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Foreword to the Special Issue of Mathematics and Computers in Simulation on Complex Dynamics in Economics and Finance
No full textA dynamic model of oligopoly with R&D externalities along networks- Part I
No full textThis paper formulates and analyzes a two-stage oligopoly game where firms can invest in cost-reducing R&D activity with the possibility of sharing R&D results with partner firms as well as gaining knowledge for free through spillovers. Firms are arranged within networks (or districts) inside which they can cooperate by bilateral agreements for sharing knowledge and compete in the market. An adaptive dynamic mechanism is proposed to describe how firms in a two-networks system repeatedly decide their R&D efforts over time. This adaptive adjustment may converge to a Nash equilibrium in the long run, or exhibit more complex dynamic behaviors. Analytical results about stability of equilibrium points are given, as well as numerical simulations to show global dynamical properties, including coexistence of attractors and complicated structures of their basins. In a second paper (Part II) sonic analytical results will be given for some relevant benchmark cases. together with numerical experiments that stress the role of the level of connectivity (i.e. the collaboration attitude) inside networks, as well as the effects of involuntary knowledge spillovers inside each network and among different competing networks
Routes to complexity induced by constraints in Cournot oligopoly games with linear reaction functions
No full textWithin a classical discrete-time Cournot oligopoly model with linear demand and quadratic cost functions, minimum and maximum production constraints are imposed in order to explore their effects on the dynamic of the system. Due to the presence of such constraints, the dynamic model assumes the form of a continuous piecewise linear map of the plane. The study of Nash equilibria of the oligopoly game, together with an analytical and numerical investigation of the different kinds of attractors of the dynamical system, shows how the presence of production constraints generates so called border collision bifurcations, a kind of global bifurcations recently introduced in the literature on non-smooth dynamical systems, which gives rise to a quite rich spectrum of dynamic scenarios, characterized by drastic changes in the qualitative dynamic properties of the system
Methematical Bioeconomic Modelling in the Interaction between Aquaculture and Open-Sea Fisheries
No full textKnowledge accumulation in an R&D network
Get PDFIn this chapter we propose an oligopoly model where firms invest in cost reducing R&D for producing homogeneous goods that are sold in a market. In particular, we assume that R&D efforts build up a "stock of knowledge", which, in turn, reduces marginal costs of production. Moreover, though all firms are competitors in the marketplace, they can decide to collaborate through cooperation agreements in a network for sharing their R&D results
Border Collision Bifurcation in a simple oligopoly model with constraints
No full textIn this paper, we run through an example of oligopoly, recently introduced in the literature, where firms operate under constraints. The dynamical system describing firms' choices over time assumes the form of a piecewise-smooth map because of such constraints. By carrying on a leading example, we show possible routes to complexity in the model, mainly due to border collision and homoclinic bifurcations
“Strategic interaction and imitation dynamics in patch differentiated exploitation of fisheries”
No full textIn this paper we propose a discrete-time dynamic model for studying the time evolution of fish stocks in an aquatic environment divided into two adjacent patches, one characterized by an imposed constant fishing effort and another one where fishermen are free to decide the quantity to harvest according to oligopolistic competition taking into account economic and biologic externalities. Given the total number of fishermen, we propose an evolutionary switching mechanism, based on imitation dynamics, that endogenously regulates the fraction of fishermen that, at each time period, decide to operate in one of the two regions on the basis of observed past profits. Numerical simulations provide some insights into the role of the main parameters. This model has been motivated by a project for the creation of a marine protected area (MPA) in the Adriatic sea
A Competition game with Knowledge Accumulation and Spillovers"
No full textIn this paper a repeated game is proposed to model competition among firms, with profit maximizing resource allocation. The proposed model differs from the usual com-petition models because efforts that players exert are not seen as sunk costs, but they accumulate to form a stock of knowledge that has a cost-reducing effect. In modelling knowledge accumulation, we also consider the (knowledge) spillovers, that is, involun-tary leakage of useful technological information. The game with n boundedly rational agents is modelled by a 2n-dimensional discrete dynamical system, whose state variables are the R&D efforts and the stock of accumulated knowledge of each firm involved in the competition. The model is characterized by some counteracting forces: Efforts are costly but can increase future profits; immediate expenditures of each firm can have cost-reducing effects in the long run, since accumulated knowledge can decrease both own costs and competitors ’ ones, because of spillover effects. In the case of two homoge-neous firms we prove the existence of a unique equilibrium and its stability. Starting from these analytic results, numerical simulations are performed in order to study the effects induced by heterogeneities between the players on stability and transient dynamics, as well as the influence of the main parameters on the basins of attraction
Il ruolo delle riserve marine nella gestione sostenibile della pesca. Costi, benefici, modelli
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