Preface 1. Decision-Theoretic Foundations 1.1 Game Theory, Rationality, and Intelligence 1.2 Basic Concepts of Decision Theory 1.3 Axioms 1.4 The Expected-Utility Maximization Theorem 1.5 Equivalent Representations 1.6 Bayesian Conditional-Probability Systems 1.7 Limitations of the Bayesian Model 1.8 Domination 1.9 Proofs of the Domination Theorems Exercises 2. Basic Models 2.1 Games in Extensive Form 2.2 Strategic Form and the Normal Representation 2.3 Equivalence of Strategic-Form Games 2.4 Reduced Normal Representations 2.5 Elimination of Dominated Strategies 2.6 Multiagent Representations 2.7 Common Knowledge 2.8 Bayesian Games 2.9 Modeling Games with Incomplete Information Exercises 3. Equilibria of Strategic-Form Games 3.1 Domination and Ratonalizability 3.2 Nash Equilibrium 3.3 Computing Nash Equilibria 3.4 Significance of Nash Equilibria 3.5 The Focal-Point Effect 3.6 The Decision-Analytic Approach to Games 3.7 Evolution. Resistance. and Risk Dominance 3.8 Two-Person Zero-Sum Games 3.9 Bayesian Equilibria 3.10 Purification of Randomized Strategies in Equilibria 3.11 Auctions 3.12 Proof of Existence of Equilibrium 3.13 Infinite Strategy Sets Exercises 4. Sequential Equilibria of Extensive-Form Games 4.1 Mixed Strategies and Behavioral Strategies 4.2 Equilibria in Behavioral Strategies 4.3 Sequential Rationality at Information States with Positive Probability 4.4 Consistent Beliefs and Sequential Rationality at All Information States 4.5 Computing Sequential Equilibria 4.6 Subgame-Perfect Equilibria 4.7 Games with Perfect Information 4.8 Adding Chance Events with Small Probability 4.9 Forward Induction 4.10 Voting and Binary Agendas 4.11 Technical Proofs Exercises 5. Refinements of Equilibrium in Strategic Form 5.1 Introduction 5.2 Perfect Equilibria 5.3 Existence of Perfect and Sequential Equilibria 5.4 Proper Equilibria 5.5 Persistent Equilibria 5.6 Stable Sets 01 Equilibria 5.7 Generic Properties 5.8 Conclusions Exercises 6. Games with Communication 6.1 Contracts and Correlated Strategies 6.2 Correlated Equilibria 6.3 Bayesian Games with Communication 6.4 Bayesian Collective-Choice Problems and Bayesian Bargaining Problems 6.5 Trading Problems with Linear Utility 6.6 General Participation Constraints for Bayesian Games with Contracts 6.7 Sender-Receiver Games 6.8 Acceptable and Predominant Correlated Equilibria 6.9 Communication in Extensive-Form and Multistage Games Exercises Bibliographic Note 7. Repeated Games 7.1 The Repeated Prisoners Dilemma 7.2 A General Model of Repeated Garnet 7.3 Stationary Equilibria of Repeated Games with Complete State Information and Discounting 7.4 Repeated Games with Standard Information: Examples 7.5 General Feasibility Theorems for Standard Repeated Games 7.6 Finitely Repeated Games and the Role of Initial Doubt 7.7 Imperfect Observability of Moves 7.8 Repeated Wines in Large Decentralized Groups 7.9 Repeated Games with Incomplete Information 7.10 Continuous Time 7.11 Evolutionary Simulation of Repeated Games Exercises 8. Bargaining and Cooperation in Two-Person Games 8.1 Noncooperative Foundations of Cooperative Game Theory 8.2 Two-Person Bargaining Problems and the Nash Bargaining Solution 8.3 Interpersonal Comparisons of Weighted Utility 8.4 Transferable Utility 8.5 Rational Threats 8.6 Other Bargaining Solutions 8.7 An Alternating-Offer Bargaining Game 8.8 An Alternating-Offer Game with Incomplete Information 8.9 A Discrete Alternating-Offer Game 8.10 Renegotiation Exercises 9. Coalitions in Cooperative Games 9.1 Introduction to Coalitional Analysis 9.2 Characteristic Functions with Transferable Utility 9.3 The Core 9.4 The Shapkey Value 9.5 Values with Cooperation Structures 9.6 Other Solution Concepts 9.7 Colational Games with Nontransferable Utility 9.8 Cores without Transferable Utility 9.9 Values without Transferable Utility Exercises Bibliographic Note 10. Cooperation under Uncertainty 10.1 Introduction 10.2 Concepts of Efficiency 10.3 An Example 10.4 Ex Post Inefficiency and Subsequent Oilers 10.5 Computing Incentive-Efficient Mechanisms 10.6 Inscrutability and Durability 10.7 Mechanism Selection by an Informed Principal 10.8 Neutral Bargaining Solutions 10.9 Dynamic Matching Processes with Incomplete Information Exercises Bibliography Index

博弈论 : 矛盾冲突分析 = Game theory : analysis of conflict

The use of statistical techniques to build approximations of expensive computer analysis codes pervades much of today’s engineering design. These statistical approximations, or metamodels, are used to replace the actual expensive computer analyses, facilitating multidisciplinary, multiobjective optimization and concept exploration. In this paper, we review several of these techniques, including design of experiments, response surface methodology, Taguchi methods, neural networks, inductive learning and kriging. We survey their existing application in engineering design, and then address the dangers of applying traditional statistical techniques to approximate deterministic computer analysis codes. We conclude with recommendations for the appropriate use of statistical approximation techniques in given situations, and how common pitfalls can be avoided.

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Metamodels for Computer-Based Engineering Design: Survey and Recommendations

Systems engineering of products, processes, and organizations requires tools and techniques for system decomposition and integration. A design structure matrix (DSM) provides a simple, compact, and visual representation of a complex system that supports innovative solutions to decomposition and integration problems. The advantages of DSMs vis-a-vis alternative system representation and analysis techniques have led to their increasing use in a variety of contexts, including product development; project planning, project management, systems engineering, and organization design. This paper reviews two types of DSMs, static and time-based DSMs, and four DSM applications: (1) component-based or architecture DSM, useful for modeling system component relationships and facilitating appropriate architectural decomposition strategies; (2) team-based or organization DSM, beneficial for designing integrated organization structures that account for team interactions; (3) activity-based or schedule DSM, advantageous for modeling the information flow among process activities; and (4) parameter-based (or low-level schedule) DSM, effective for integrating low-level design processes based on physical design parameter relationships. A discussion of each application is accompanied by an industrial example. The review leads to conclusions regarding the benefits of DSMs in practice and barriers to their use. The paper also discusses research directions and new DSM applications, both of which may be approached with a perspective on the four types of DSMs and their relationships.

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Applying the design structure matrix to system decomposition and integration problems: a review and new directions

Computation-intensive design problems are becoming increasingly common in manufacturing industries. The computation burden is often caused by expensive analysis and simulation processes in order to reach a comparable level of accuracy as physical testing data. To address such a challenge, approximation or metamodeling techniques are often used. Metamodeling techniques have been developed from many different disciplines including statistics, mathematics, computer science, and various engineering disciplines. These metamodels are initially developed as “surrogates” of the expensive simulation process in order to improve the overall computation efficiency. They are then found to be a valuable tool to support a wide scope of activities in modern engineering design, especially design optimization. This work reviews the state-of-the-art metamodel-based techniques from a practitioner’s perspective according to the role of metamodeling in supporting design optimization, including model approximation, design space exploration, problem formulation, and solving various types of optimization problems. Challenges and future development of metamodeling in support of engineering design is also analyzed and discussed.Copyright © 2006 by ASME

https://www.sfu.ca/~gwa5/index_files/Microsoft%20Word%20-%20ASME-Metamodeling-6-12-06.pdf

Review of Metamodeling Techniques in Support of Engineering Design Optimization

As a common concept in multi-objective optimization, minimizing a weighted sum constitutes an independent method as well as a component of other methods. Consequently, insight into characteristics of the weighted sum method has far reaching implications. However, despite the many published applications for this method and the literature addressing its pitfalls with respect to depicting the Pareto optimal set, there is little comprehensive discussion concerning the conceptual significance of the weights and techniques for maximizing the effectiveness of the method with respect to a priori articulation of preferences. Thus, in this paper, we investigate the fundamental significance of the weights in terms of preferences, the Pareto optimal set, and objective-function values. We determine the factors that dictate which solution point results from a particular set of weights. Fundamental deficiencies are identified in terms of a priori articulation of preferences, and guidelines are provided to help avoid blind use of the method.

The weighted sum method for multi-objective optimization: new insights

Decomposition methods provide a systematic approach for decoupling large engineering systems into smaller, coupled subsystems identified by disciplines or by engineering tasks. The paper develops a general decomposition approach for multidisciplinary optimization that is applicable for non-hierarchic systems in which a distinct system hierarchy is difficult to identify. The approach is implemented in a structural synthesis problem for verification purposes. The optimal design of a ten-bar truss for minimum weight subject to displacement and stress constraints is considered. Subsystems are defined in terms of sizing and space variables. The approach allows for implementation of specialized methods for analysis in each subsystem and the ability to incorporate human intervention and decision making. Results demonstrate that the Concurrent Subspace Optimization approach is a versatile method that potentially offers exceptional computational as well as data management advantages.

Non-hierarchic system decomposition in structural optimization

A modified paradigm of Computational Steering (CS), termed Visual Design Steering (VDS), is developed in this paper. The VDS paradigm is applied to optimal design problems to provide a means for capturing and enabling designer insights. VDS allows a designer to make decisions before, during or after an analysis or optimization via a visual environment, in order to effectively steer the solution process. The objective of VDS is to obtain a better solution in less time through the use of designer knowledge and expertise. Using visual representations of complex systems in this manner enables human experience and judgement to be incorporated into the optimal design process at appropriate steps, rather than having traditional black box solvers return solutions from a prescribed input set. Part I of this paper focuses on the research issues pertaining to the Graph Morphing visualization method created to represent an n-dimensional optimization problem using 2-dimensional and 3-dimensional visualizations. Part II investigates the implementation of the VDS paradigm, using the Graph Morphing approach, to improve an optimal design process. Specifically, the following issues are addressed: impact of design variable changes on the optimal design space; identification of possible constraint redundancies; impact of constraint tolerances on the optimal solution; and smoothness of the objective function contours. It is demonstrated that Graph Morphing can effectively reduce the complexity and computational time associated with some optimization problems.

Development of visual design steering as an aid in large-scale multidisciplinary design optimization. Part I: method development

The design process associated with large engineering systems requires an initial decomposition of the complex system into modules of design tasks which are coupled through the transference of output data. In analyzing or optimizing such a coupled system, it is essential to be able to determine which interactions figure prominently enough to significantly affect the accuracy of the system solution. Many decomposition approaches assume the capability is available to determine what design tasks and interactions exist and what order of execution will be imposed during the analysis process. Unfortunately, this is often a complex problem and beyond the capabilities of a human design manager. A new feature for DeMAID (Design Manager's Aid for Intelligent Decomposition) will allow the design manager to use coupling strength information to find a proper sequence for ordering the design tasks. In addition, these coupling strengths aid in deciding if certain tasks or couplings could be removed (or temporarily suspended) from consideration to achieve computational savings without a significant loss of system accuracy. New rules are presented and two small test cases are used to show the effects of using coupling strengths in this manner.

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Ordering design tasks based on coupling strengths

The present paper investigates the applicability of the Global Sensitivity Equation (GSE) method in the multidisciplinary synthesis of aeronautical vehicles. The GSE method provides an efficient approach for representing a large coupled system by smaller subsystems and accounts for the subsystem interactions by means of first-order behavior sensitivities. This approach was applied in an aircraft synthesis problem with performance constraints stemming from the disciplines of structures, aerodynamics, and flight mechanics. Approximation methods were considered in an attempt to reduce problem dimensionality and to improve the efficiency of the optimization process. The influence of efficient constraint representations, the choice of design variables, and design variable scaling on the conditioning of the system matrix was also investigated.

Application of global sensitivity equations in multidisciplinary aircraft synthesis

The verification of a method for computing sensitivity derivatives of a coupled system is presented. The method deals with a system whose analysis can be partitioned into subsets that correspond to disciplines and/or physical subsystems that exchange input-output data with each other. The method uses the partial sensitivity derivatives of the output with respect to input obtained for each subset separately to assemble a set of linear, simultaneous, algebraic equations that are solved for the derivatives of the coupled system response. This sensitivity analysis is verified using an example of a cantilever beam augmented with an active control system to limit the beam's dynamic displacements under an excitation force. The verification shows good agreement of the method with reference data obtained by a finite difference technique involving entire system analysis. The usefulness of a system sensitivity method in optimization applications by employing a piecewise-linear approach to the same numerical example is demonstrated. The method's principal merits are its intrinsically superior accuracy in comparison with the finite difference technique, and its compatibility with the traditional division of work in complex engineering tasks among specialty groups.

/pdf/sensitivity-of-control-augmented-structure-obtained-by-a-4101deoyvn.pdf

Christina Bloebaum

Papers

Non-hierarchic system decomposition in structural optimization

Development of visual design steering as an aid in large-scale multidisciplinary design optimization. Part I: method development

Ordering design tasks based on coupling strengths

Application of global sensitivity equations in multidisciplinary aircraft synthesis

Sensitivity of control-augmented structure obtained by a system decomposition method