Agent‐based simulation of an N‐person game with parabolic payoff functions

We report computer simulation experiments based on our agent‐based simulation tool to model a new N‐person game based on John Conway's Game of Life. The individual agents may choose between two behavior options: cooperation or defection. The payoff (reward/penalty) functions are given as two parabolas: one for each option. After a certain number of iterations, the behavior of the agents stabilizes to either a constant value or oscillates around such a value. The simulation's goal is to investigate the effects of intermediate behavior on a society of agents. We have performed a systematic investigation of this game for all six possible cases of the mutual positions of parabolic payoff functions crossing each other at two points: x = 0.3 and 0.7 where x is the ratio of the cooperation choice to the total number of agents in the agent's neighborhood. The global ratios X(t) of the total number of cooperators in the entire array of agents as functions of time (iterations) and the solutions of the game X_final as functions of X₀ were observed for each case for Pavlovian, greedy, and conformist agents. The solutions have predictable tendencies only when the neighborhood is the entire array of greedy or conformist agents. In all other cases unexpected properties emerge. © 2009 Wiley Periodicals, Inc. Complexity, 2010     

Agent‐based computational models and generative social science

This article argues that the agent‐based computational model permits a distinctive approach to social science for which the term “generative” is suitable. In defending this terminology, features distinguishing the approach from both “inductive” and “deductive” science are given. Then, the following specific contributions to social science are discussed: The agent‐based computational model is a new tool for empirical research. It offers a natural environment for the study of connectionist phenomena in social science. Agent‐based modeling provides a powerful way to address certain enduring—and especially interdisciplinary—questions. It allows one to subject certain core theories—such as neoclassical microeconomics—to important types of stress (e.g., the effect of evolving preferences). It permits one to study how rules of individual behavior give rise—or “map up”—to macroscopic regularities and organizations. In turn, one can employ laboratory behavioral research findings to select among competing agent‐based (“bottom up”) models. The agent‐based approach may well have the important effect of decoupling individual rationality from macroscopic equilibrium and of separating decision science from social science more generally. Agent‐based modeling offers powerful new forms of hybrid theoretical‐computational work; these are particularly relevant to the study of non‐equilibrium systems. The agent‐based approach invites the interpretation of society as a distributed computational device, and in turn the interpretation of social dynamics as a type of computation. This interpretation raises important foundational issues in social science—some related to intractability, and some to undecidability proper. Finally, since “emergence” figures prominently in this literature, I take up the connection between agent‐based modeling and classical emergentism, criticizing the latter and arguing that the two are incompatible. © 1999 John Wiley & Sons, Inc.     

The effects of mental model formation on group decision making: An agent‐based simulation

We investigated dynamics of group decision making on complex problems when agents can form mental models of others from discussion history. Results indicated that as the agents' memory capacity increases, the group reaches superficial consensus more easily. Surprisingly, however, the shared mental model of the problem develops only within a limited area of the problem space, because incorporating knowledge from others into one's own knowledge quickly creates local agreement on where relevant solutions are, leaving other potentially useful solutions beyond the scope of discussion. The mechanisms stifling group‐level exploration and their implications for decision making research are discussed. © 2010 Wiley Periodicals, Inc. Complexity 16: 49–57, 2011     

Multiscale agent‐based consumer market modeling

Consumer markets have been studied in great depth, and many techniques have been used to represent them. These have included regression‐based models, logit models, and theoretical market‐level models, such as the NBD‐Dirichlet approach. Although many important contributions and insights have resulted from studies that relied on these models, there is still a need for a model that could more holistically represent the interdependencies of the decisions made by consumers, retailers, and manufacturers. When the need is for a model that could be used repeatedly over time to support decisions in an industrial setting, it is particularly critical. Although some existing methods can, in principle, represent such complex interdependencies, their capabilities might be outstripped if they had to be used for industrial applications, because of the details this type of modeling requires. However, a complementary method—agent‐based modeling—shows promise for addressing these issues. Agent‐based models use business‐driven rules for individuals (e.g., individual consumer rules for buying items, individual retailer rules for stocking items, or individual firm rules for advertizing items) to determine holistic, system‐level outcomes (e.g., to determine if brand X's market share is increasing). We applied agent‐based modeling to develop a multi‐scale consumer market model. We then conducted calibration, verification, and validation tests of this model. The model was successfully applied by Procter & Gamble to several challenging business problems. In these situations, it directly influenced managerial decision making and produced substantial cost savings. © 2010 Wiley Periodicals, Inc. Complexity, 2010     

(CMMSE paper) A finite‐difference model for indoctrination dynamics

In this work, a system of non‐linear difference equations is employed to model the opinion dynamics between a small group of agents (the target group) and a very persuasive agent (the indoctrinator). Two scenarios are investigated: the indoctrination of a homogeneous target group, in which each agent grants the same weight to his (or her) partner's opinion and the indoctrination of a heterogenous target group, in which each agent may grant a different weight to his or her partner's opinion. Simulations are performed to study the required times by the indoctrinator to convince a group. Initially, these groups are in a consensus about a doctrine different to that of the ideologist. The interactions between the agents are pairwise.     

Alcohol consumption among college students: An agent‐based computational simulation

An agent‐based C++ program was developed to model student drinking. Student‐agents interact with each other and are randomly subjected to good or bad drinking experiences, to stories of other students' experiences, and to peer pressure. The program outputs drinking rates as functions of time based on various input parameters. The intent of this project is to simulate alcohol use, eventually adding other drugs, and possibly creating a simulation game for use as an educational tool. © 2008 Wiley Periodicals, Inc. Complexity, 2009     

A systematic analysis of the N‐person chicken game

We report computer simulation experiments based on our agent‐based simulation tool to model the multiperson Chicken dilemma game for the case when the agents are greedy simpletons who imitate the action of that of their neighbors who received the highest payoff for its previous action. The individual agents may cooperate with each other for the collective interest or may defect, i.e., pursue their selfish interests only. After a certain number of iterations the proportion of cooperators stabilizes to either a constant value or oscillates around such a value. The payoff (reward/penalty) functions are given as two straight lines: one for the cooperators and another for the defectors. The payoff curves are functions of the ratio of cooperators to the total number of agents. Even for linear payoff functions, we have four free parameters that determine the payoff functions that have the following properties: (1) Both payoff functions increase with the increasing number of cooperators. (2) In the region of low cooperation the cooperators have a higher reward than the defectors. (3) When the cooperation rate is high, there is a higher payoff for defecting behavior than for cooperating behavior. (4) As a consequence, the slope of the D function is greater than that of the C function and the two payoff functions intersect. (5) All agents receive a lower payoff if all defect than if all cooperate. We have investigated the behavior of the agents systematically. The results show that the solutions have predictable tendencies but they are nontrivial and quite irregular. The solutions show drastic changes in the parameter ranges 0.6 ≤ R ≤ 0.65 for all values of S and 0 ≤ S ≤ 0.2 when R < 0.6 (R is the reward for mutual cooperation and S is the sucker's payoff to a lonely cooperator). © 2010 Wiley Periodicals, Inc. Complexity, 2010     

Multistrain edge‐based compartmental model on networks

Multistrain diseases, which are infected through individual contacts, pose severe public health threat nowadays. In this paper, we build competitive and mutative two‐strain edge‐based compartmental models using probability generation function (PGF) and pair approximation (PA). Both of them are ordinary differential equations. Their basic reproduction numbers and final size formulas are explicitly derived. We show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We further consider competitive and mutative multistrain diseases spreading models and compute their basic reproduction numbers. We perform numerical simulations that show some dynamical properties of the competitive and mutative two‐strain models.     

Global well‐posedness for free boundary problem of the Oldroyd‐B model fluid flow

In this paper, we prove the global well‐posedness of non‐Newtonian viscous fluid flow of the Oldroyd‐B model with free surface in a bounded domain of N‐dimensional Euclidean space . The assumption of the problem is that the initial data are small enough and orthogonal to rigid motions. Copyright © 2015 John Wiley & Sons, Ltd.     

An efficient splitting technique for two‐layer shallow‐water model

We consider the numerical approximation of the weak solutions of the two‐layer shallow‐water equations. The model under consideration is made of two usual one‐layer shallow‐water model coupled by nonconservative products. Because of the nonconservative products of the system, which couple both one‐layer shallow‐water subsystems, the usual numerical methods have to consider the full model. Of course, uncoupled numerical techniques, just involving finite volume schemes for the basic shallow‐water equations, are very attractive since they are very easy to implement and they are costless. Recently, a stable layer splitting technique was introduced [Bouchut and Morales de Luna, M2AN Math Model Numer Anal 42 (2008), 683–698]. In the same spirit, we exhibit new splitting technique, which is proved to be well balanced and non‐negative preserving. The main benefit issuing from the here derived uncoupled method is the ability to correctly approximate the solution of very severe benchmarks. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1396–1423, 2015     

A linearization‐based approach of homotopy analysis method for non‐linear time‐fractional parabolic PDEs

In this paper, a novel approach, namely, the linearization‐based approach of homotopy analysis method, to analytically treat non‐linear time‐fractional PDEs is proposed. The presented approach suggests a new optimized structure of the homotopy series solution based on a linear approximation of the non‐linear problem. A comparative study between the proposed approach and standard homotopy analysis approach is illustrated by solving two examples involving non‐linear time‐fractional parabolic PDEs. The performed numerical simulations demonstrate that the linearization‐based approach reduces the computational complexity and improves the performance of the homotopy analysis method.     

Synchronization of memristor‐based delayed BAM neural networks with fractional‐order derivatives

This article deals with the problem of synchronization of fractional‐order memristor‐based BAM neural networks (FMBNNs) with time‐delay. We investigate the sufficient conditions for adaptive synchronization of FMBNNs with fractional‐order 0 < α < 1. The analysis is based on suitable Lyapunov functional, differential inclusions theory, and master‐slave synchronization setup. We extend the analysis to provide some useful criteria to ensure the finite‐time synchronization of FMBNNs with fractional‐order 1 < α < 2, using Mittag‐Leffler functions, Laplace transform, and linear feedback control techniques. Numerical simulations with two numerical examples are given to validate our theoretical results. Presence of time‐delay and fractional‐order in the model shows interesting dynamics. © 2016 Wiley Periodicals, Inc. Complexity 21: 412–426, 2016     

Co‐existence of Poisson and non‐Poisson processes in ordered parallel multilane pedestrian traffic

We show that non‐Poisson and Poisson processes can coexist in ordered parallel multilane pedestrian traffic, in the presence of lane switching which asymmetrically benefits the switchers and nonswitchers. Pedestrians join at the tail end of a queue and transact at the opposite front end. Their aim is to complete a transaction within the shortest possible time, and they can transfer to a shorter queue with probability p_s. Traffic is described by the utilization parameter U = λ〈t_s〉/N, where λ is the average rate of pedestrians entering the system, 〈t_s〉 is the average transaction time, and N is the number of lanes. Using an agent‐based model, we investigate the dependence of the average completion time 〈t_c〉 with variable K = 1 + (1 ? U)^?1 for different N and 〈t_s〉 values. In the absence of switching (p_s = 0), we found that 〈t_c〉 ∝ K^τ, where τ ≈ 1 regardless of N and 〈t_s〉. Lane switching (p_s = 1) reduces 〈t_c〉 for a given K, but its characteristic dependence with K differs for nonswitchers and switchers in the same traffic system. For the nonswitchers, 〈t_c〉 ∝ K^τ, where τ < 1. At low K values, switchers have a larger 〈t_c〉 that also increases more rapidly with K. At large K, the increase rates become equal for both. For nonswitchers, the possible t_c values obey an exponentially decaying probability density function p(t_c). The switchers on the other hand, are described by a fat‐tailed p(t_c) implying that a few are penalized with t_c values that are considerably longer than any of those experienced by nonswitchers. © 2006 Wiley Periodicals, Inc. Complexity 11: 35–42, 2006     

An optimization model for software component selection under multiple applications development

Component based software development (CBSD) is well acknowledged as a methodology which establishes reusability of software and reduce development cost effectively. While developing enterprise application using component based software engineering (CBSE) methods, software component selection plays a very important role in the process of component retrieval, adaptation and assembly. However, most of current researches focus on technical aspects from domain engineering and application engineering to improve reusability and system efficiency rather than application of optimization methods in CBSD management, especially application in component selection. Moreover, few existing researches have concerned about the situation where a software developer or enterprise develops multi-applications at the same time. By introducing the concept of reusability and a new formulation of compatibility matrix, an optimization model is proposed to solve component selection problem considering reusability and compatibility simultaneously. The model can be used to assist software developers in selecting software components when multi-applications are undertaken concurrently. Four experiments are conducted with the purpose to provide some insights in management perspective.     

Analytical solutions of N‐person games

The possibility of analytical solutions of N‐person games is presented. A simple formula provides valuable information about the outcomes of such games with linear payoff functions and Pavlovian agents. Experiments performed with our simulation tool for the multiagent stag hunt dilemma game are presented. For the case of Pavlovian agents the game has nontrivial but remarkably regular solutions. If both payoff functions are linear and the real solutions of Eq. (2) are both positive, then the analytical solutions are remarkably accurate. © 2012 Wiley Periodicals, Inc. Complexity, 2012     

Evaluating an hepatic enzyme induction mechanism through coarse‐ and fine‐grained measurements of an in silico liver

Results from simulation experiments falsified the hypothesis that a uniform distribution of simulated drug passing through an in silico liver (ISL) will produce a uniform extent of enzyme induction (EI). Wet‐lab EI experiments, as formulated, are infeasible. The simulated EI is intended to have a hepatic counterpart. The ISL is synthetic, physiologically based, fine‐grained, and multi‐agent. It has been validated against in situ drug disposition data. We discuss methodological considerations regarding the phenomenal manifold, multi‐level observation, and manipulation of synthetic models and their referents. Interestingly, a lower probability of metabolism caused higher EI and, counter‐intuitively, more extraction. © 2008 Wiley Periodicals, Inc. Complexity, 2009     

Digital game‐based learning for K–12 mathematics education: A meta‐analysis

Digital games (e.g., video games or computer games) have been reported as an effective educational method that can improve students' motivation and performance in mathematics education. This meta‐analysis study (a) investigates the current trend of digital game‐based learning (DGBL) by reviewing the research studies on the use of DGBL for mathematics learning, (b) examines the overall effect size of DGBL on K‐12 students' achievement in mathematics learning, and (c) discusses future directions for DGBL research in the context of mathematics learning. In total, 296 studies were collected for the review, but of those studies, only 33 research studies were identified as empirical studies and systematically analyzed to investigate the current research trends. In addition, due to insufficient statistical data, only 17 out of the 33 studies were analyzed to calculate the overall effect size of digital games on mathematics education. This study will contribute to the research community by analyzing recent trends in significant DGBL research, especially for those who are interested in using DGBL for mathematics education.     

Modified modulus‐based matrix splitting iteration methods for linear complementarity problems

For solving the large sparse linear complementarity problems, we establish modified modulus‐based matrix splitting iteration methods and present the convergence analysis when the system matrices are H₊‐matrices. The optima of parameters involved under some scopes are also analyzed. Numerical results show that in computing efficiency, our new methods are superior to classical modulus‐based matrix splitting iteration methods under suitable conditions. Copyright © 2015 John Wiley & Sons, Ltd.     

Complexity of clique‐coloring odd‐hole‐free graphs

In this paper we investigate the problem of clique‐coloring, which consists in coloring the vertices of a graph in such a way that no monochromatic maximal clique appears, and we focus on odd‐hole‐free graphs. On the one hand we do not know any odd‐hole‐free graph that is not 3‐clique‐colorable, but on the other hand it is NP‐hard to decide if they are 2‐clique‐colorable, and we do not know if there exists any bound k₀ such that they are all k₀ ‐clique‐colorable. First we will prove that (odd hole, codiamond)‐free graphs are 2‐clique‐colorable. Then we will demonstrate that the complexity of 2‐clique‐coloring odd‐hole‐free graphs is actually Σ₂ P‐complete. Finally we will study the complexity of deciding whether or not a graph and all its subgraphs are 2‐clique‐colorable. © 2009 Wiley Periodicals, Inc. J Graph Theory 62: 139–156, 2009