Dynamic games arise between players (individuals, firms, countries, animals, etc.) when the strategic interactions among them recur over time and decisions made during one period affect both current and future payoffs. Dynamic games provide conceptually rich paradigms and tools to deal with these situations. This volume provides a uniform approach to game theory and illustrates it with present-day applications to economics and management, including environmental, with the emphasis on dynamic games. At the end of each chapter a case study called game engineering (GE) is provided, to help readers understand how problems of high social priority, such as environmental negotiations, exploitation of common resources, can be modeled as games and how solutions can be engineered. Errata(s) Errata Contents:IntroductionClassical Theory of Games:Description of a GameEquilibrium Solutions for Noncooperative GamesExtensions and Refinements of the Equilibrium ConceptsDeterministic Dynamic Games:Repeated Games and Memory StrategiesMultistage GamesDifferential GamesStochastic Games:Equilibria in Games Played over Event TreesMarkov GamesPiecewise Deterministic Differential GamesStochastic-Diffusion Games Readership: Advanced undergraduate and graduate students in game theory, economics, management, marketing, and game engineering; researchers interested in dynamic games.
Game theory is a rich and active area of research of which this new volume of the Annals of the International Society of Dynamic Games is yet fresh evidence. Since the second half of the 20th century, the area of dynamic games has man aged to attract outstanding mathematicians, who found exciting open questions requiring tools from a wide variety of mathematical disciplines; economists, so cial and political scientists, who used game theory to model and study competition and cooperative behavior; and engineers, who used games in computer sciences, telecommunications, and other areas. The contents of this volume are primarily based on selected presentation made at the 8th International Symposium of Dynamic Games and Applications, held in Chateau Vaalsbroek, Maastricht, the Netherlands, July 5-8, 1998; this conference took place under the auspices of the International Society of Dynamic Games (ISDG), established in 1990. The conference has been cosponsored by the Control Systems Society of the IEEE, IFAC (International Federation of Automatic Con trol), INRIA (Institute National de Recherche en Informatique et Automatique), and the University of Maastricht. One ofthe activities of the ISDG is the publica tion of the Annals. Every paper that appears in this volume has passed through a stringent reviewing process, as is the case with publications for archival journals.
This volume contains eleven articles which deal with different aspects of dynaoic and differential game theory and its applications in economic modeling and decision making. All but one of these were presented as invited papers in special sessions I organized at the 7th Annual Conference on Economic Dynamics and Control in London, England, during the period June 26-28, 1985. The first article, which comprises Chapter 1, provides a general introduction to the topic of dynamic and differential game theory, discusses various noncooperative equilibrium solution concepts, includ ing Nash, Stackelberg, and Consistent Conjectural Variations equilibria, and a number of issues such as feedback and time-consistency. The second chapter deals with the role of information in Nash equilibria and the role of leadership in Stackelberg problems. A special type of a Stackelberg problem is the one in which one dominant player (leader) acquires dynamic information involving the actions of the others (followers), and constructs policies (so-called incentives) which enforce a certain type of behavior on the followers; Chapter 3 deals with such a class of problems and presents some new theoretical results on the existence of affine incentive policies. The topic of Chapter 4 is the computation of equilibria in discounted stochastic dynamic games. Here, for problems with finite state and decision spaces, existing algorithms are reviewed, with a comparative study of their speeds of convergence, and a new algorithm for the computation of nonzero-sum game equilibria is presented.
In this essay, I study how forward-induction reasoning affect plausibility/stability of agreements in which players in a dynamic interaction enforces cooperation with the threat of mutually destructive punishment. While the traditional theory using equilibrium concept shows that such strategy profile is self-enforcing, under a modification of the model, such strategy profile fails to be consistent with players' rationality.In the first chapter I provide the simplest setting under which this non-rationalizability result of deterrence can be shown. The game is a two-player three-stage game: in the first stage, the players choose whether to enter the strategic interaction by paying some cost; in the second stage, the players play a prisoners' dilemma game; and in the third stage, the players play a coordination game. Each move is simultaneous and the players' past actions are perfectly monitored. While there exists a subgame-perfect equilibrium in which players can cooperate with the threat of punishment provided the punishment is strong enough, I show that the strategy profile does not consists of rationalizable strategies under a certain parameter values. This occurs because choosing to enter, unilaterally defect, and then punish the opponent is strictly dominated by a mixture of the two strategies ``do not enter'' and ``enter, defect, but do not punish.'' This result shows that a simple modification of the game and forward-induction consideration encoded in rationalizability might cast doubt on the idea of deterring defection by the threat of mutual punishment.The other two chapters study to what extent the result in the fist chapter does or does not apply in different settings. The second chapter considers the infinite-horizon extension of the model in the first chapter. In the first period (denoted as period 0), the players choose whether to enter the game. After the players choose to enter, the continuation game is the infinite repetition of the stage game which consists of two phases: in the first phase players play prisoners' dilemma game, after which players simultaneously choose to continue the game, exit from the game without punishing the opponent, or punish the opponent and exit from the game. I show that with a similar condition as in the result in the first chapter, strategy which entails defection and punishment in the first stage is not rationalizable. Moreover, since the exit-without-punishment option works as an outside option in later stages of the game, we also obtain a result which provides conditions under which punishment after defection is excluded by rationalizability.The third chapter extends the model in the first chapter toward an incomplete-information model in that it considers a model of random number of players, who are sequentially matched and play the game as in the first chapter. I assume that while the past actions in the stage games are not observable, occurrences of punishment is publicly observable to all the players (the typical example is the formation of cartels and the occurrence of leniency applications). I explore how this observable punishment works as a signaling device and how this model gives rise to a rationalizable use of punishment. I first show that a simple repetition of games does not give rise to a rationalizable punishment because of the assumption that the players cannot distinguish the non-occurrence of deviation and failure to punishment. I then discuss possible modifications to recover the punishment being an equilibrium action; i.e., that a small perturbation in payoffs can recover the possibility of punishment.
Numerical Methods, Algorithms, and Applications to Ecology and Economics
Author: Steffen Jorgensen
Publisher: Springer Science & Business Media
This collection of selected contributions gives an account of recent developments in dynamic game theory and its applications, covering both theoretical advances and new applications of dynamic games in such areas as pursuit-evasion games, ecology, and economics. Written by experts in their respective disciplines, the chapters include stochastic and differential games; dynamic games and their applications in various areas, such as ecology and economics; pursuit-evasion games; and evolutionary game theory and applications. The work will serve as a state-of-the art account of recent advances in dynamic game theory and its applications for researchers, practitioners, and advanced students in applied mathematics, mathematical finance, and engineering.
Applications to Economics, Finance, Optimization, and Stochastic Control
Author: Andrzej S. Nowak
Publisher: Springer Science & Business Media
Category: Business & Economics
This book focuses on various aspects of dynamic game theory, presenting state-of-the-art research and serving as a guide to the vitality and growth of the field. A valuable reference for researchers and practitioners in dynamic game theory, it covers a broad range of topics and applications, including repeated and stochastic games, differential dynamic games, optimal stopping games, and numerical methods and algorithms for solving dynamic games. The diverse topics included will also benefit researchers and graduate students in applied mathematics, economics, engineering, systems and control, and environmental science.
Dynamic games continue to attract strong interest from researchers interested in modelling competitive as well as conflict situations exhibiting an intertemporel aspect. Applications of dynamic games have proven to be a suitable methodology to study the behaviour of players (decision-makers) and to predict the outcome of such situations in many areas including engineering, economics, management science, military, biology and political science. Dynamic Games: Theory and Applications collects thirteen articles written by established researchers. It is an excellent reference for researchers and graduate students covering a wide range of emerging and revisited problems in both cooperative and non-cooperative games in different areas of applications, especially in economics and management science.
Theory, Applications, and Numerical Methods for Differential and Stochastic Games
Author: Michèle Breton
Publisher: Springer Science & Business Media
This book focuses on various aspects of dynamic game theory, presenting state-of-the-art research and serving as a testament to the vitality and growth of the field of dynamic games and their applications. The selected contributions, written by experts in their respective disciplines, are outgrowths of presentations originally given at the 13th International Symposium of Dynamic Games and Applications held in Wrocław. The book covers a variety of topics, ranging from theoretical developments in game theory and algorithmic methods to applications, examples, and analysis in fields as varied as environmental management, finance and economics, engineering, guidance and control, and social interaction.
This book presents current advances in the theory of dynamic games and their applications in several disciplines. The selected contributions cover a variety of topics ranging from purely theoretical developments in game theory, to numerical analysis of various dynamic games, and then progressing to applications of dynamic games in economics, finance, and energy supply. A unified collection of state-of-the-art advances in theoretical and numerical analysis of dynamic games and their applications, the work is suitable for researchers, practitioners, and graduate students in applied mathematics, engineering, economics, as well as environmental and management sciences.
Annals of the International Society of Dynamic Games
Author: Jan G. Olsder
Publisher: Springer Science & Business Media
The theory of dynamic games is very rich in nature and very much alive! If the reader does not already agree with this statement, I hope he/she will surely do so after having consulted the contents of the current volume. The activities which fall under the heading of 'dynamic games' cannot easily be put into one scientific discipline. On the theoretical side one deals with differential games, difference games (the underlying models are described by differential, respec tively difference equations) and games based on Markov chains, with determin istic and stochastic games, zero-sum and nonzero-sum games, two-player and many-player games - all under various forms of equilibria. On the practical side, one sees applications to economics (stimulated by the recent Nobel prize for economics which went to three prominent scientists in game theory), biology, management science, and engineering. The contents of this volume are primarily based on selected presentations made at the Sixth International Symposium on Dynamic Games and Applica tions, held in St Jovite, Quebec, Canada, 13-15 July 1994. Every paper that appears in this volume has passed through a stringent reviewing process, as is the case with publications for archival technical journals. This conference, as well as its predecessor which was held in Grimentz, 1992, took place under the auspices of the International Society of Dynamic Games (ISDG), established in 1990. One of the activities of the ISDG is the publication of these Annals. The contributions in this volume have been grouped around five themes.