In this paper we analyze a dynamic game of Cournot competition with heterogeneous firms choosing between two different adaptive behavioral rules in deciding output strategies. The underlying oligopoly structure is standard: using a constant return to scale technology, N firms produce homogeneous goods, which are sold in a market characterized by constant price elasticity. In this setup, we assume that a fraction of firms employs a quite rough rule of thumb, the so-called Local Monopolistic Approximation (LMA), whereas the complementary fraction plays Best Reply (BR), a more demanding strategy in terms of information and computation requirements. The model is first considered with exogenously fixed fractions of firms in the two complementary groups. Then it is generalized by considering an endogenous evolutionary switching process between the two behavioral strategies based on profit-driven replicator dynamics. The role of the number of firms, information costs and inertia (or anchoring attitude) in production decisions is analyzed, as well as the influence in the evolutionary process of random noise in the demand function and memory of past profits. Global properties of the oligopoly with evolutionary pressure between behavioral rules are discussed, with particular regard to cases in which the Nash equilibrium is unstable

In this paper, we propose a bioeconomic model which describes a fishery in which each of two noninteracting species is harvested by a given group of fishers during a defined time period. Then the Fishing Regulatory Authority allows each fisher to reconsider the harvesting decision at fixed (discrete) periods of time. The model derives from an Italian fisheries management experience in the Northern Adriatic Sea, where this kind of “self‐adjusting” fishing policy has been proposed to regulate harvesting of two shellfish species. The proposed dynamic model assumes the form of a hybrid system, as the natural growth functions of the two species (in continuous time) are coupled with a discrete time adaptive system that regulates how agents switch from one harvesting strategy to the other period by period according to an evolutionary mechanism based on profit comparison. In order to obtain some insights into the basic mechanisms of the system, some relevant benchmark cases are analyzed before tackling (mainly numerically) the complete hybrid model. Our results suggest that, for proper sets of parameters, this kind of myopic and adaptive self‐regulation may ensure a virtuous trade‐off between profit maximization and resource conservation, driven by cost externalities and market pressure.

In this paper, we propose a dynamical model of technology adoption for the exploitation of a renewable natural resource. Each technology has a different efficiency and environmental impact. The process of technology adoption over time is modeled through an evolutionary game employed by profit maximizing exploiters. The loss in profits due to lower efficiency levels of environmentally-friendly technologies can be counterbalanced by the higher consumers' propensity to pay for greener goods. The dynamics of the resource take place in continuous time, whereas the technology choice can be revised either in continuous-time or in discrete-time. In the latter case, the model assumes the form of a hybrid system, whose dynamics is mainly explored numerically. We shows that: (1) overexploitation of the resource arises whenever the reduction in harvesting due to a lower efficiency of clean technology is more than compensated by a higher propensity to pay for greener goods; (2) the difference between the fixed costs of these technologies can be exogenously fixed to provide an incentive for adopting clean technology without affecting the long-run level of the resource; and (3) in some cases, discrete switching of the technology causes overshooting in the dynamics whereas in others it enhances the stability of the system

We propose a dynamic model to describe a fishery where both preys and predators are harvested by a population of fishermen who are allowed to catch only one of the two species at a time. According to the strategy currently employed by each agent, i.e. the harvested variety, at each time period the population of fishermen is partitioned into two groups, and an evolutionary mechanism regulates how agents dynamically switch from one strategy to the other in order to improve their profits. Among the various dynamic models proposed, the most realistic is a hybrid system formed by two ordinary differential equations, describing the dynamics of the interacting species under fishing pressure, and an impulsive variable that evolves in a discrete time scale, in order to describe the changes of the fraction of fishermen that harvest a given stock. The aim of the paper is to analyze the economic consequences of this kind of self-regulating fishery, as well as its biological sustainability, in comparison with other regulatory policies. Our analytic and numerical results give evidence that in some cases this kind of myopic, evolutionary self-regulation might ensure a satisfactory trade-off between profit maximization and resource conservation.

An important contribution in sociophysics is the Galam's model of rumors spreading. This model provides an explanation of rumors spreading in a population and explains some interesting social phenomena such as the diffusion of hoaxes. In this paper the model has been reformulated as a Markov process highlighting the stochastic nature of the phenomena. This formalization allows us to derive conditions for consensus to be reached and for the existence of some interesting phenomena such as the emergence of impasses. The proposed formulation allows a deeper and more comprehensive analysis of the diffusion of rumors