Economic Control of Quality of Manufactured Product.

The Theory of Stochastic Processes. By D. R. Cox and H. D. Miller. Pp. x, 398. 70s. (Methuen)

This chapter is devoted to a more detailed examination of game theory. Game theory is an important tool for analyzing strategic behavior, is concerned with how individuals make decisions when they recognize that their actions affect, and are affected by, the actions of other individuals or groups. Strategic behavior recognizes that the decision-making process is frequently mutually interdependent. Game theory is the study of the strategic behavior involving the interaction of two or more individuals, teams, or firms, usually referred to as players. Two game theoretic scenarios were examined in this chapter: Simultaneous-move and multi-stage games. In simultaneous-move games the players effectively move at the same time. A normal-form game summarizes the players, possible strategies and payoffs from alternative strategies in a simultaneous-move game. Simultaneous-move games may be either noncooperative or cooperative. In contrast to noncooperative games, players of cooperative games engage in collusive behavior. A Nash equilibrium, which is a solution to a problem in game theory, occurs when the players’ payoffs cannot be improved by changing strategies. Simultaneous-move games may be either one-shot or repeated games. One-shot games are played only once. Repeated games are games that are played more than once. Infinitely-repeated games are played over and over again without end. Finitely-repeated games are played a limited number of times. Finitely-repeated games have certain or uncertain ends.

An Introduction to Game Theory

Chapter 8 establishes the relationship between the input and output power spectral densities of a linear system. Limitations on results are carefully detailed and the case of oscillator noise is considered. The theory is extended to multiple input-multiple output systems.

Linear System Theory

http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac2008/data/papers/2395.pdf

Brief paper: Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities

The research is oriented to the control of discrete — time linear systems with randomly changing parameters which can be described by a finite — state Markov chain. The cost critrion is a quadratic form of the controls and states of the system. The criterion parameters also depend on the states of the Markov chain. Two models of observation of the Markov chain are adopted — delay for one step and undelay. It is shown that under appropriate mean square detectability and stability conditions the infinite horizon optimal control problem for the general case of Markovian jump linear quadratic systems has a unique solution when the control system is mean square stable. Necessary and sufficient conditions are given to determine if a system is mean square stable.

http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.baztech-article-BAT2-0001-0364/c/szajowski_koning.pdf

Discrete-time Markovian jump linear systems

This chapter discusses stochastic games. We focus on nonzero-sum games and provide a detailed survey of selected recent results. In Section 1, we consider stochastic Markov games. A correlation of strategies of the players, involving “public signals,” is described, and a correlated equilibrium theorem proved recently by Nowak and Raghavan for discounted stochastic games with general state space is presented. We also resport an extension of this result to a class of undiscounted stochastic games, satisfying some uniform ergodicity condition. Stopping games are related to stochastic Markov games. In Section 2, we describe a version of Dynkin’s game related to observation of a Markov process with random assignment mechanism of states to the players. Some recent constributions of the second author in this area are reported. The chapter also provides a brief overview of the theory of nonzero-sum stochastic games and stopping games.

/pdf/nonzero-sum-stochastic-games-4p3k20uoxe.pdf

Nonzero-sum Stochastic Games

Preface Contributors Part I. Repeated and Stochastic Games Information and the Existence of Stationary Markovian Equilibrium / Ioannis Karatzas, Martin Shubik, and William D. Sudderth Markov Games under a Geometric Drift Condition / Heinz-Uwe Kuenle A Simple Two-Person Stochastic Game with Money / Piercesare Secchi and William D. Sudderth New Approaches and Recent Advances in Two-Person Zero-Sum Repeated Games / Sylvain Sorin Notes on Risk-Sensitive Nash Equilibria / Andrzej S. Nowak Continuous Convex Stochastic Games of Capital Accumulation / Piotr Wiecek Part II. Differential Dynamic Games Dynamical Core of Fuzzy Dynamical Cooperative Games / Jean-Pierre Aubin Normalized Overtaking Nash Equilibrium for a Class of Distributed Parameter Dynamic Games / Dean A. Carlson Cooperative Differential Games / Leon A. Petrosjan Part III. Stopping Games Selection by Committee / Thomas S. Ferguson Stopping Game Problem for Dynamic Fuzzy Systems / Yuji Yoshida, Masami Yasuda, Masami Kurano, and Jun-ichi Nakagami On Randomized Stopping Games / Elzbieta Z. Ferenstein Stopping Games -- Recent Results / Eilon Solan and Nicolas Vieille Dynkin's Games with Randomized Optimal Stopping Rules / Victor Domansky Modified Strategies in a Competitive Best Choice Problem with Random Priority / Zdzislaw Porosinski Bilateral Approach to the Secretary Problem / David Ramsey and Krzysztof Szajowski Optimal Stopping Games where Players have Weighted Privilege / Minoru Sakaguchi Equilibrium in an Arbitration Procedure / Vladimir V. Mazalov and Anatoliy A. Zabelin Part IV. Applications of Dynamic Games to Economics, Finance and Queuing Theory Applications of Dynamic Games in Queues / Eitan Altman Equilibria for Multiclass Routing Problems inMulti-Agent Networks / Eitan Altman and Hisao Kameda Endogenous Shocks and Evolutionary Strategy: Application to a Three-Players Game / Ekkehard C. Ernst, Bruno Amable and Stefano Palombarini Robust Control Approach to Option Pricing, Including Transaction Costs / Pierre Bernhard S-Adapted Equilibria in Games Played over Event Trees: An Overview / Alain Haurie and Georges Zaccour Existence of Nash Equilibria in Endogenous Rent-Seeking Games / Koji Okuguchi A Dynamic Game with Continuum of Players and its Counterpart with Finitely Many Players / Agnieszka Wiszniewska-Matyszkiel Part V. Numerical Methods and Algorithms for Solving Dynamics Games Distributed Algorithms for Nash Equilibria of Flow Control Games / Tansu Alpcan and Tamer Basar A Taylor Series Expansion of H-infinity Control of Perturbed Markov Jump Linear Systems / Rachid El Azouzi, Eitan Altman and Mohammed Abbad Advances in Parallel Algorithms for the Isaacs Equation / Maurizio Falcone and Paolo Stefani Numerical Algorithm for Cross-Coupled Algebraic Riccati Equations of Singularly Perturbed Systems / Hiroaki Mukaidani, Hua Xu and Koichi Mizukami Equilibrium Selection via Adaptation: Using Genetic Programming to Model Learning in a Coordination Game / Shu-Heng Chen, John Duffy and Chia-Hsuan Yeh Part VI. Parrondo's Games and Related Topics State-Space Visualization and Fractal Properties of Parrondo's Games / Andrew Allison, Derek Abbott and Charles Pearce Parrondo's Capital and History-Dependent Games / Gregory P. Harmer, Derek Abbott and Juan M. R. Parrondo Introduction to Quantum Games and a Quantum Parrondo Game / Joseph Ng and Derek Abbott A Semi-quantum Version of the Game of Life / Adrian P. Flitney and Derek Abbott

Advances in dynamic games : applications to economics, finance, optimization, and stochastic control

The objectives of this study were to report the inter-rater reliability of the Brief Psychiatric Rating Scale (BPRS 4.0) and the Groningen Social Disabilities Schedule (GSDS-II) as assessed in a randomized controlled trial on the effectiveness of psychiatric day hospitals spanning five sites in countries of Central and Western Europe.

Following brief training sessions, videotaped BPRS-interviews and written GSDS-vignettes were rated by clinically experienced researchers from all participating sites. Inter-rater reliability often proved to be poor for items assessing the severity of both psychopathology and social dysfunction, but findings suggest that both instruments allow for the assessment of the presence or absence of specific psychopathological symptoms or social disabilities. Inter-rater reliability at subscale level proved to be good for both instruments.

Results indicate that, with a brief training session and proper use of the instruments, psychopathology and social disabilities can be reliably assessed within cross-national research studies. The results are of particular interest given that the need to conduct cross-national multi-site studies including countries with different cultural backgrounds increases. Copyright © 2003 Whurr Publishers Ltd.

Inter-rater reliability of the Brief Psychiatric Rating Scale and the Groningen Social Disabilities Schedule in a European multi-site randomized controlled trial on the effectiveness of acute psychiatric day hospitals.

The following problem in risk theory is considered. An insurance company, endowed with an initial capital a>0, receives insurance premiums and pays out successive claims. The losses occur according to renewal process. At any moment, the company may broaden or narrow down the offer, what entails the change of the parameters. This change concerns the rate of income, the intensity of renewal process and the distribution of claims. After the change, the management wants to know the moment of the maximal value of the capital assets. Therefore, our goal is finding two optimal stopping times: the best moment of change the parameters and the moment of maximal value of the capital assets. We will use a dynamic programming method to calculate the expected capital at that times.

/pdf/double-optimal-stopping-of-a-risk-process-742q919c67.pdf

Krzysztof Szajowski

Papers

Discrete-time Markovian jump linear systems

Nonzero-sum Stochastic Games

Advances in dynamic games : applications to economics, finance, optimization, and stochastic control

Inter-rater reliability of the Brief Psychiatric Rating Scale and the Groningen Social Disabilities Schedule in a European multi-site randomized controlled trial on the effectiveness of acute psychiatric day hospitals.

Double optimal stopping of a risk process