies, equilibria are finite and regular. We then introduce the dynamic law governing the evolution of the population shares, and we investigate the existence and the stability of the resulting stationary equilibria. More precisely, we assume that the reproduction level of a group is related to its attractiveness degree, which depends on the social visibility level, determined by the consumption choices of the agents in that group. The attractiveness of a group is described via a generic bell-shaped map, increasing for low visibility levels, but decreasing when the visibility of the group exceeds a given threshold value, due to a congestion effect. Thanks to the combined action of the price mechanism and of the share updating rule, the model may reproduce the recurrent dynamic behavior typical of the fashion cycle, presenting booms and busts in the agents’ consumption choices, and in the groups’ attractiveness and population shares. We illustrate the emergence of fashion cycle dynamics in the case of Stone-Geary utility functions, which generalize the Cobb-Douglas utility functions, and for different formulations of the attractiveness maps, already considered in the literature.

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 performing strategy in an evolutionary perspective. The real side of the economy is described within a multiplier-accelerator framework with a nonlinear, bounded investment function. We show that strongly polarized beliefs in an evolutionary framework can introduce multiplicity of steady states, which, consisting in enhanced or depressed levels of income, reflect and reproduce the optimistic or pessimistic nature of the agents' beliefs. The polarization of these steady states, which coexist with an unbiased steady state, positively depends on that of the beliefs and on their relevance. Moreover, with a mixture of analytical and numerical tools, we show that such static characterization is inherited also at the dynamical level, with possibly complex attractors that are characterized by endogenously fluctuating pessimistic and optimistic levels of national income and price. This framework, when stochastic perturbations are included, is able to account for stylized facts commonly observed in real financial markets, such as fat tails and excess volatility in the returns distributions, as well as bubbles and crashes for stock prices., Comment: 41 pages, 10 figures

We investigate the dynamics of a cobweb type model with nonlinear demand and supply curves in which producers make forecasts on future prices with a backward looking expectation formation mechanism: the expected price for the next period is obtained by a weighted average of the prices observed in the last two periods. The study herewith presents aims at confirming the existence of a locally stabilising effect due to the presence of memory, but an increase of memory in price expectations can be globally qualitatively destabilising, in the sense that it leads to coexistence of different attractors with their respective basins of attraction.

We analyse the recurrence (Formula presented.) , where (Formula presented.) is a weighted power mean of (Formula presented.) , 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 (Formula presented.) Then, to simulate a fading memory, we consider exponentially decreasing weights. Since, in this case, the resulting recurrence does not fulfil the hypotheses of the previous convergence theorem, it is studied by reducing it to an equivalent two-dimensional autonomous map, which shares the asymptotic behaviours with a particular one-dimensional map. This allows us to prove that a long memory with sufficiently large weights has a stabilizing effect. Finally, we numerically investigate what happens when the memory ratio is not sufficiently large to provide stability, showing that, depending on the power mean and the memory ratio, either a delayed or early cascade of flip bifurcations occurs.

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 demand, but also making use of the past excess demand functions. In particular, we study the effect of computing a weighted average of the current and the previous excess demands (finite two level memory) and of all the previous excess demands (infinite memory). We show that suitable weights’ distributions have a stabilizing effect, so that the resulting price adjustment process converge toward the competitive equilibrium in a wider range of situations than the process without memory. Finally, we investigate the convergence speed toward the equilibrium of the proposed mechanisms. In particular, we show that using infinite memory with fading weights approaches the competitive equilibrium faster than with a distribution of quasi-uniform weights.

In the present paper we propose a model in which the real side of the economy, described via a Keynesian good market approach, interacts with the stock market with heterogeneous speculators, i.e., optimistic and pessimistic fundamentalists, that respectively overestimate and underestimate the reference value due to a belief bias. Agents may switch between optimism and pessimism according to which behavior is more profitable. To the best of our knowledge, this is the first contribution considering both real and financial interacting markets and an evolutionary selection process for which an analytical study is performed. Indeed, employing analytical and numerical tools, we detect the mechanisms and the channels through which the stability of the isolated real and financial sectors leads to instability for the two interacting markets. In order to perform such analysis, we introduce the “interaction degree approach”, which allows us to study the complete three-dimensional system by decomposing it into two subsystems, i.e., the isolated financial and real markets, easier to analyze, that are then linked through a parameter describing the interaction degree between the two markets. We derive the stability conditions both for the isolated markets and for the whole system with interacting markets. Next, we show how to apply the interaction degree approach to our model. Among the various scenarios we are led to analyze, the most interesting one is that in which the isolated markets are stable, but their interaction is destabilizing. We choose such setting to give an economic interpretation of the model and to explain the rationale for the emergence of boom and bust cycles. Finally, we add stochastic noises to the optimists and pessimists demands and show how the model is able to reproduce the stylized facts for the real output data in the US.

We study a triopoly game with heterogeneous players. The market is characterized by a nonlinear (isoelastic) demand function and three competitors. The main novelty is the double route to complex dynamics that we find and is quite rare in heterogeneous triopoly models. We show that the two routes have important implications for the economic interpretation of the dynamics emerging when the Cournot–Nash equilibrium becomes locally unstable. Moreover the model displays multistability of different attractors, requiring a global analysis of the dynamical system.

We formulate an evolutionary oligopoly model where quantity setting players produce following either the static expectation best response or a performance-proportional imitation rule. The choice on how to behave is driven by an evolutionary selection mechanism according to which the rule that brought the highest performance attracts more followers. The model has a stationary state that represents a heterogeneous population where rational and imitative rules coexist and where players produce at the Cournot–Nash level. We find that the intensity of choice, a parameter representing the evolutionary propensity to switch to the most profitable rule, the cost of the best response implementation as well as the number of players have ambiguous roles in determining the stability property of the Cournot–Nash equilibrium. This marks important differences with most of the results from evolutionary models and oligopoly competitions. Such differences should be referred to the particular imitative behavior we consider in the present modeling setup. Moreover, the global analysis of the model reveals that the above-mentioned parameters introduce further elements of complexity, conditioning the convergence toward an inner attractor. In particular, even when the Cournot–Nash equilibrium loses its stability, outputs of players little differ from the Cournot–Nash level and most of the dynamics is due to wide variations of imitators’ relative fraction. This describes dynamic scenarios where shares of players produce more or less at the same level alternating their decision mechanisms.

We propose a discrete-time exchange economy evolutionary model, in which two groups of agents are characterized by different preference structures. The reproduction level of a group is related to its attractiveness degree, which depends on the social visibility level, determined by the consumption choices of the agents in that group. The attractiveness of a group is initially increasing with its visibility level, but it becomes decreasing when its visibility exceeds a given threshold value, due to a congestion effect. Thanks to the combined action of the price mechanism and of the share updating rule, the model is able to reproduce the recurrent dynamic behavior typical of the fashion cycle, presenting booms and busts both in the agents' consumption choices and in the population shares. More precisely, we investigate the existence of equilibria and their stability, and we perform a qualitative bifurcation analysis on varying the parameter describing the group's heterogeneity degree. From a global viewpoint, we detect, among others, multistability phenomena in which the group coexistence is dynamic, either regular or irregular, and the fashion cycle occurs. The existence of complex dynamics is proven via the method of the turbulent maps, working with homoclinic orbits. Finally, we provide a social and economic interpretation of the main scenarios.

The simple pure exchange model with two individuals and two goods introduced by Day and Pianigiani in 1991, later extensively analyzed by Day and taken up again by Mukherji, is discussed and extended with the purpose of showing that chaos in a discrete tâtonnement process of this kind can be controlled if the auctioneer uses a smooth, non-linear formulation of the price evolution process such that the price adjustment is a sigmoid-shaped function of the excess demand, with given lower and upper limits. In particular, we show that, given the price adjustment speed and the excess demand function, the auctioneer can (a) stabilize the dynamics, (b) reduce the complexity of the attractor and (c) increase the economic significance of the adjustment process by simply acting on the lower and/or upper limits that constrain price dynamics.

We propose an exchange economy evolutionary model with discrete time, in which there are two groups of agents characterized by different structures of preferences. The share updating mechanism depends in a monotone manner on the goods’ consumption, described in terms of the calorie intakes. In such framework we investigate the existence of equilibria, their stability and the occurrence of multistability phenomena via a qualitative bifurcation analysis, which also highlights the presence of transcritical bifurcations.

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.

In the rank of behavioral rules, imitation-based heuristics has received special attention in economics (see [14] and [12]). In particular, imitative behavior is considered in order to understand the evidences arising in experimental oligopolies which reveal that the Cournot-Nash equilibrium does not emerge as unique outcome and show that an important component of the production at the competitive level is observed (see e.g.[1,3,9] or [7,10]). By considering the pioneering groundbreaking approach of [2], we build a dynamical model of linear oligopolies where heterogeneous decision mechanisms of players are made explicit. In particular, we consider two different types of quantity setting players characterized by different decision mechanisms that coexist and operate simultaneously: agents that adaptively adjust their choices towards the direction that increases their profit are embedded with imitator agents. The latter ones use a particular form of proportional imitation rule that considers the awareness about the presence of strategic interactions. It is noteworthy that the Cournot-Nash outcome is a stationary state of our models. Our thesis is that the chaotic dynamics arousing from a dynamical model, where heterogeneous players are considered, are capable to qualitatively reproduce the outcomes of experimental oligopolies.

We analyze a class of congestion games where two agents must send a finite amount of goods from an initial location to a terminal one. To do so the agents must use resources which are costly and costs are load dependent. In this context we assume that the agents have limited computational capability and they use a gradient rule as a decision mechanism. By introducing an appropriate dynamical system, which has the steady state exactly at the unique Nash equilibrium of the static congestion game, we investigate the dynamical behavior of the game. We provide a local stability condition in terms of the agents’ reactivity and the nonlinearity of the cost functions. In particular we show numerically that there is a route to complex dynamics: a cascade of flip-bifurcation leading to periodic cycles and finally to chaos.