Systemic risk on different interbank network topologies

In this paper we develop an interbank market with heterogeneous financial institutions that enter into lending agreements on different network structures. Credit relationships (links) evolve endogenously via a fitness mechanism based on agents’ performance. By changing the agent’s trust on its neighbor’s performance, interbank linkages self-organize themselves into very different network architectures, ranging from random to scale-free topologies. We study which network architecture can make the financial system more resilient to random attacks and how systemic risk spreads over the network. To perturb the system, we generate a random attack via a liquidity shock. The hit bank is not automatically eliminated, but its failure is endogenously driven by its incapacity to raise liquidity in the interbank network. Our analysis shows that a random financial network can be more resilient than a scale free one in case of agents’ heterogeneity.     

Partner selection method in cooperative spatial modulation (CSM) system

In this work, to achieve higher capacity, spatial modulation (SM) is utilized in a cooperative scheme in two different models of Cooperative SM, where SM is applied either at the source or the selected partner through an antenna array. A theoretical model of SM capacity is defined based on closed form lower and upper bound of the SM capacity. Based on the theoretical analysis of the channel capacity in both CSM systems the simplest and easier to implement selection criteria have been suggested to select a single partner to maximize CSM capacity. The CSM system in which SM is applied through the partner’s antenna array is providing significant enhancement over the other CSM model and cooperative multiple-input-multiple-output (CO-MIMO) networks based on multiple partners. Moreover, the system with a single randomly selected partner equipped with four antennas, behaves similarly as the best configuration of CO-MIMO based on the cooperation of four partners with the computational complexity linearly increases with the number of available partners to help. All of the theoretical findings are verified through simulation studies.     

Individual and group dynamics in purchasing activity

As a major part of the daily operation in an enterprise, purchasing frequency is in constant change. Recent approaches on the human dynamics can provide some new insights into the economic behavior of companies in the supply chain. This paper captures the attributes of creation times of purchase orders to an individual vendor, as well as to all vendors, and further investigates whether they have some kind of dynamics by applying logarithmic binning to the construction of distribution plots. It’s found that the former displays a power-law distribution with approximate exponent 2.0, while the latter is fitted by a mixture distribution with both power-law and exponential characteristics. Obviously, two distinctive characteristics are presented for the interval time distribution from the perspective of individual dynamics and group dynamics. Actually, this mixing feature can be attributed to the fitting deviations as they are negligible for individual dynamics, but those of different vendors are cumulated and then lead to an exponential factor for group dynamics. To better describe the mechanism generating the heterogeneity of the purchase order assignment process from the objective company to all its vendors, a model driven by product life cycle is introduced, and then the analytical distribution and the simulation result are obtained, which are in good agreement with the empirical data.     

Evolutionary games on scale-free networks with a preferential selection mechanism

Considering the heterogeneity of individuals’ influence in the real world, we introduce a preferential selection mechanism to evolutionary games (the Prisoner’s Dilemma Game and the Snowdrift Game) on scale-free networks and focus on the cooperative behavior of the system. In every step, each agent chooses an individual from all its neighbors with a probability proportional to k^α indicating the influence of the neighbor, where k is the degree. Simulation results show that the cooperation level has a non-trivial dependence on α. To understand the effect of preferential selection mechanism on the evolution of the system, we investigate the time series of the cooperator frequency in detail. It is found that the cooperator frequency is greatly influenced by the initial strategy of hub nodes when α>0. This observation is confirmed by investigating the system behavior when some hub nodes’ strategies are fixed.     

Hierarchical quantum-information splitting

We present a scheme for asymmetric quantum-information splitting, where a sender distributes asymmetrically a quantum secret (quantum state) to distant partners in a network. The asymmetric distribution leads to that the partners have different powers to recover the sender’s secret. In other words, their authorities for getting the secret are hierarchized. In the scheme, the partners do not need to make any nonlocal operation. The scheme can also be modified to implement threshold-controlled teleportation.     

Promoting cooperation by local contribution under stochastic win-stay-lose-shift mechanism

We introduce a stochastic win-stay-lose-shift (WSLS) mechanism into evolutionary Prisoner’s Dilemma on small-world networks. At each time step, after playing with all its immediate neighbors, each individual gets a score to evaluate its performance in the game. The score is a linear combination of an individual’s total payoff (i.e., individual gain from the group) and local contribution to its neighbors (i.e., individual donation to the group). If one’s actual score is not larger than its desired score aspiration, it switches current strategy to the opposite one with the probability depending on the difference between the two scores. Under this stochastic WSLS regime, we assume that each focal individual gains its fixed score aspiration under the condition of full cooperation in its neighborhood, and find that cooperation is significantly enhanced under some certain parameters of the model by studying the evolution of cooperation. We also explore the influences of different values of learning rate and intensity of deterministic switch on the evolution of cooperation. Simulation results show that cooperation level monotonically increases with the relative weight of the local contribution to the score. For much low intensity of deterministic switch, cooperation is to a large extent independent of learning rate, and full cooperation can be reached when relative weight is not less than 0.5. Otherwise, cooperation level is affected by the value of learning rate. Besides, we find that the cooperation level is not sensitive to the topological parameters. To explain these simulation results, we provide corresponding analytical results based on mean-field approximation, and find out that simulation results are in close agreement with the analytical ones. Our work may be helpful in understanding the cooperative behavior in social systems based on this stochastic WSLS mechanism.     

Elimination mechanism promotes cooperation in coevolutionary prisoner’s dilemma games

We propose an elimination mechanism in the study of the evolutionary prisoner’s dilemma games on evolving networks. It assumes that after each round of playing, players whose payoffs are below a certain threshold will be eliminated from the game and the same number of new nodes will be added to the network to maintain the size of the network constant. Numerical results show that moderate values of elimination threshold can result in a maximum cooperation level in the evolutionary prisoner’s dilemma game. Moreover, the elimination mechanism can make the network structure evolve into a high heterogeneity in degree distribution, which is considered to be helpful in promoting cooperation in evolutionary games. The present study may provide new insight for understanding the evolution of cooperation in light of the law ‘survival of the fittest’ in nature.     

Scaling theory of polymer thermodiffusion

The motion of a linear polymer chain in a good solvent under a temperature gradient is examined theoretically by breaking up the flexible chain into Brownian rigid rods, and writing down an equation of motion for each rod. The motion is driven by two forces. The first one is Waldmann’s thermophoretic force (stemming from the departure of the solvent’s molecular-velocity distribution from Maxwell’s equilibrium distribution) which here is extrapolated to a dense medium. The second force is due to the fact that the viscous friction varies with position owing to the temperature gradient, which brings an important correction to the Stokes law of friction. We use scaling considerations relying upon disparate length scales and omitting non-universal numerical prefactors. The present scaling theory is compared with recent experiments on the thermodiffusion of polymers and is shown to account for (i) the existence of both signs of the thermodiffusion coefficient of long chains, (ii) the order of magnitude of the coefficient, (iii) its independence of the chain length in the high-polymer limit and (iv) its dependence on the solvent viscosity.     

A multi-agent dynamic model based on different kinds of bequests

We investigate how wealth transfer that happens at the end of an agent’s life affects its final distribution based on a multi-agent dynamic model. We discuss two kinds of wealth transfers: to a single agent and to charities. The first kind of bequest is common in our realistic world and is always regarded by the public as unequal inheritance. The bequests to charities will be gathered and then equally redistributed among the survivors in our model. We find that when all the decedents choose the second kind of bequest, the final distribution is the Gibbs exponential function. When all the decedents choose the first kind of bequest, the result is condensation that a single individual accumulates all the available wealth. When an increasing portion of decedents choose the one-heir bequests, the exponential distribution evolves towards a power law shape (accompanied by deteriorating inequality). This shape firstly appears from the intermediate range of wealth and extends towards the top end of the simulated distribution, while the distribution remains exponential for high values of the wealth. At the same time, the Gini coefficient increases and the wealth accumulation becomes serious. At last, we analyze the source of the inequality. We find that not only unequal inheritances, but also equal division of the charity’s wealth can relatively contribute to an inequality of wealth distribution.     

The effect of asymmetric payoff mechanism on evolutionary networked prisoner’s dilemma game

In social and biological systems, there are obvious individual divergence and asymmetric payoff phenomenon due to the strength, power and influence differences. In this paper, we introduce an asymmetric payoff mechanism to evolutionary Prisoner’s Dilemma Game (PDG) on scale-free networks. The co-effects of individual diversity and asymmetric payoff mechanism on the evolution of cooperation and the wealth distribution under different updating rules are investigated. Numerical results show that the cooperation is highly promoted when the hub nodes are favored in the payoff matrix, which seems to harm the interest of the majority. But the inequality of social wealth distribution grows with the unbalanced payoff rule. However, when the node difference is eliminated in the learning strategy, the asymmetric payoff rule will not affect the cooperation level. Our work may sharpen the understanding of the cooperative behavior and wealth inequality in the society.     

The significant digit law in statistical physics

The occurrence of the nonzero leftmost digit, i.e., 1,2,…,9, of numbers from many real world sources is not uniformly distributed as one might naively expect, but instead, the nature favors smaller ones according to a logarithmic distribution, named Benford’s law. We investigate three kinds of widely used physical statistics, i.e., the Boltzmann-Gibbs (BG) distribution, the Fermi-Dirac (FD) distribution, and the Bose-Einstein (BE) distribution, and find that the BG and FD distributions both fluctuate slightly in a periodic manner around Benford’s distribution with respect to the temperature of the system, while the BE distribution conforms to it exactly whatever the temperature is. Thus Benford’s law seems to present a general pattern for physical statistics and might be even more fundamental and profound in nature. Furthermore, various elegant properties of Benford’s law, especially the mantissa distribution of data sets, are discussed.     

Trading model with pair pattern strategies

A simple trading model based on pair pattern strategy space with holding periods is proposed. Power-law behavior is observed for the return variance σ², the price impact H and the predictability K for both models, with linear and square root impact functions. The sum of the traders’ wealth displays a positive value for the model with a square root price impact function, and a qualitative explanation is given based on the observation of the conditional excess demand 〈A|u〉. The cumulative wealth distribution also obeys a power-law behavior with an exponent close to that of real markets. An evolutionary trading model is further proposed. The elimination mechanism effectively changes the behavior of traders, and a power-law behavior is observed in the measure of zero return distribution P(r=0). The trading model with other types of traders, e.g., traders with the MG’s strategies and producers, are also carefully studied.     

Conditional strategies in iterated quantum games

Iterated bipartite quantum games are implemented in terms of the discrete-time quantum walk on the line. Our proposal allows for conditional strategies, as two rational agents make a choice from a restricted set of two-qubit unitary operations. We discuss how several classical strategies are related to families of quantum strategies. A quantum version of the well known Prisoner’s Dilemma bipartite game, in which both players use mixed strategies, is presented as a specific example.     

The ambivalent effect of lattice structure on a spatial game

The evolution of cooperation is studied in lattice-structured populations, in which each individual who adopts one of the following strategies ‘always defect’ (ALLD), ‘tit-for-tat’ (TFT), and ‘always cooperate’ (ALLC) plays the repeated Prisoner’s Dilemma game with its neighbors according to an asynchronous update rule. Computer simulations are applied to analyse the dynamics depending on major parameters. Mathematical analyses based on invasion probability analysis, mean-field approximation, as well as pair approximation are also used. We find that the lattice structure promotes the evolution of cooperation compared with a non-spatial population, this is also confirmed by invasion probability analysis in one dimension. Meanwhile, it also inhibits the evolution of cooperation due to the advantage of being spiteful, which indicates the key role of specific life-history assumptions. Mean-field approximation fails to predict the outcome of computer simulations. Pair approximation is accurate in two dimensions but fails in one dimension.     

An experimental and theoretical model of children’s search behavior in relation to target conspicuity and spatial distribution

This work explores search trajectories of children attempting to find targets distributed on a playing field. This task, of ludic nature, was developed to test the effect of conspicuity and spatial distribution of targets on the searcher’s performance. The searcher’s path was recorded by a Global Positioning System (GPS) device attached to the child’s waist. Participants were not rewarded nor their performance rated. Variation in the conspicuity of the targets influenced search performance as expected; cryptic targets resulted in slower searches and longer, more tortuous paths. Extracting the main features of the paths showed that the children: (1) paid little attention to the spatial distribution and at least in the conspicuous condition approximately followed a nearest neighbor pattern of target collection, (2) were strongly influenced by the conspicuity of the targets. We implemented a simple statistical model for the search rules mimicking the children’s behavior at the level of individual (coarsened) steps. The model reproduced the main features of the children’s paths without the participation of memory or planning.     

Mean-field approximation for two- and three-person Prisoner’s Dilemmas

We consider the mean-field approximation (MFA) to the system of interacting agents playing two- and three-person Prisoner’s Dilemma games (2-PD and 3-PD). The agents have three available strategies: All-C, All-D, and a third one, which we choose in various ways. Long-time distribution of the strategies is compared for both games. The latter game admits coexistence of larger number of strategies in the long run. In the case of external pressure for cooperation, more pressure is in general necessary for 3-PD than for 2-PD to guarantee cooperation for almost all initial compositions of the strategies. Results for different types of tit-for-tat strategies for 3-PD are discussed. Unlike the 2-PD case, the more forgiving tit-for-tat strategy can survive in the long run in 3-PD.     

A network model of the interbank market

This work introduces a network model of an interbank market based on interbank credit lending relationships. It generates some network features identified through empirical analysis. The critical issue to construct an interbank network is to decide the edges among banks, which is realized in this paper based on the interbank’s degree of trust. Through simulation analysis of the interbank network model, some typical structural features are identified in our interbank network, which are also proved to exist in real interbank networks. They are namely, a low clustering coefficient and a relatively short average path length, community structures, and a two-power-law distribution of out-degree and in-degree.     

Properties of wealth distribution in multi-agent systems of a complex network

We present a simple model for examining the wealth distribution with agents playing evolutionary games (the Prisoners’ Dilemma and the Snowdrift Game) on complex networks. Pareto’s power law distribution of wealth (from 1897) is reproduced on a scale-free network, and the Gibbs or log-normal distribution for a low income population is reproduced on a random graph. The Pareto exponents of a scale-free network are in agreement with empirical observations. The Gini coefficient of an ER random graph shows a sudden increment with game parameters. We suggest that the social network of a high income group is scale-free, whereas it is more like a random graph for a low income group.     

Testing the Goodwin growth-cycle macroeconomic dynamics in Brazil

This paper discusses the empirical validity of Goodwin’s (1967) macroeconomic model of growth with cycles by assuming that the individual income distribution of the Brazilian society is described by the Gompertz–Pareto distribution (GPD). This is formed by the combination of the Gompertz curve, representing the overwhelming majority of the population (∼99%), with the Pareto power law, representing the tiny richest part (∼1%). In line with Goodwin’s original model, we identify the Gompertzian part with the workers and the Paretian component with the class of capitalists. Since the GPD parameters are obtained for each year and the Goodwin macroeconomics is a time evolving model, we use previously determined, and further extended here, Brazilian GPD parameters, as well as unemployment data, to study the time evolution of these quantities in Brazil from 1981 to 2009 by means of the Goodwin dynamics. This is done in the original Goodwin model and an extension advanced by Desai et al. (2006). As far as Brazilian data is concerned, our results show partial qualitative and quantitative agreement with both models in the studied time period, although the original one provides better data fit. Nevertheless, both models fall short of a good empirical agreement as they predict single center cycles which were not found in the data. We discuss the specific points where the Goodwin dynamics must be improved in order to provide a more realistic representation of the dynamics of economic systems.     

From shape to randomness: A classification of Langevin stochasticity

The Langevin equation–perhaps the most elemental stochastic differential equation in the physical sciences–describes the dynamics of a random motion driven simultaneously by a deterministic potential field and by a stochastic white noise. The Langevin equation is, in effect, a mechanism that maps the stochastic white-noise input to a stochastic output: a stationary steady state distribution in the case of potential wells, and a transient extremum distribution in the case of potential gradients. In this paper we explore the degree of randomness of the Langevin equation’s stochastic output, and classify it à la Mandelbrot into five states of randomness ranging from “infra-mild” to “ultra-wild”. We establish closed-form and highly implementable analytic results that determine the randomness of the Langevin equation’s stochastic output–based on the shape of the Langevin equation’s potential field.