scholarly journals On the significance of borders: the emergence of endogenous dynamics

2020 ◽  
Author(s):  
Ingrid Kubin ◽  
Laura Gardini
Keyword(s):  
Complex Dynamics ◽  
Capacity Constraint ◽  
Linear Functions ◽  
Prototype Model ◽  
Market Dynamics ◽  
Functional Relationships ◽  
Border Collision Bifurcations ◽  
Economic Reasoning ◽  
Production Decision ◽  
Dynamic Phenomena

Abstract We propose a prototype model of market dynamics in which all functional relationships are linear. We take into account three borders, defined by linear functions, that are intrinsic to the economic reasoning: non-negativity of prices; downward rigidity of capacity (depreciation); and a capacity constraint for the production decision. Given the linear specification, the borders are the only source for the emerging of cyclical and more complex dynamics. In particular, we discuss centre bifurcations, border collision bifurcations and degenerate flip bifurcations—dynamic phenomena the occurrence of which are intimately related to the existence of borders.

scholarly journals Sampling heuristics for active function learning

2021 ◽  
Author(s):  
Rebekah Gelpi ◽  
Nayan Saxena ◽  
George Lifchits ◽  
Daphna Buchsbaum ◽  
Christopher G. Lucas
Keyword(s):  
Extreme Values ◽  
Opportunity To Learn ◽  
Sampling Strategy ◽  
Linear Functions ◽  
Cognitive Resources ◽  
Functional Relationships ◽  
Active Function ◽  
Linear Relationships ◽  
Non Linear ◽  
Simple Sampling

People are capable of learning diverse functional relationships from data; nevertheless, they are most accurate when learning linear relationships, and deviate further from estimating the true relationship when presented with non-linear functions. We investigate whether, when given the opportunity to learn actively, people choose samples in an efficient fashion, and whether better sampling policies improve their ability to learn linear and non-linear functions. We find that, across multiple different function families, people make informative sampling choices consistent with a simple, low-effort policy that minimizes uncertainty at extreme values without requiring adaptation to evidence. While participants were most accurate at learning linear functions, those who more closely adhered to the simple sampling strategy also made better predictions across all non-linear functions. We discuss how the use of this heuristic might reflect rational allocation of limited cognitive resources.

MULTIASSET MARKET DYNAMICS

2004 ◽  
Vol 8 (5) ◽  
pp. 596-616 ◽  
Author(s):  
FRANK H. WESTERHOFF
Keyword(s):  
Stock Prices ◽  
Complex Dynamics ◽  
Asset Markets ◽  
Market Dynamics ◽  
Artificial Markets ◽  
Price Trends ◽  
Random Shocks ◽  
High Degree

This paper explores multiasset market dynamics. We consider a limited number of markets on which two types of agents are active. Fundamentalists specialize in a certain market to gather expertise. Chartists may switch between markets since they use simple extrapolative methods. Specifically, chartists prefer markets that display price trends but that are not too misaligned. The interaction between the traders causes complex dynamics. Even in the absence of random shocks, our artificial markets mimic the behavior of actual asset markets closely. Our model also offers reasons for the high degree of comovements in stock prices observed empirically.

scholarly journals Endogenous Instability in Credit-Constrained Emerging Economies with Leontief Technology

2008 ◽  
Vol 2008 ◽  
pp. 1-16
Author(s):  
Cristiana Mammana ◽  
Elisabetta Michetti
Keyword(s):  
Open Economy ◽  
Emerging Economies ◽  
Complex Dynamics ◽  
Small Open Economy ◽  
Capital Inflows ◽  
Border Collision Bifurcations ◽  
Mobile Capital ◽  
Increase Risk ◽  
Bifurcation And Stability

This work provides a framework to analyze the role of financial development as a source of endogenous instability in emerging economies subject to moral hazard problems. We propose and study a dynamic model describing a small open economy with a tradeable good produced by internationally mobile capital and a country specific input, using Leontief technology. We demonstrate that emerging markets could be endogenously unstable since large capital inflows increase risk and exacerbate asymmetric information problems, according to empirical evidences. Using bifurcation and stability analysis, we describe the properties of the system attractors, we assess the plausibility for complex dynamics and, we find out that border collision bifurcations can emerge due to the fact that the state space is piecewise smooth. As a consequence, when a fixed or periodic point loses its stability, the final dynamics may become suddenly chaotic. This fact may explain how financial crises occurred in emerging economies.

Complex Dynamics of Bouncing Motions at Boundaries and Corners in a Discontinuous Dynamical System

2017 ◽  
Vol 12 (6) ◽  
Author(s):  
Jianzhe Huang ◽  
Albert C. J. Luo
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Vector Fields ◽  
Complex Dynamics ◽  
Singularity Theory ◽  
Local Theory ◽  
Periodic Motions ◽  
Border Collision Bifurcations ◽  
Discontinuous Dynamical System ◽  
Stability And Bifurcations

In this paper, from the local theory of flow at the corner in discontinuous dynamical systems, obtained are analytical conditions for switching impact-alike chatter at corners. The objective of this investigation is to find the dynamics mechanism of border-collision bifurcations in discontinuous dynamical systems. Multivalued linear vector fields are employed, and generic mappings are defined among boundaries and corners. From mapping structures, periodic motions switching at the boundaries and corners are determined, and the corresponding stability and bifurcations of periodic motions are investigated by eigenvalue analysis. However, the grazing and sliding bifurcations are determined by the local singularity theory of discontinuous dynamical systems. From such analytical conditions, the corresponding parameter map is developed for periodic motions in such a multivalued dynamical system in the single domain with corners. Numerical simulations of periodic motions are presented for illustrations of motions complexity and catastrophe in such a discontinuous dynamical system.

scholarly journals Complex Dynamics in a Growth Model with Corruption in Public Procurement

2011 ◽  
Vol 2011 ◽  
pp. 1-27 ◽  
Author(s):  
Serena Brianzoni ◽  
Raffaella Coppier ◽  
Elisabetta Michetti
Keyword(s):  
Economic Growth ◽  
Multiple Equilibria ◽  
Complex Dynamics ◽  
Public Procurement ◽  
Point Of View ◽  
Border Collision Bifurcations ◽  
Long Run ◽  
Analytical Point ◽  
Productive Process ◽  
Local And Global Bifurcations

We study the relationship between corruption in public procurement and economic growth within the Solow framework in discrete time, while assuming that the public good is an input in the productive process and that the State fixes a monitoring level on corruption. The resulting model is a bidimensional triangular dynamic system able to generate endogenous fluctuations for certain values of some relevant parameters. We study the model from the analytical point of view and find that multiple equilibria with nonconnected basins are likely to emerge. We also perform a stability analysis and prove the existence of a compact global attractor. Finally, we focus on local and global bifurcations causing the transition to more and more complex asymptotic dynamics. In particular, as our map is nondifferentiable in a subset of the states space, we show that border collision bifurcations occur. Several numerical simulations support the analysis. Our study aims at demonstrating that no long-run equilibria with zero corruption exist and, furthermore, that periodic or aperiodic fluctuations in economic growth are likely to emerge. As a consequence, the economic system may be unpredictable or structurally unstable.

scholarly journals Analysis and Control of the Complex Dynamics of a Multimarket Cournot Investment Game with Bounded Rationality

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
LiuWei Zhao
Keyword(s):  
Demand Function ◽  
Complex Dynamics ◽  
Delayed Feedback Control ◽  
Flip Bifurcation ◽  
Bifurcation And Chaos ◽  
Stability And Instability ◽  
The Stability ◽  
And Control ◽  
Time Delayed Feedback ◽  
Dynamic Phenomena

A dynamic multimarket Cournot model is introduced based on a specific inverse demand function. Puu’s incomplete information approach, as a realistic method, is used to contract the corresponding dynamical model under this function. Therefore, some stability analysis is carried out on the model to detect the stability and instability conditions of the system’s Nash equilibrium. Based on the analysis, some dynamic phenomena such as bifurcation and chaos are found. Numerical simulations are used to provide experimental evidence for the complicated behaviors of the system evolution. It is observed that the equilibrium of the system can lose stability via flip bifurcation or Neimark-Sacker bifurcation and time-delayed feedback control is used to stabilize the chaotic behaviors of the system.

Predictive Error Reduction and the Twofold Nature of Aesthetic Pleasure

2016 ◽  
Vol 4 (4) ◽  
pp. 327-338 ◽  
Author(s):  
Gianluca Consoli
Keyword(s):  
Common Core ◽  
Subjective Experience ◽  
Aesthetic Experience ◽  
Complex Dynamics ◽  
Predictive Coding ◽  
Aesthetic Perception ◽  
Perceptual Inference ◽  
Functional Relationships ◽  
Aesthetic Pleasure ◽  
Points Of View

Recently, the predictive coding account of perceptual inference has been extended to visual aesthetic experience, in particular to the experience enabled by artworks that challenge habitual predictions and ordinary perceptual routines. By virtue of its dynamical approaches, the predictive coding account of visual art catches aesthetic perception and evaluation as a complex dynamics of intertwined perpetual, affective and cognitive processes. On the basis of some of the most relevant findings of these dynamical approaches, I argue that aesthetic pleasure has a complex and original nature, something akin to a twofold nature. Specifically, I argue that aesthetic pleasure is twofold from different points of view: (a) it represents the connection of two very different functions, namely anticipation and reaction; (b) its different forms share a specific common core; however, this common core can be instantiated by very different functional relationships of causes and effects; (c) aesthetic pleasure represents a positive affective appraisal accompanying first-order elaboration, but it can also co-activate negative subjective experience, mixing together positive and negative affect.

Capacitated Assortment Optimization: Hardness and Approximation

2021 ◽  
Author(s):  
Antoine Désir ◽  
Vineet Goyal ◽  
Jiawei Zhang
Keyword(s):  
Large Class ◽  
Logit Model ◽  
Multinomial Logit Model ◽  
Multinomial Logit ◽  
Choice Models ◽  
Capacity Constraint ◽  
Linear Functions ◽  
Nested Logit ◽  
Assortment Optimization ◽  
Unconstrained Problem

Assortment optimization is an important problem arising in various applications. In many practical settings, the assortment is subject to a capacity constraint. In “Capacitated Assortment Optimization: Hardness and Approximation,” Désir, Goyal, and Zhang study the capacitated assortment optimization problem. The authors first show that adding a general capacity constraint makes the problem NP-hard even for the simple multinomial logit model. They also show that under the mixture of multinomial logit model, even the unconstrained problem is hard to approximate within any reasonable factor when the number of mixtures is not constant. In view of these hardness results, the authors present near-optimal algorithms for a large class of parametric choice models including the mixture of multinomial logit, Markov chain, nested logit, and d-level nested logit choice models. In fact, their approach extends to a large class of objective functions that depend only on a small number of linear functions.

MODELING AND COMPLEXITY STUDY OF OUTPUT GAME AMONG MULTIPLE OLIGOPOLISTIC MANUFACTURERS IN THE SUPPLY CHAIN SYSTEM

2013 ◽  
Vol 23 (03) ◽  
pp. 1350038 ◽  
Author(s):  
GUANHUI WANG ◽  
JUNHAI MA
Keyword(s):  
Supply Chain ◽  
Information Asymmetry ◽  
Complex Dynamics ◽  
Great Influence ◽  
Supply Chain System ◽  
Chain System ◽  
Proposed Model ◽  
Adjustment Speed ◽  
The Impact ◽  
Production Decision

Supply chain system is a complex system in which node enterprises play important roles and exert great influence. This paper proposes an output game model among multiple oligopolistic manufacturers under the circumstances of information asymmetry and analyzes the Nash equilibrium in the model. The manufacturers usually base their production decision making on the volume of order from distributors and the production decisions made by other manufacturers. They also suitably adjust the output. If the adjustment speed accelerates, chaos will be caused in the manufacturers' production decision. This paper analyzes the proposed model from a perspective of complex dynamics and discusses the impact of system parameter on the complexity of this discrete chaotic system. The measures to retain chaos among manufacturers are suggested.

Sign in / Sign up

Export Citation Format

Share Document