Preference Games and Sink Equilibria

In this thesis we present a new foundation for game theory. Our model for a game is defined precisely by the response graph, a natural object underlying all classical games. We call this model a preference game. Preference games generalise classical games in that all classical games have an associated preference game. Preference games also have a natural choice of solution concept: the sink equilibria, which are the sink strongly connected components of this graph. These exist in all games, and generalise pure Nash equilibria. We argue that preference games and sink equilibria form a predictive and well-founded model of strategic interaction that both clarifies problems from classical game theory and presents new solutions and predictions. Our approach is three-pronged. First, we show preference games are axiomatically well-motivated and so are broadly-applicable models of strategic interaction. We obtain these games by weakening the classical formulation of game theory with two axioms: ordinality, asserting the model requires only that players know a discrete order over the outcomes; and relevance, asserting that our model depends only on preferences over outcomes players can choose between. We give a new discussion of the Prisoner's Dilemma, where we show that the paradox can be rephrased as a consequence of Nash equilibria satisfying the relevance axiom, while Pareto efficiency satisfies only the ordinality axiom. We show further that preference games implicitly capture in their graph structure the equivalences caused by renaming players or strategies, while expressing these equivalences in classical games is cumbersome. Second, we show preference games give new insight into strategic interaction. We examine two-player games, with a focus on zero-sum and potential games. Despite both being classically defined in terms of utility functions, we show that their strategic structure can be easily understood through preference games, which make clear the duality between these two classes. We use this to prove a new theorem of classical game theory: in every two-player game, every non-iteratively-dominated strategy takes part in a 2x2 subgame with the preference structure of Matching Pennies or 2x2 Coordination. As a consequence, any two-player game sharing a response graph with both a zero-sum game and a potential game is dominance-solvable. The proofs are combinatorial. Thirdly, we show preference games are compatible with game dynamics, while classical games and mixed Nash equilibria are not. Game dynamics---the mathematical model of strategic adjustment used in evolutionary game theory---cannot generically converge to mixed Nash equilibria. By contrast, pure Nash equilibria are attracting fixed-points; the natural generalisation of this dynamic concept is the sink chain components, a topological object defined by the Fundamental Theorem of Dynamical Systems. While these do not exist in general, we prove an open problem establishing their existence under the replicator dynamic, the best-known game dynamic. We prove that sink chain components under the replicator always contain sink equilibria, and we conjecture that this relationship is always one-to-one. Thus we obtain the surprising result that the complex, sometimes chaotic, behaviour of the replicator dynamic is governed in the long run by the response graph of the game, with the outcome determined by a simple combinatorial object---sink equilibria. Sink equilibria also describe the long-run outcomes of all discrete dynamics defined by Markov chains on the response graph. We conclude with a number of open problems that emerge from preference games

A systematic approach for integrated product, materials, and design-process design

Designers are challenged to manage customer, technology, and socio-economic uncertainty causing dynamic, unquenchable demands on limited resources. In this context, increased concept flexibility, referring to a designer s ability to generate concepts, is crucial. Concept flexibility can be significantly increased through the integrated design of product and material concepts. Hence, the challenge is to leverage knowledge of material structure-property relations that significantly affect system concepts for function-based, systematic design of product and materials concepts in an integrated fashion. However, having selected an integrated product and material system concept, managing complexity in embodiment design-processes is important. Facing a complex network of decisions and evolving analysis models a designer needs the flexibility to systematically generate and evaluate embodiment design-process alternatives. In order to address these challenges and respond to the primary research question of how to increase a designer s concept and design-process flexibility to enhance product creation in the conceptual and early embodiment design phases, the primary hypothesis in this dissertation is embodied as a systematic approach for integrated product, materials and design-process design. The systematic approach consists of two components i) a function-based, systematic approach to the integrated design of product and material concepts from a systems perspective, and ii) a systematic strategy to design-process generation and selection based on a decision-centric perspective and a value-of-information-based Process Performance Indicator. The systematic approach is validated using the validation-square approach that consists of theoretical and empirical validation. Empirical validation of the framework is carried out using various examples including: i) design of a reactive material containment system, and ii) design of an optoelectronic communication system.Ph.D.Committee Chair: Allen, Janet K.; Committee Member: Aidun, Cyrus K.; Committee Member: Klein, Benjamin; Committee Member: McDowell, David L.; Committee Member: Mistree, Farrokh; Committee Member: Yoder, Douglas P

Adaptive complex system modeling for realistic modern ground warfare simulation analysis based on evolutionary multi-objective meta-heuristic techniques

Dissertação apresentada à Escola Superior de Tecnologia e Gestão do IPL para obtenção do grau de Mestre em Engenharia Informática - Computação Móvel, orientada pelo Professor Silvio Priem Mendes.The battlefield is a harsh and inhuman environment, where deaths and destruction take lead role. Through many millennia there was blood shed all over the world, people who many time died in a battle that sometimes they didn‘t even care about. Today, the battle field is very different, machines take most damage and there are less casualties, this is because of the advancements made in the fields of aeronautics, weaponry, nautical, vehicles, armor, and psychology. Also there is another important party that throughout the last decades made a special and decisive advantage to the side which is more advanced in this field, it is intelligence and simulation. Intelligence today gives enormous advantage to one country as you ―see and feel‖ the battlefield hundreds or thousands kilometers away. Then, with the data provided by intelligence, countries can simulate the battle in order to deploy the most efficient units into battle. In this thesis we propose a warfare simulator analysis tool using a multi-objective approach and artificial intelligence. Further on, the 1991 Gulf war scenario is used to simulate and the results are presented and analyzed. The approach used in this thesis is difficult to be used in games due to its processing complexity and computing demands

Procedures for the Establishment of Standards. Final Report. Vol.2

This final report summarizes two years of research on analyzing procedures for the establishment of standards. The research was sponsored by the Volkswagenwerk Foundation and jointly carried out at the International Institute for Applied Systems Analysis at Laxenburg and the Kernforschungszentrum Karlsruhe. The final report is meant to be both a problem-oriented review of related work in the area of environmental standard setting and an executive summary of the main research done during the contract period. The following eleven technical papers (Volume II of the Final Report) are reference reports written to accompany Volume I. They describe the studies and findings performed under the contract in more detail, and they have been either published as IIASA Research Memoranda or as outside publications, or were especially written for this report. These technical reports are structured in four parts: (1) policy analyses of standard setting procedures; (2) decision and game theoretic models for standard setting; (3) applications of decision game theoretic models to specific standard setting problems; and (4) biological basis for standard setting

Mastering Uncertainty in Mechanical Engineering

This open access book reports on innovative methods, technologies and strategies for mastering uncertainty in technical systems. Despite the fact that current research on uncertainty is mainly focusing on uncertainty quantification and analysis, this book gives emphasis to innovative ways to master uncertainty in engineering design, production and product usage alike. It gathers authoritative contributions by more than 30 scientists reporting on years of research in the areas of engineering, applied mathematics and law, thus offering a timely, comprehensive and multidisciplinary account of theories and methods for quantifying data, model and structural uncertainty, and of fundamental strategies for mastering uncertainty. It covers key concepts such as robustness, flexibility and resilience in detail. All the described methods, technologies and strategies have been validated with the help of three technical systems, i.e. the Modular Active Spring-Damper System, the Active Air Spring and the 3D Servo Press, which have been in turn developed and tested during more than ten years of cooperative research. Overall, this book offers a timely, practice-oriented reference guide to graduate students, researchers and professionals dealing with uncertainty in the broad field of mechanical engineering

Emergence through conflict : the Multi-Disciplinary Design System (MDDS)

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture, 2009.Includes bibliographical references (p. 413-430).This dissertation proposes a framework and a group of systematic methodologies to construct a computational Multi-Disciplinary Design System (MDDS) that can support the design of complex systems within a variety of domains. The way in which the resulting design system is constructed, and the capabilities it brings to bare, are totally different from the methods used in traditional sequential design. The MDDS embraces diverse areas of research that include design science, systems theory, artificial intelligence, design synthesis and generative algorithms, mathematical modeling and disciplinary analyses, optimization theory, data management and model integration, and experimental design among many others. There are five phases to generate the MDDS. These phases involve decomposition, formulation, modeling, integration, and exploration. These phases are not carried out in a sequential manner, but rather in a continuous move back and forth between the different phases. The process of building the MDDS begins with a top-down decomposition of a design concept. The design, seen as an object, is decomposed into its components and aspects, while the design, seen as a process, is decomposed into developmental levels and design activities. Then based on the process decomposition, the architecture of the MDDS is formulated into hierarchical levels each of which comprises a group of design cycles that include design modules at different degrees of abstraction. Based on the design object decomposition, the design activities which include synthesis, analysis, evaluation and optimization are modeled within the design modules.(cont.) Subsequently through a bottom-up approach, the design modules are integrated into a data flow network. This network forms MDDS as an integrated system that acts as a holistic structured functional unit that explores the design space in search of satisfactory solutions. The MDDS emergent properties are not detectable through the properties and behaviors of its parts, and can only be enucleated through a holistic approach. The MDDS is an adaptable system that is continuously dependent on, and responsive to, the uncertainties of the design process. The evolving MDDS is thus characterized a multi-level, multi-module, multi-variable and multi-resolution system. Although the MDDS framework is intended to be domain-independent, several MDDS prototypes were developed within this dissertation to generate exploratory building designs.by Anas Alfaris.Ph.D

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum