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The authors consider the economic problem of consumers' demand under the assumption of bounded rationality. They move from the hypothesis that the consumer does not know the amount of the good maximizing the utility but he/she is able to understand, at each time period, if the current consumption is above or below than the optimal choice and decide consequently for the next period. Moreover, they also take into consideration the role of a reference amount of consumption that can influence the consumption choice of the consumer. They show that this assumption led to a failure in the convergence process towards the rational choice because the equilibrium of the model, even when locally stable, is located on an intermediate value between the rational choice and the reference quantity.

A dynamic model is proposed to describe the time evolution of production location choices of a multinational enterprise that can decide between two possible manufacturing locations: a stylized developed economy and a developing economy. The model is based on an evolutionary approach according to a replicator dynamics driven by expected profits. The production in each country is determined by the availability of labor inputs and their relative productivity, on wages of skilled and unskilled workers, as well as on cost externalities due to knowledge spillovers and public goods availability. The model includes the effects of relative demand and supply on earnings distribution with two different types of workers (high and low skilled) and the substitution between the two categories is captured by a CES aggregate production function. Behavioral parameters are also considered, such as the cognitive bias that overestimates the convenience of offshoring in term of labor cost and the “made in” effect that brings consumers to pay higher prices for products manufactured in a developed country.

Why is populism emerging now in Europe? Why is it present in USA and Latin America? What model of political choice may explain these facts? Our paper addresses these questions by building an evolutionary game with two groups of players that decide whether to support a populist party by weighting demand for redistribution and demand for tough policy against immigration. Fundamentally, it is assumed that agents care about immigration the more they fear it and the higher number of other people care about it. Overall, positive shifts in the fear of immigration and increases in inequality drive citizens to converge toward supporting populists. The stability of the equilibria depends on the crucial parameters of the model, namely: fear of immigrants, the effect that the population type (the number of citizens supporting populism) have on individual preferences, economic inequality. Different equilibria represent different cases of populism: South-American left-wing populism and European right-wing populism. We propose that an economic society with a low inequality of wealth and with a low fear of immigrants is needed to avoid populism.

We propose an oligopoly model where players can choose between two kinds of behaviors, denoted as cooperative and aggressive, respectively. Each cooperative agent chooses the quantity to produce in order to maximize her own profit as well as the profits of other agents (at least partially), whereas an aggressive player decides the quantity to produce by maximizing his own profit while damaging (at least partially) competitors’ profits. At each discrete time, players face a binary choice to select the kind of behavior to adopt, according to a proportional imitation rule, expressed by a replicator equation based on a comparison between accumulated profits. This means that the behavioral decisions are driven by an evolutionary process where fitness is measured in terms of current profits as well as a weighted sum of past gains. The model proposed is expressed by a nonlinear two-dimensional iterated map, whose asymptotic behavior describes the long-run population distribution of cooperative and aggressive agents. We show under which conditions one of the following long-run behaviors prevails: (i) all players choose the same strategy; (ii) both behaviors coexist according to a mixed stationary equilibrium; and (iii) a self-sustained (i.e. endogenous) oscillatory (periodic or chaotic) time pattern occurs. The influence of memory and that of the levels of cooperative/aggressive attitudes on the dynamics are analyzed as well.

In this paper, the location patterns of Multinational Enterprises are modeled by an evolutionary two-country model in which producing in a developed economy offers strong cost-reducing externalities of within-country spillovers and opting for a developing economy entails cheap labor but also extra operational costs due to the undersupply of public goods. The offshoring process, that is, manufacturing activity outsourced in the developing economy, increases the bargaining power of its workers and, with it, its labor cost. The investigation underlines that an increasing labor-productivity remuneration in the developing economy may spark a reshoring process that depends on the agglomeration and endowment drivers characterizing an industry. The reshoring process can be narrowed by a flexible labor remuneration scheme, with wages indexed to the domestic concentration of manufacturing activity. The presence of sub-optimal location patterns points out the existence of a trade-off between stability and efficiency, which underlines that policy measures designed to make a country a more efficient location are neither sufficient nor necessary for preventing offshoring or ensuring reshoring.

This special issue on “Nonlinear Economic Dynamics” contains a selection of papers presented at the 9th International Conference on Nonlinear Economic Dynamics (NED2015), that took place on June 25-27, 2015, at Chuo University, Tokyo, Japan. The goal of this special issue is to provide the reader with an overview of new directions in the global analysis of economic dynamics and to show applications of concepts from the qualitative theory of nonlinear dynamical systems in the fields of economics, finance, environment, and strategic interaction in social decisions. The wide spectrum of applications and the mathematical methods employed in the dynamic analysis are intended to offer a broad view on the different research streams that contribute to the blossoming literature on Nonlinear Economic Dynamics.

We propose a simple dynamic adjustment mechanism, equivalent to the standard replicator dynamics in discrete time, to study the time evolution of a population of players facing a binary choice game, and apply this mechanism to minority games in order to investigate the effects of memory on the stability of the unique Nash equilibrium. Two different kinds of memory are considered, one where the players take into account the current and the previous payoffs in order to decide the strategy chosen in the next period, and the other one where the players consider the whole series of payoffs observed in the past through a discounted sum with exponentially fading weights. Both the memory representations proposed lead to an analytically tractable two-dimensional dynamical system, so that analytical results can be given for the stability of the Nash equilibrium. However, a global analysis of the models – performed by numerical methods and guided by the analytical results – shows that some complexities arise for intermediate values of the memory parameter, even if the stabilization effect of uniform memory is stated in both cases.

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

In this paper, we propose a unitary formulation for evolutionary oligopoly models with memory. In particular, we consider behavioral rules that are stationary at the Nash equilibria so that we can study the stability of the oligopolistic model with memory with generic strategies for determining quantities. Although the introduction of memory does not affect the local stability properties of equilibria, we show how the presence of memory impacts the global dynamics of the system and how the question about the role of memory does not always provide a clear answer in terms of model complexity.

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.

In this paper we consider a nonlinear discrete-time dynamic model proposed by Farris et al. (2005) as a market share attraction model with two firms that decide marketing efforts over time according to best reply strategies with naïve expectations. The model also considers an adaptive adjustment toward best reply, a form of inertia or anchoring attitude, and we investigate the effects of heterogeneities among firms. A rich scenario of local and global bifurcations is obtained even with just two competing firms, and a comparison is proposed with apparently similar duopoly models based on repeated best reply dynamics with naïve expectations and adaptive adjustment.

The concept of the ‘postmodern consumer’ plays a central role in the debate, started in the early 80s, about economic, social and cultural changes in developed countries in the years following the end of the second world war. These changes were interpreted as a passage from modern to postmodern society. According to this literature, postmodern conditions have had a significant impact on the consumer, especially with regard to his/her psychological characteristics. In this new framework the consumer is viewed as someone more interested in the symbolic or cultural value of products and services than in their functional and utility value. At the same time, he/she is represented as an active player in the market scenario, exercising the freedom to move in search of trademarks, symbols and experiences through which he/she can communicate his/her own identity. The figure of the postmodern consumer is difficult to place in the framework of standard neoclassical theories on consumerism, which highlights the shortcomings of this theoretical approach in studying the behavior of the postmodern consumer. These shortcomings are likely to be more relevant when considering the consumer of food products, given the strong nexus between consumption and the well-being of the consumer and the symbolic and cultural value that food products project. The main goal of the paper is to provide an interdisciplinary overview of the postmodern consumer of food products by means of an analysis of scientific literature, mainly in the areas of behavioral economics, sociology and psychology. Following this, the paper focuses on questions regarding information and the rational behavior of consumers as being the main hypothesis upon which standard neoclassical theories are based, adding to the traditional approach to consumer choice the new insights provided by this different perspective. Finally, the implications of this type of analysis for food safety and quality policies are considered, together with a discussion on further research needed to define more effective policies.