Nicolò Pecora

Nonlinear dynamics of a Cournot duopoly game with differentiated products

In this paper we investigate the dynamics of a Cournot duopoly game with differentiated goods in which boundedly rational firms apply a gradient adjustment mechanism to update the quantity produced in each period. As in Ahmed et al. (2015), the demand functions are derived from an underlying CES utility function. The present analysis reveals that a higher degree of product differentiation may destabilize the Nash equilibrium. Through local analysis we provide conditions for the stability of the market equilibrium and through global analysis we investigate some bifurcations which cause qualitative changes in the structure of the attractors and of their basins as some parameters are allowed to vary. Since a higher degree of product differentiation tends to reduce competition and may generate undesirable fluctuations, an implication of our findings is that a stronger competition could help in stabilizing the unique Nash equilibrium.

Real and financial market interactions in a multiplier-accelerator model: Nonlinear dynamics, multistability and stylized facts

In the present paper, we investigate the dynamics of a model in which the real part of the economy, described within a multiplier-accelerator framework, interacts with a financial market with heterogeneous speculators, in order to study the channels through which the two sectors influence each other. Employing analytical and numerical tools, we investigate stability conditions as well as bifurcations and possible periodic, quasi-periodic, and chaotic dynamics, enlightening how the degree of market interaction, together with the accelerator parameter and the intervention of the fiscal authority, may affect the business cycle and the course of the financial market. In particular, we show that even if the steady state is locally stable, multistability phenomena can occur, with several and complex dynamic structures coexisting with the steady state. Finally, simulations reveal that the proposed model is able to explain several statistical properties and stylized facts observed in real financial markets, including persistent high volatility, fat-tailed return distributions, volatility clustering, and positive autocorrelation of absolute returns.

Discovering SIFIs in interbank communities

This paper proposes a new methodology based on non-negative matrix factorization to detect communities and to identify central nodes in a network as well as within communities. The method is specifically designed for directed weighted networks and, consequently, it has been applied to the interbank network derived from the e-MID interbank market. In an interbank network indeed links are directed, representing flows of funds between lenders and borrowers. Besides distinguishing between Systemically Important Borrowers and Lenders, the technique complements the detection of systemically important banks, revealing the community structure of the network, that proxies the most plausible areas of contagion of institutions’ distress.

Memory, market stability and attractors coexistence in a nonlinear cobweb model

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.

A cobweb model with gradient adjustment mechanism: nonlinear dynamics and multistability

ABSTRACT A cobweb model, characterized by boundedly rational producers with a production adjustment mechanism based on the gradient rule, is described by a nonlinear discrete time dynamical system of the plane. Firms do not have a complete knowledge of the demand function and try to infer how the market will respond to their production changes by an empirical estimates of the marginal profits. Analytical conditions for local stability of the market equilibrium are provided, showing that the stability loss of the market equilibrium may give rise to chaotic dynamic as well. When memory is introduced in the production adjustment mechanism, a locally stabilizing effect is revealed as well as a globally qualitatively destabilizing role for memory. This is related to the occurrence of period doubling and Neimark–Sacker bifurcations, the latter being of supercritical nature as analytically proved. Endogenous fluctuations and multistability, with consequent loss of predictability in the long run dynamics, are observed.

A multi-way analysis of international bilateral claims

Abstract The paper presents a new methodology aimed at detecting the modularity structure of an evolving weighted directed network, identifying communities and central nodes inside each of them, and tracking their common activity over time. The method is based on tensor factorization and it is applied to the Consolidated Banking Statistic, provided by the Bank of International Settlements. Findings show that data are well represented by three communities. The temporal pattern of each community varies according to the events involving the member nodes, showing a decrease of activities during crisis periods, such as the 2008 financial crisis and the European sovereign debt crisis.

Correction: Discovering SIFIs in Interbank Communities

[This corrects the article DOI: 10.1371/journal.pone.0167781.].

Monetary feedback rules and equilibrium determinacy in pure exchange overlapping generations models

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. A leaning against the wind policy seems to be more desirable from an equilibrium determinacy point of view. On the contrary, a leaning with the wind policy could not be the recommended policy for the Central Bank.

Dynamical Analysis of Cournot Oligopoly Models: Neimark-Sacker bifurcation and related mechanisms

This chapter describes some properties of the nonlinear dynamics emerging from two oligopoly models in discrete time. The target of this chapter is the investigation of some local and global bifurcations which are responsible for the changes in the qualitative behaviors of the trajectories of discrete dynamical systems. Two different kinds of oligopoly models are considered: the first one deals with the presence of differentiated goods and gradient adjustment mechanism, while the second considers the demand function of the producers to be dependent on advertising expenditures and adaptive adjustment of the moves. In both models the standard local stability analysis of the Cournot-Nash equilibrium points is performed, as well as the global bifurcations of both attractors and (their) basins of attraction are investigated.

Maps with Vanishing Denominator and Their Applications

We survey the theoretical findings and a set of applications in several different fields concerning two-dimensional maps characterized by a vanishing denominator. This family of maps, and the related dynamic properties, were originally brought to the attention of the researchers through their appearance in an economic application. Nowadays such maps have also been used in other research areas such as ecology or biology confirming a broader application of the theoretical results about plane maps with vanishing denominator to various research areas.