Successive one-sided Hodrick-Prescott filter with incremental filtering algorithm for nonlinear economic time series

We propose a successive one-sided Hodrick-Prescott (SOHP) filter from multiple time scale decomposition perspective to derive trend estimate for a time series. The idea is to apply the one-sided HP (OHP) filter recursively on the updated cyclical component to extract the trend residual on multiple time scales, thereby to improve the trend estimate. To address the issue of optimization with a moving horizon as that of the SOHP filter, we present an incremental HP filtering algorithm, which greatly simplifies the involved inverse matrix operation and reduces the computational demand of the basic HP filtering. Actually, the new algorithm also applies effectively to other HP-type filters, especially for large-size or expanding data scenario. Numerical examples on real economic data show the better performance of the SOHP filter in comparison with other known HP-type filters

Swarm splitting and multiple targets seeking in multi-agent dynamic systems

This paper presents an approach to swarm split control of a system of multi-agents with limited sensing capabilities. The control scheme utilizes the competition between the inter-agent repulsive and attractive interactions and can split one cohesive swarm into several clustered subswarms along the direction perpendicular to the common heading direction of agents. The cohesion and collision avoidance of agents are ensured by long-range attractive and short-range repulsive interactions between agents. The split of swarm is achieved via a Gaussian-like repulsive interaction between agents, whose magnitude affects the number of subswarm clusters and can be designed to control the swarm splitting/rejoining maneuver, and whose maximum location mainly affects the relative distance between clustered subswarms. The split control law is also applied to double targets seeking task in a swarm of 100 agents, and simulations are worked out. These results are of interest in understanding and utilizing the splitting dynamics in swarms of agents with local coupling interactions.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000295049105038&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Automation & Control SystemsEngineering, Electrical & ElectronicEICPCI-S(ISTP)

Resolution of the stochastic strategy spatial prisoner's dilemma by means of particle swarm optimization

We study the evolution of cooperation among selfish individuals in the stochastic strategy spatial prisoner's dilemma game. We equip players with the particle swarm optimization technique, and find that it may lead to highly cooperative states even if the temptations to defect are strong. The concept of particle swarm optimization was originally introduced within a simple model of social dynamics that can describe the formation of a swarm, i.e., analogous to a swarm of bees searching for a food source. Essentially, particle swarm optimization foresees changes in the velocity profile of each player, such that the best locations are targeted and eventually occupied. In our case, each player keeps track of the highest payoff attained within a local topological neighborhood and its individual highest payoff. Thus, players make use of their own memory that keeps score of the most profitable strategy in previous actions, as well as use of the knowledge gained by the swarm as a whole, to find the best available strategy for themselves and the society. Following extensive simulations of this setup, we find a significant increase in the level of cooperation for a wide range of parameters, and also a full resolution of the prisoner's dilemma. We also demonstrate extreme efficiency of the optimization algorithm when dealing with environments that strongly favor the proliferation of defection, which in turn suggests that swarming could be an important phenomenon by means of which cooperation can be sustained even under highly unfavorable conditions. We thus present an alternative way of understanding the evolution of cooperative behavior and its ubiquitous presence in nature, and we hope that this study will be inspirational for future efforts aimed in this direction.Comment: 12 pages, 4 figures; accepted for publication in PLoS ON

Adaptive Evolution of Cooperation through Darwinian Dynamics in Public Goods Games

The linear or threshold Public Goods game (PGG) is extensively accepted as a paradigmatic model to approach the evolution of cooperation in social dilemmas. Here we explore the significant effect of nonlinearity of the structures of public goods on the evolution of cooperation within the well-mixed population by adopting Darwinian dynamics, which simultaneously consider the evolution of populations and strategies on a continuous adaptive landscape, and extend the concept of evolutionarily stable strategy (ESS) as a coalition of strategies that is both convergent-stable and resistant to invasion. Results show (i) that in the linear PGG contributing nothing is an ESS, which contradicts experimental data, (ii) that in the threshold PGG contributing the threshold value is a fragile ESS, which cannot resist the invasion of contributing nothing, and (iii) that there exists a robust ESS of contributing more than half in the sigmoid PGG if the return rate is relatively high. This work reveals the significant effect of the nonlinearity of the structures of public goods on the evolution of cooperation, and suggests that, compared with the linear or threshold PGG, the sigmoid PGG might be a more proper model for the evolution of cooperation within the well-mixed population

Action Being Character: A Promising Perspective on the Solution Concept of Game Theory

The inconsistency of predictions from solution concepts of conventional game theory with experimental observations is an enduring question. These solution concepts are based on the canonical rationality assumption that people are exclusively self-regarding utility maximizers. In this article, we think this assumption is problematic and, instead, assume that rational economic agents act as if they were maximizing their implicit utilities, which turns out to be a natural extension of the canonical rationality assumption. Implicit utility is defined by a player's character to reflect his personal weighting between cooperative, individualistic, and competitive social value orientations. The player who actually faces an implicit game chooses his strategy based on the common belief about the character distribution for a general player and the self-estimation of his own character, and he is not concerned about which strategies other players will choose and will never feel regret about his decision. It is shown by solving five paradigmatic games, the Dictator game, the Ultimatum game, the Prisoner's Dilemma game, the Public Goods game, and the Battle of the Sexes game, that the framework of implicit game and its corresponding solution concept, implicit equilibrium, based on this alternative assumption have potential for better explaining people's actual behaviors in social decision making situations

New necessary and sufficient conditions for absolute stability of neural networks

This paper presents new necessary and sufficient conditions for absolute stability of asymmetric neural networks. The main result is based on a solvable Lie algebra condition, which generalizes existing results for symmetric and normal neural networks. An exponential convergence estimate of the neural networks is also obtained. Further, it is demonstrated how to generate larger sets of weight matrices for absolute stability of the neural networks from known normal weight matrices through simple procedures. The approach is nontrivial in the sense that non-normal matrices can possibly be contained in the resulting weight matrix set. And the results also provide finite checking for robust stability of neural networks in the presence of parameter uncertainties

Optimal control of logical control network with noisy inputs

This paper considers the optimal control of the logical control network with noisy inputs. The optimal control problem concerning the minority game (MG) with mixed population is formulated. In the game the producers are represented by the states of nodes in the Boolean control network, the speculators and the noise traders are identified as the controllable inputs and the noisy inputs of the nodes. The speculators aim at achieving the maximum profits but the noise traders make the issue complicated. The Boolean logical variables and functions are transformed into the algebraic form by using the recently developed Semi-tensor Product of matrices technique. In this manner, we calculate the optimal cycles that lead to the optimal control and analyze the effect of noisy input based on the definition of score. Although we develop our method within the context of MG, it actually can be applied to other general cases of logical networks with noisy inputs. To avoid the computational expensive calculation of the optimal cycles for all states in the input-state network, we further propose a simplified algorithm with formulas for large scale MG case. An illustrative example is included to show the validity and efficiency of the simplified algorithm.Automation & Control SystemsEngineering, Electrical & ElectronicEICPCI-S(ISTP)

New necessary and sufficient conditions for absolute stability of neural networks

This paper presents new necessary and sufficient conditions for absolute stability of neural networks. The main result is based on a solvable Lie algebra condition, which generalizes existing results for symmetric and normal neural networks. It also demonstrates how to generate larger sets of weight matrices for absolute stability of the neural networks from known normal weight matrices through simple procedures. The approach is nontrivial in the sense that it is applicable to a class of neural networks with non-normal weight matrices