Unifying temporal and organizational scales in multiscale decision-making

In enterprise systems, making decisions is a complex task for agents at all levels of the organizational hierarchy. To calculate an optimal course of action, an agent has to include uncertainties and the anticipated decisions of other agents, recognizing that they also engage in a stochastic, game-theoretic reasoning process. Furthermore, higher-level agents seek to align the interests of their subordinates by providing incentives. Incentive-giving and receiving agents need to include the effect of the incentive on their payoffs in the optimal strategy calculations. In this paper, we present a multiscale decision-making model that accounts for uncertainties and organizational interdependencies over time. Multiscale decision-making combines stochastic games with hierarchical Markov decision processes to model and solve multi-organizational-scale and multi-time-scale problems. This is the first model that unifies the organizational and temporal scales and can solve a 3-agent, 3-period problem. Solutions can be derived as analytic equations with low computational effort. We apply the model to a service enterprise challenge that illustrates the applicability and relevance of the model. This paper makes an important contribution to the foundation of multiscale decision theory and represents a key step towards solving the general X-agent, T-period problem.     

Compliance signaling games: toward modeling the deterrence of insider threats

In a typical workplace, organizational policies and their compliance requirements set the stage upon which the behavioral patterns of individual agents evolve. The agents’ personal utilities, access to information, and strategic deceptions shape the signaling systems of an intricate information-asymmetric game, thus mystifying assessment and management of organizational risks, which are primarily due to unintentional insider threats. Compliance games, as discussed here, model a rudimentary version of this signaling game between a sender (employee) and a receiver (organization). The analysis of these games’ equilibria as well as their dynamics in repeated game settings illuminate the effectiveness or risks of an organizational policy. These questions are explored via a repeated and agent-based simulation of compliance signaling games, leading to the following: (1) a simple but broadly applicable model for interactions between sender agents (employees) and receiver agents (principals in the organization), (2) an investigation of how the game theoretic approach yields the plausible dynamics of compliance, and (3) design of experiments to estimate parameters of the systems: evolutionary learning rates of agents, the efficacy of auditing using a trembling hand strategy, effects of non-stationary and multiple principal agents, and ultimately, the robustness of the system under perturbation of various related parameters (costs, penalties, benefits, etc.). The paper concludes with a number of empirical studies, illustrating a battery of compliance games under varying environments designed to investigate agent based learning, system control, and optimization. The studies indicate how agents through limited interactions described by behavior traces may learn and optimize responses to a stationary defense, expose sensitive parameters and emergent properties and indicate the possibility of controlling interventions which actuate game parameters. We believe that the work is of practical importance—for example, in constraining the vulnerability surfaces arising from compliance games.     

A Generalized Two-Agent Location Problem: Asymmetric Dynamics and Coordination

We generalize a static two-agent location problem into dynamic, asymmetric settings. The dynamics is due to the ability of the agents to move at limited speeds. Since each agent has its own objective (demand) function and these functions are interdependent, decisions made by each agent may affect the performance of the other agent and thus affect the overall performance of the system. We show that, under a broad range of system’s parameters, centralized (system-wide optimal) and non-cooperative (Nash) behavior of the agents are characterized by a similar structure. The timing of these trajectories and the intermediate speeds are however different. Moreover, non-cooperative agents travel more and may never rest and thus the system performance deteriorates under decentralized decision-making. We show that a static linear reward approach, recently developed in Golany and Rothblum (Nav. Res. Logist. 53(1):1–15, 2006), can be generalized to provide coordination of the moving agents and suggest its dynamic modification. When the reward scheme is applied, the agents are induced to choose the system-wide optimal solution, even though they operate in a decentralized decision-making mode.     

Emergent learning behaviour in a simulated organization faced with tasks requiring team effort

We conceptualize organizational learning as a result of the collective learning behaviour of knowledge agents in an organization. Each agent provides a range of attributes that may be required to perform organizational tasks. We devised a computational model consisting of three processes to simulate an organization's response to performing repeated tasks: (1) Expert Selection Process for selecting the winner knowledge agent or lead agent; (2) Plan Formation Process for deciding what additional attributes are needed, but not possessed by the winner expert agent, and iteratively selecting further agents with the needed attributes until the task can be accomplished by the combined attributes of the ‘coalition of agents’ so formed; and (3) Capital Modification Process for rewarding participating agents according to the success of their combined organizational performance. We observed the simulated results for different combinations of three levels of task difficulty (requiring, respectively, 5, 10 and, 15 different attributes, each at a sufficient level in the coalition or team to complete the task), and three levels of selection, during plan formation, for knowledge agent performance (the extent to which selection favours knowledge agents with much capital or large strength versus knowledge agents without much capital or large strength). The simulated organization exhibited aspects of both single loop and double loop learning, in repeatedly performing the same task, and ‘learning to perform the task’ with the smallest possible team.     

湍流不同尺度间的近程和共振作用规律及应用

从Navier-Stokes方程出发,研究了湍流不同尺度间的相互作用规律,给出相近尺度间近程粘性应力的积分和微分表达式．引入极相近尺度之间共振相互作用的概念,得到共振粘性应力的微分表达式．利用共振粘性应力张量获得不含经验关系和常数、近似封闭的大涡模拟（LES）方程组．利用近程和共振粘性应力张量获得不含经验关系和常数、近似封闭的湍流多尺度方程组．讨论了湍流多尺度方程的性质及用于湍流计算的优点,尺度间相互作用的近程特性说明:多尺度模拟是湍流计算很有价值的方法,并列举了算例．     

Robust investment–reinsurance optimization with multiscale stochastic volatility

This paper investigates the investment and reinsurance problem in the presence of stochastic volatility for an ambiguity-averse insurer (AAI) with a general concave utility function. The AAI concerns about model uncertainty and seeks for an optimal robust decision. We consider a Brownian motion with drift for the surplus of the AAI who invests in a risky asset following a multiscale stochastic volatility (SV) model. We formulate the robust optimal investment and reinsurance problem for a general class of utility functions under a general SV model. Applying perturbation techniques to the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation associated with our problem, we derive an investment–reinsurance strategy that well approximates the optimal strategy of the robust optimization problem under a multiscale SV model. We also provide a practical strategy that requires no tracking of volatility factors. Numerical study is conducted to demonstrate the practical use of theoretical results and to draw economic interpretations from the robust decision rules.     

Energy analysis and improved regularity estimates for multiscale deconvolution models of incompressible flows

This paper presents new analytical results and the first numerical results for a recently proposed multiscale deconvolution model (MDM) recently proposed. The model involves a large‐eddy simulation closure that uses a novel deconvolution approach based on the introduction of two distinct filtering length scales. We establish connections between the MDM and two other models, and, on the basis of one of these connections, we establish an improved regularity estimate for MDM solutions. We also prove that the MDM preserves Taylor‐eddy solutions of the Navier–Stokes equations and therefore does not distort this particular vortex structure. Simulations of the MDM are performed to examine the accuracy of the MDM and the effect of the filtering length scales on energy spectra for three‐dimensional homogeneous and isotropic flows. Numerical evidence for all tests clearly indicates that the MDM gives very accurate coarse‐mesh solutions and that this multiscale approach to deconvolution is effective. Copyright © 2015 John Wiley & Sons, Ltd.     

Multiscale analysis in Sobolev spaces on bounded domains

We study a multiscale scheme for the approximation of Sobolev functions on bounded domains. Our method employs scattered data sites and compactly supported radial basis functions of varying support radii at scattered data sites. The actual multiscale approximation is constructed by a sequence of residual corrections, where different support radii are employed to accommodate different scales. Convergence theorems for the scheme are proven, and it is shown that the condition numbers of the linear systems at each level are independent of the level, thereby establishing for the first time a mathematical theory for multiscale approximation with scaled versions of a single compactly supported radial basis function at scattered data points on a bounded domain.     

An Interaction Value Perspective on Firms of Differing Size

We present a general model of a network of interacting individuals, each of whom derives a known, real-valued benefit from each possible dyadic interaction. The model views interactions as knowledge-transfer exchanges that add value to the organization. We use this model to derive interaction patterns within an organization. We assume that the value of dyadic interaction benefits is distributed as a randomly permuted geometric series. Moreover, interactions only add value when a large enough waiting period is observed between interaction attempts. We show that an organization optimized for knowledge transfer has a distribution of interaction frequencies which correlates well with observations. Organizations of differing sizes can have similar optimal structures as long they have similar normalized levels of interdependence between interactions, and distribution of interaction benefit values. This research has implications for the design of communication infrastructure in a growing organization, as well as for the predictive value of modeling organizations at different scales.     

Passing the buck in the garbage can model of organizational choice

We reconstruct Cohen, March and Olsen’s Garbage Can model of organizational choice as an agent-based model. In the original model, the members of an organization can postpone decision-making. We add another means for avoiding making decisions, that of buck-passing difficult problems to colleagues. We find that selfish individual behavior, such as postponing decision-making and buck-passing, does not necessarily imply dysfunctional consequences for an organization.     

Generating Signals with Multiscale Time Irreversibility: The Asymmetric Weierstrass Function

Time irreversibility (asymmetry with respect to time reversal) is an important property of many time series derived from processes in nature. Some time series (e.g., healthy heart rate dynamics) demonstrate even more complex, multiscale irreversibility, such that not only the original but also coarse-grained time series are asymmetric over a wide range of scales. Several indices to quantify multiscale asymmetry have been introduced. However, there has been no simple generator of model time series with "tunable" multiscale asymmetry to test such indices. We introduce an asymmetric Weierstrass function W(A) (constructed from asymmetric sawtooth functions instead of cosine waves) that can be used to construct time series with any given value of the multiscale asymmetry. We show that multiscale asymmetry appears to be independent of other multiscale complexity indices, such as fractal dimension and multiscale entropy. We further generalize the concept of multiscale asymmetry by introducing time-dependent (local) multiscale asymmetry and provide examples of such time series. The W(A) function combines two essential features of complex fluctuations, namely fractality (self-similarity) and irreversibility (multiscale time asymmetry); moreover, each of these features can be tuned independently. The proposed family of functions can be used to compare and refine multiscale measures of time series asymmetry.     

A STEADY-STATE SATISFACTORY SOLUTION TO AN ENVIRONMENTAL GAME WITH PIECE-WISE DEFINED PAYOFFS

We model a pollution accumulation process through a nonlinear, nondifferentiable state equation and also as dependent on an environmental levy. Then the payoff function to an economic agent is defined piece-wise. However, for a simple demand and cost structure, the combined payoff function of all agents is diagonally strictly concave. This implies that a steady-state Nash equilibrium is unique and can be controlled by the levy. We analytically compute a steady-state Nash equilibrium solution for the agents, and use a Decision Support Tool to determine a satisfactory solution for the interactions between the agents and a legislator responsible for the levy.     

How behaviors spread in dynamic social networks

In this paper, we explore how decentralized local interactions of autonomous agents in a network relate to collective behaviors. Earlier work in this area has modeled social networks with fixed agent relations. We instead focus on dynamic social networks in which agents can rationally adjust their neighborhoods based on their individual interests. We propose a new connection evaluation theory, the Highest Weighted Reward (HWR) rule: agents dynamically choose their neighbors in order to maximize their own utilities based on rewards from previous interactions. We prove that, in the two-action pure coordination game, our system would stabilize to a clustering state in which all relationships in the network are rewarded with an optimal payoff. Our experiments verify this theory and also reveal additional interesting patterns in the network.     

Multiscale behavior and fractional kinetics from the data of solar wind–magnetosphere coupling

Multiscale phenomena are ubiquitous in nature as well as in laboratories. A broad range of interacting space and time scales determines the dynamics of many systems which are inherently multiscale. In many systems multiscale phenomena are not only prominent, but also they often play the dominant role. In the solar wind–magnetosphere interaction, multiscale features coexist along with the global or coherent features. Underlying these phenomena are the mathematical and theoretical approaches such as phase transitions, turbulence, self-organization, fractional kinetics, percolation, etc. The fractional kinetic equations provide a suitable mathematical framework for multiscale behavior. In the fractional kinetic equations the multiscale nature is described through fractional derivatives and the solutions of these equations yield infinite moments, showing strong multiscale behavior. Using a Lévy flights approach, we analyze the correlated data of the solar wind–magnetosphere coupling. Based on this analysis a model of the multiscale features is proposed and compared with the solutions of diffusion-type equations. The equation with fractional spatial derivative shows strong multiscale behavior with infinite moments. On the other hand, the equation with space dependent diffusion coefficients yield finite moments, indicating Gaussian type solutions and absence of long tails typically associated with multiscale behavior.     

Collective increase of first impression bias

We propose a simple model of first impression bias (FIB), where agents tend to ignore features which contradict their initial view. We consider a population of agents which are all in contact with a media, communicating randomly chosen features of an object. In some cases, we observe on simulations that FIB is significantly more frequent when the agents interact with each other than when they are only in contact with the media. We design an analytical aggregated model of the global agent‐based model behavior, which helps to explain the higher number of FIB due to the interactions. © 2009 Wiley Periodicals, Inc. Complexity, 2010     

Convention evolution in organizations and markets

Conventions are essential for the coordination of multi-agent systems. However, in many systems conventions can not be legislated in advance and need to emerge during the system's activity. As designers of such systems we may wish to ensure that conventions will evolve rapidly. Given a classical model for convention evolution where agents tend to mimic agents they interact with, the designer can control the organizational structure of the system in order to speedup the evolution of conventions. This paper introduces a study of convention evolution in the context of basic organizational structures. Our study sheds light on a basic aspect of organizational design which has not been discussed in the literature, and which is crucial for efficient design of non-trivial multi-agent systems.     

A stochastic multiscale model for electricity generation capacity expansion

Long-term planning for electric power systems, or capacity expansion, has traditionally been modeled using simplified models or heuristics to approximate the short-term dynamics. However, current trends such as increasing penetration of intermittent renewable generation and increased demand response requires a coupling of both the long and short term dynamics. We present an efficient method for coupling multiple temporal scales using the framework of singular perturbation theory for the control of Markov processes in continuous time. We show that the uncertainties that exist in many energy planning problems, in particular load demand uncertainty and uncertainties in generation availability, can be captured with a multiscale model. We then use a dimensionality reduction technique, which is valid if the scale separation present in the model is large enough, to derive a computationally tractable model. We show that both wind data and electricity demand data do exhibit sufficient scale separation. A numerical example using real data and a finite difference approximation of the Hamilton–Jacobi–Bellman equation is used to illustrate the proposed method. We compare the results of our approximate model with those of the exact model. We also show that the proposed approximation outperforms a commonly used heuristic used in capacity expansion models.     

Two-agent single-machine scheduling problems under increasing linear deterioration

A new scheduling model in which both two-agent and increasing linear deterioration exist simultaneously is investigated in this paper. The processing time of a job is defined as an increasing linear function of its starting time. Two agents compete to perform their respective jobs on a common single machine and each agent has his own criterion to optimize. We introduce an increasing linear deterioration model into the two-agent single-machine scheduling, where the goal is to minimize the objective function of the first agent with the restriction that the objective function of the second agent cannot exceed a given upper bound. We study two scheduling problems with the different combinations of two agents’ objective functions: makespan, maximum lateness, maximum cost and total completion time. We propose the optimal properties and present the optimal polynomial time algorithms to solve the scheduling problems, respectively.     

A combined approach for two-agent scheduling with sum-of-processing-times-based learning effect

This paper considers a scheduling model involving two agents, job release times, and the sum-of-processing-times-based learning effect. The sum-of-processing-times-based learning effect means that the actual processing time of a job of either agent is a decreasing function of the sum of the processing times of the jobs already scheduled in a given schedule. The goal is to seek for an optimal schedule that minimizes the total weighted completion time of the first agent, subject to no tardy job for the second agent. We first provide a branch-and-bound method to solve the problem. We then develop an approach that combines genetic algorithm and simulated annealing to seek for approximate solutions for the problem. We carry on extensive computational tests to assess the performance of the proposed algorithms.