Davide Radi

We consider a financial market model in which the market maker sets prices based on orders placed by chartists and fundamentalists. To sustain profitability, the market maker adjusts prices more strongly when price fluctuations become too calm. The dynamics of this model is described by a two-dimensional discontinuous piecewise-linear map that generates endogenous oscillations. Interestingly, this dynamics appears chaotic but is in fact quasiperiodic, corresponding to a recently discovered new kind of attractor, which we call a Weird Quasiperiodic Attractor (WQA). The bifurcation mechanisms leading to these attractors are not yet fully understood. Here, we describe some mechanisms underlying the appearance and disappearance of WQAs, related to eigenvectors of a particular composite map, as well as contact bifurcations leading to changes in the structure of WQAs.

We examine environmental protection in an oligopolistic setting in which a Pigouvian pollution tax is levied whenever environmental degradation exceeds a certain threshold set by a regulator. This threshold mechanism defines two scenarios, one with low environmental degradation in which firms do not internalize pollution, and one with high degradation in which firms are involved not only in production activities but also in abatement to ease the burden of the environmental tax. The purpose of this paper is to examine how the periodic dynamics of environmental degradation, described by a Lorenz map, are influenced by the main policy parameters. Regarding policy implications, we show how to construct a careful alignment between the border of the no-tax area and the level of taxation, which is crucial for reducing environmental degradation and avoiding fluctuations.

In this work, we consider a class of n-dimensional, [ ], piecewise linear discontinuous maps that can exhibit a new type of attractor, called a weird quasiperiodic attractor. While the dynamics associated with these attractors may appear chaotic, we prove that chaotic attractors cannot occur. The considered class of n-dimensional maps allows for any finite number of partitions, separated by various types of discontinuity sets. The key characteristic, beyond discontinuity, is that all functions defining the map have the same real fixed point. These maps cannot have hyperbolic cycles other than the fixed point itself. We consider the two-dimensional case in detail. We prove that in nongeneric cases, the restriction, or the first return, of the map to a segment of straight line issuing from the fixed point is reducible to a piecewise linear circle map. The generic attractor, different from the fixed point, is a weird quasiperiodic attractor, which may coexist with other attractors or attracting sets. We illustrate the existence of these attractors through numerous examples, using functions with different types of Jacobian matrices, as well as with different types of discontinuity sets. An application to a financial market modeling shows the role of regulator that maps in our class can have, leading to endogenous nonregular dynamics. In some cases, we describe possible mechanisms leading to the appearance of these attractors. We also give examples in the three-dimensional space. Several properties of this new type of attractor remain open for further investigation.

The paper examines how auditing and punishment can be employed to manage a common property resource, specifically a fishery, through a regulation scheme that involves pre-assigned multi-annual quotas. The decision to adhere to or exceed the assigned fishing quota is modeled as a two-player game. In the absence of auditing, the model yields noncompliance with the quota, known as the tragedy of the commons, which is the only Nash equilibrium of the game. With the introduction of formal enforcement, which offsets the additional profit from noncompliance, and extensive auditing through an integrated data control system, adherence to the quota becomes the only Nash equilibrium of the model. A dynamic version of this game, with logistic biomass growth and quadratic costs of harvesting, confirms that a digitized and integrated fishery control system may enhance sustainability. However, the study also highlights the potential risks associated with fishing quotas and enforcement that are not properly adjusted for the resource and are not updated as frequently as necessary.

We propose an evolutionary competition model to investigate the green transition of firms, highlighting the role of adjustment costs, dynamically adjusted transition risk, and green technology progress in this process. Firms base their decisions to adopt either green or brown technologies on relative performance. To incorporate the costs of switching to another technology into their decision-making process, we generalize the classical exponential replicator dynamics. Our global analysis reveals that increasing transition risk, e.g., by threatening to impose stricter environmental regulations, effectively incentivizes the green transition. Economic policy recommendations derived from our model further suggest maintaining high transition risk regardless of the industry's level of greenness. Subsidizing the costs of adopting green technologies can reduce the risk of a failed green transition. While advances in green technologies can amplify the effects of green policies, they do not completely eliminate the possibility of a failed green transition. Finally, evolutionary pressures favor the green transition when green technologies are profitable.

In this foreword to the Special Issue “Nonlinear dynamics and game-theoretical modeling in economics and finance” we review the contributions in the issue highlighting the economic results and the connections with aspects of dynamic analysis. Indeed, the common theme of the contributions is the focus on system dynamics and the latest analytical techniques. This issue is devoted to celebrating the 70th birthday of Professor Laura Gardini, who inspired a generation of scholars in the study of discrete-time systems and global methods of analysis.