Theory and Decision Library C – serie

This Festschrift in honor ofChristian Seidl combines a group of prominent authors who are experts in areas like public economics, welfare economic, decision theory, and experimental economics in a unique volume. Christian Seidl who has edited together with Salvador Barber` a ` and Peter Hammond the Handbook of Utility Theory (appearing at Kluwer Academic Publishers/Springer Economics), has dedicated most of his research to utility and decision theory, social choice theory, welfare economics, and public economics. During the last decade, he has turned part of his attention to a research tool that is increasingly gaining in importance in economics: the laboratory experiment. This volume is an attempt to illuminate all facets of Christian Seidl’s ambitious research agenda by presenting a collection of both theoretical and expe- mental papers on Utility,Choice,andWelfare written by his closest friends, former students, and much valued colleagues. Christian Seidl was born on August 5, 1940, in Vienna, Austria. Beginning Winter term 1962/63, he studied Economics and Business Administration at the Vienna School of Economics (then “Hochschule fff¨ ur ¨ Welthandel”). 1966 he was awarded an MBA by the Vienna School of Economics and 1969 a doctoral degree in Economics. In October 1968 Christian became a research assistant at the Institute of Economics at the University of Vienna. 1973 he acquired his habilitation (right to teach) in Economics — supervised by Wilhelm Weber — from the Department of Law and Economics of the University of Vienna. He was awarded the Dr.

During the last decade I have explored the consequences of what I have chosen to call the 'consistent preferences' approach to deductive reasoning in games. To a great extent this work has been done in coop­ eration with my co-authors Martin Dufwenberg, Andres Perea, and Ylva Sovik, and it has lead to a series of journal articles. This book presents the results of this research program. Since the present format permits a more extensive motivation for and presentation of the analysis, it is my hope that the content will be of interest to a wider audience than the corresponding journal articles can reach. In addition to active researcher in the field, it is intended for graduate students and others that wish to study epistemic conditions for equilibrium and rationalizability concepts in game theory. Structure of the book This book consists of twelve chapters. The main interactions between the chapters are illustrated in Table 0.1. As Table 0.1 indicates, the chapters can be organized into four dif­ ferent parts. Chapters 1 and 2 motivate the subsequent analysis by introducing the 'consistent preferences' approach, and by presenting ex­ amples and concepts that are revisited throughout the book. Chapters 3 and 4 present the decision-theoretic framework and the belief operators that are used in later chapters. Chapters 5, 6, 10, and 11 analyze games in the strategic form, while the remaining chapters-Chapters 7, 8, 9, and 12-are concerned with games in the extensive form.

This book is about the interplay of theory and experimentation on group decision making in economics. The theories that the book subjects to experimental testing mostly come from the theory of games. The decisions investigated in the book mostly concern economic interaction like strict competition. two-person bargaining. and coalition formation. The underlying philosophy of the articles collected in this book is consistent with the opinion of a growing number of economists and psychologists that economic issues cannot be understood fully just by thinking about them. Rather. the interplay between theory and experimentation is critical for the development of economics as an observational science (Smith. 1989). Reports of laboratory experiments in decision making and economics date back more than thirty years (e.g .• Allais. 1953; Davidson. Suppes. and Siegel. 1957; Flood. 1958; Friedman. 1%3; Kalisch. Milnor. Nash. and Nering. 1954; Lieberman. 1%0; Mosteller and Nogee. 1951; Rapoport. Chammah. Dwyer. and Gyr. I %2; Siegel and Fouraker. I %0; Stone. 1958). However. only in the last ten or fifteen years has laboratory experimentation in economics started its steady transformation from an occasional curiosity into a regular means for investigating various economic phenomena and examining the role of economic institutions. Groups of researchers in the USA and abroad have used experimental methods with increasing sophistication to attack economic problems that arise in individual decision making under risk. two-person bargaining.

The motivation for this monograph can be traced to a seminar on Simple Games given by Professor S.H. Tijs of the Catholic University at Nijmegen way back in 1981 or 1982 at the Delhi campus of the Indian Statistical Institute. As an ap­ plied statistician and a consultant in quality control, I was naturally interested in Reliability Theory. I was aquainted with topics in reliability like coherent systems, importance of components etc., mainly through Barlow and Proschan's book. At the seminar given by Professor Tijs, I noticed the striking similarity between the concepts in reliability and simple games and this kindled my interest in simple games. When I started going deep into the literature of simple games, I noticed that a number of concepts as well as results which were well known in game theory were rediscovered much later by researchers in reliability. Though the conceptual equivalence of coherent structures and simple games has been noticed quite early, it is not that much well known. In fact, the theoretical developments have taken place practically independent of each other, with considerable duplication of research effort. The basic objective of this monograph is to unify some of the concepts and developments in reliability and simple games so as to avoid further duplication.

The present book treats a highly specialized topic, namely effec­ tivity functions, which are a tool for describing the power structure implicit in social choice situations of various kind. One of the ad­ vantages of effectivity functions is that they seem to contain exactly the information which is needed in several problems of implementa­ tion, that is in designing the rules for individual behaviour given that this behaviour at equilibrium should result in a prescribed functional connection between preferences and outcome. We shall be interested in both formal properties of effectiv­ ity functions and applications of them in social choice theory, and among such applications in particular the implementation problem. This choice of emphasis necessarily means that some other topics are treated only superficially or not at all. We do not attempt to cover all contributions to the field, rather we try to put some of the results together in order to get a reasonably coherent theory about the role of the power structure in cooperative implementation. The authors are indebted to many persons for assistance and advice during the work on this book. In particular, we would like to thank Peter Fristrup and Bodil Hansen for critical reading of the manuscript, and Lene Petersen for typesetting in '.lEX.

Many social or economic conflict situations can be modeled by specifying the alternatives on which the involved parties may agree, and a special alternative which summarizes what happens in the event that no agreement is reached. Such a model is called a bargaining game, and a prescription assigning an alternative to each bargaining game is called a bargaining solution. In the cooperative game-theoretical approach, bargaining solutions are mathematically characterized by desirable properties, usually called axioms. In the noncooperative approach, solutions are derived as equilibria of strategic models describing an underlying bargaining procedure. Axiomatic Bargaining Game Theory provides the reader with an up-to-date survey of cooperative, axiomatic models of bargaining, starting with Nash's seminal paper, The Bargaining Problem. It presents an overview of the main results in this area during the past four decades. Axiomatic Bargaining Game Theory provides a chapter on noncooperative models of bargaining, in particular on those models leading to bargaining solutions that also result from the axiomatic approach. The main existing axiomatizations of solutions for coalitional bargaining games are included, as well as an auxiliary chapter on the relevant demands from utility theory.

The concept of a value of a coalitional game, in the spirit of R.J. Aumann and L.S. Shapley, is extended to the case of games with fuzzy coalitions, providing heuristically meaningful insights into the game theoretical context, which have some impact on balance and equilibria analysis in a co-operative environment. Using the suggestive and philosophical power of the concept of fuzzy sets introduced by L.A. Zadeh, this text aims to develop the mathematical machinery of triangular norm-based measures, i.e. valuations preserving binary operations induced by triangular norms on [0, 1 ]. These results show the existence of Aumann-Shapley values for large classes of games with fuzzy coalitions satisfying certain differentiability conditions, and allow the extension of the domain of such values to games with crisp coalitions, and the application to real life situations such as rate problems for services in bulk.

This book aims to develop an institutional approach to general economic equi­ librium. Thus far, institutional economics has essentially been confined to purely verbal discourse. Here I argue the case that general equilibrium theory forms a well rounded basis for the development of an institutional economic the­ ory. The fundamental economic trade mechanism underlying this refocusing is that of the Edgeworthian barter mechanism modelled through the equilibrium notion of the core of an economy. There is an extensive literature that links the core with the Walrasian price mechanism, which is explored in this book. Next I develop an alternative model of explicitly nonsovereign trade in the setting of an institutionally structured economy. In this book the core and several of its extensions are considered to be descriptions of the equilibrium allocations resulting from institutionalized barter processes, thereby providing a basis of an institutionally based economic theory. Traditionally finite economies have been assessed as the most natural represen­ tations of real life economies, in particular of market economies. Many funda­ mental insights have been developed. In the first half of the book I summarize the most influential and important results in the literature on finite economies regarding the relationship of the Walrasian model of a perfectly competitive market system and the Edgeworthian theory of individually based, pure barter processes. I use the axiomatic method as the main methodological framework according to which I construct my models.

In six chapters this text introduces a micro-economic model where trade takes place through a stable structure of bilateral exchange institutions. The main problem in such models is that, for well-known equilibrium concepts, equilibrium may fail to exist in the corresponding game. In this work an adaptation of such models - hierarchically structured economies - is introduced. The possibilities and limitations of the use of the concept of subgame perfect equilibrium within the context of this kind of models is discussed. Furthermore, it is shown that some well-known market forms, viz. Walrasian and monopolistic markets, occur as special cases. A modification of the concept of subgame perfect equilibrium is introduced to formulate and prove a general theorem on the existence of equilibrium in hierarchically structured economies.

In this book applications of cooperative game theory that arise from combinatorial optimization problems are described. It is well known that the mathematical modeling of various real-world decision-making situations gives rise to combinatorial optimization problems. For situations where more than one decision-maker is involved classical combinatorial optimization theory does not suffice and it is here that cooperative game theory can make an important contribution. If a group of decision-makers decide to undertake a project together in order to increase the total revenue or decrease the total costs, they face two problems. The first one is how to execute the project in an optimal way so as to increase revenue. The second one is how to divide the revenue attained among the participants. It is with this second problem that cooperative game theory can help. The solution concepts from cooperative game theory can be applied to arrive at revenue allocation schemes. In this book the type of problems described above are examined. Although the choice of topics is application-driven, it also discusses theoretical questions that arise from the situations that are studied. For all the games described attention will be paid to the appropriateness of several game-theoretic solution concepts in the particular contexts that are considered. The computation complexity of the game-theoretic solution concepts in the situation at hand will also be considered.

A central problem of prescriptive decision making is the mismatch between the elegant formal models of decision theory and the less elegant, informal thinking of decision makers, especially when dealing with ill-structured situations. This problem has been a central concern of the authors and their colleagues over the past two decades. They have wisely (to my mind) realized that any viable solution must be informed by a deep understanding of both the structural properties of alternative formalisms and the cognitive demands that they impose on decision makers. Considering the two in parallel reduces the risk of forcing decision makers to say things and endorse models that they do not really understand. It opens the door for creative solutions, incorporating insights from both decision theory and cognitive psychology. It is this opportunity that the authors have so ably exploited in this important book. Under the pressures of an interview situation, people will often answer a question that is put to them. Thus, they may be willing to provide a decision consultant with probability and utility assessments for all manner of things. However, if they do not fully understand the implications of what they are saying and the use to which it will be put, then they cannot maintain cognitive mastery of the decision models intended to represent their beliefs and interests.

Game Theoretical Applications to Economics and Operations Research deals with various aspects of game theory and their applications to Economics and OR related problems. It brings together the contributions of a wide spectrum of disciplines such as Statistics, Mathematics, Mathematical Economics and OR. The contributions include decision theory, stochastic games, cooperative and noncooperative games. The papers in the volume are classified under five different sections. The first four sections are devoted to the theory of two-person games, linear complimentarity problems and game theory, cooperative and noncooperative games. The fifth section contains diverse applications of these various theories. Taken together they exhibit a rich versatility of these theories and lively interaction between the mathematical theory of games and significant economic problems.

Coalition Formation and Social Choice provides a unified and comprehensive study of coalition formation and collective decision-making in committees. It discusses the main existing theories including the size principle, conflict of interest theory, dominant player theory, policy distance theory and power excess theory. In addition, the book offers new theories of coalition formation in which the endogenous formation of preferences for coalitions is basic. Both simple game theory and social choice theory are extensively applied in the treatment of the theories. This combined application not only leads to new theories but also offers a new and fresh perspective on coalition formation and collective decision-making in committees. The book covers the fundamental concepts and results of social choice theory including Arrow's Impossibility Theorem. Furthermore, it gives a coherent treatment of the theory of simple games. Besides more traditional topics in simple game theory like power indices, it also introduces new aspects of simple games such as the Chow parameter, the Chow vector and the notion of similar games.

This book arose out of a conference on "Epistemic Logic and the Theory of Games and Decisions" that took place in January 1994 at the Centre Inter- national de Recherches Mathematiques in Marseille. The convergence of game theory and epistemic logic has been in progress for two decades. The aim of the conference was to explore this rapprochement further by gathering spe- cialists from different professional communities, i. e. , economics, mathematics, philosophy, and computer science. Also, the organizors aimed at fostering the work centered on the issues of knowledge and belief that has recently been pursued amongst game theorists and decision theorists. The conference was funded by the following institutions: Centre National de la Recherche Sci- entifique (France), Ministere de l'Enseignement Superieur et de la Recherche (France), Association pour Ie Developpement de la Recherche en Economie et Statistique (France). It was also supported by the Human Capital and Mobility Programme of the EU, as well as, locally, by the Ville de Marseille. We would like to express our gratitude to these institutions for their generous help.Despite the success of the conference, it was not the editors' intention to circulate just another volume of proceedings in the usual style. Throughout the more than two-year editorial process, they have pursued the goal of providing a no doubt non-exhaustive, but hopefully thorough and accurate, state of the art account of a promising field of research.

Social and Economic Networks in Cooperative Game Theory presents a coherent overview of theoretical literature that studies the influence and formation of networks in social and economic situations in which the relations between participants who are not included in a particular participant's network are not of consequence to this participant.The material is organized in two parts. In Part I the authors concentrate on the question how network structures affect economic outcomes. Part II of the book presents the formation of networks by agents who engage in a network-formation process to be able to realize the possible gains from cooperation.

This chapter is organized as follows. The economic problem on which this book focuses is motivated in Section 1. The two tools used to study this economic problem, which are real options theory and game theory, are discussed in Sections 2 and 3, respectively. Section 4 surveys the contents of this book. In Section 5 some promising extensions of the research presented in this book are listed. 1. TECHNOLOGY INVESTMENT Investment expenditures of companies govern economic growth. Es­ pecially investments in new and more efficient technologies are an impor­ tant determinant. In particular, in the last two decades an increasing part of the investment expenditures concerns investments in informa­ tion and communication technology. Kriebel, 1989 notes that (already) in 1989 roughly 50 percent of new corporate capital expenditures by major United States companies was in information and communication technology. Due to the rapid progress in these technologies, the tech­ nology investment decision of the individual firm has become a very complex matter. As an example of the very high pace of technological improvement consider the market for personal computers. IBM intro­ duced its Pentium personal computers in the early 1990s at the same price at which it introduced its 80286 personal computers in the 1980s. Therefore it took less than a decade to improve on the order of twenty times in terms of both speed and memory capacities, without increasing the cost (Yorukoglu, 1998).

I would like to use this preface to thank some persons and institutions which have been important during the various stages of writing this book. First of all, I am grateful to Kluwer Academic Publishers for giving me the opportunity to write this book. I started writing the book in 1998 while I was working at the Departament d'Economia i d'Historia Economica at Universidad Autonoma de Barcelona, and continued the writing job from september 1998 to september 2000 at the Departamento de Economfa at Universidad Carlos III de Madrid. The book has been completed while I was visiting the Department of Quantitative Economics at the University of Maastricht from october 2000 to august 2001. I wish to thank these three departments for their hospitality. The book has improved substantially by comments and critique from the following persons who have read parts of the manuscript: Geir Asheim, Eric van Damme, Janos Flesch, Mari-Angeles de Frutos, Diego Moreno, Hans Peters, Antonio Romero and Dries Vermeulen.I should also mention my discussions with Peter Wakker about the decision-theoretic foundations of noncooperative game theory, which have had an important impact on various parts of the book. Finally, I wish to express my warmest gratitude to my parents, my brother and my sister, and, last but not least, to Cati, to whom I dedicate this book.

The aim of Cooperative Games on Combinatorial Structures is to analyze conflict situations in which two or more players can make coalitions and obtain prizes and penalties. This approach to situations of competition and cooperation was given in the seminal treatise by John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior. Cooperative game theory has succeeded in providing many applications of game theory. In this volume, games defined on combinatorial structures will be analyzed, i.e. a set system over a set of players. In many situations the author will work in a closure space. Examples of closure operators are the spanning operator of linear algebra and all convex hull operators. Chapters 1-4 constitute a review of mathematical concepts from Cooperative Game Theory, Graph Theory, Linear and Integer Programming, Combinatorial Optimization, Discrete Convex Analysis and Computational Complexity. The table of contents is a short guide to the topics and methods covered in this book. In Chapters 11 and 12, several notebooks are presented with the system Mathematica by Wolfram in the contexts of the packages DiscreteMath (Skiena) and Cooperative (Carter). There will also be found in the book several research projects. These are intended to offer new ideas that the reader should consider with caution. This book will be of interest to graduate students with some experience in game theory or mathematical programming and professional researchers in game theory, operational research and its applications in economic theory, and the political and social sciences. In addition, it will be especially useful for professionals who are interested in models for understanding and managing conflicts: management and operational research scientists, political and military scientists, and professional negotiators.

This text is devoted to the computation of equilibria, fixed points and stationary points. It has been written with three goals in mind: to give a comprehensive introduction to fixed point methods and to the definition and construction of Grobner bases; to discuss several interesting applications of these methods in the fields of general equilibrium theory, game theory, mathematical programming, algebra and symbolic computation; and to introduce several advanced fixed point and stationary point theorems. These methods and topics should be of interest not only to economists and game theorists concerned with the computation and existence of equilibrium outcomes in economic models and co-operative and non-co-operative games, but also to applied mathematicians, computer scientists and engineers dealing with models of highly nonlinear systems of equations (or polynomial equations).

This book describes highly applicable mathematics without using calculus or limits in general. The study agrees with the opinion that the traditional calculus/analysis is not necessarily the only proper grounding for academics who wish to apply mathematics. The choice of topics is based on a desire to present those facets of mathematics which will be useful to economists and social/behavioral scientists. The volume is divided into seven chapters. Chapter I presents a brief review of the solution of systems of linear equations by the use of matrices. Chapter III introduces the theory of probability. The rest of the book deals with new developments in mathematics such as linear and dynamic programming, the theory of networks and the theory of games. These developments are generally recognized as the most important field in the `new mathematics' and they also have specific applications in the management sciences.

In cooperative games, one generally assumes that the agents know exactly the joint (monetary) gains that can be achieved by any possible coalition of cooperating agents. In reality, however, only little is known with certainty. This does not necessarily imply that traditional cooperative game theory cannot be applied in practical situations, for in various cases knowledge of the expected gains suffices. In many other cases, however, it is just the sharing of risk that is beneficial. Joint ventures, for instance, exist since cooperation reduces the risk of the investment for the individual parties. Since the existing models fail to incorporate such risks, they are not suitable for analyzing cooperative decision-making under risk. This book aims to rectify this deficiency by discussing a model of cooperative games with random payoffs.

This collection of papers is an outgrowth of the "Game Practice I" th th conference held in Genoa from 28 to 30 June 1998. More precisely, it is the result of the call for papers that was issued in association with that conference: actually, nearly half of the contributions to this book are papers that were presented in Genoa. The name chosen for the conference and for this book is in evident and provocative contrast with "Game Theory": this choice needs some explanation, and to that we shall devote a few words of this Preface. Let us say at the outset that "Game Practice" would not exist without Game Theory. As one can see, the overall content of this book is firmly rooted in the existing Game Theory. It could be hardly otherwise, given the success and influence of Game Theory (just think of the basic issues in Economic Theory), and the tremendous development that has taken place within Game Theory. This success, however, makes even more evident the existence of problems with respect to the verification of the theory. This is patent from the point of view of the predictive value of Game Theory (the "positive" side): a lot of experimental and observational evidence demon­ strates that there is a large gap between theory and "practice".

Game Theory: Stochastics, Information, Strategies and Cooperation provides a discussion of some relevant topics in game theory. It is composed partially from material compiled by Professor Joachim Rosenmüller when lecturing at IMW, the Institute of Mathematical Economics at the University of Bielefeld. On the other hand, it also contains research topics that are not presented in a typical game theory textbook. Thus, the volume may provide the basis for an advanced course in game theory; simultaneously it may be called a monograph, and, as a third aspect, it also supplies some rather elementary versions of advanced topics of the field. The volume has a non-cooperative and a cooperative part and in both of them the reader is assumed to have some basic knowledge in game theory, for instance, concerning the normal form (bimatrix games, Nash equilibria of the mixed extension, backwards induction in games with perfect information) on one hand and the coalitional function (simple games, convex games, superadditive games, the core, the Shapley volume) on the other hand. Some emphasis is laid on the probabilistic background; however, the author treats stochastic games using the language of probability in order to consider simple models in which measure theory can be omitted.

Imperfections and Behavior in Economic Organizations analyzes the organization of economic decision making in a contemporary setting. The contributors focus on two important aspects of this analysis. First, they address the issue of imperfect or incomplete information and communication in economic organizations and consider imperfections arising from the interaction of the market organization with its environment. Second, the issue of cooperation in a competitive environment is thoroughly analyzed and alternative social trade organizations are designed to dissipate the allocation problems that arise in these situations.

Mathematical economics uses mathematical tools and reasoning to describe and explain economic reality. At the core of mathematical economics is general equilibrium theory. This text describes and analyzes various general equilibrium models, treating theory from an axiomatic point of view, which may lead to a deeper understanding of problems, may help to avoid incorrect reasoning, and may improve communication within the economic science. This volume consists of four parts, each of which is self-contained. Part I deals with the mathematical and economic preliminaries. Part II considers the static aspects of disequilibrium theory. Part III determines price rigidities endogenously. Finally, Part IV deals with dynamic aspects of disequilibrium theory.

This volume focuses on the social impact of the public sector on the performance of the private sector, especially in the long term. It presents a model of the formation of social ties by economic interaction and uses this to explore the relevance of social ties and their dynamics for economic performance. The impact of public provision and stochastic migration on social ties and the (total) provision level of the public good are also examined. It discusses the role of social ties in other types of interaction, and proposes definitions of social capital and infrastructure. Furthermore, it contains a discussion of the connections between the different conceptions of these terms. Also the effects of social ties and the influence of different types of public intervention on growth are examined. The assumption of exogenously determined, stochastic migration is dropped, and migration behavior is analyzed explicitly. In this theoretical investigation of the dynamics of social ties and economic interaction a number of important effects on economic performance will be suggested.

Essays on Cooperative Games collates selected contributions on Cooperative Games. The papers cover both theoretical aspects (Coalition Formation, Values, Simple Games and Dynamic Games) and applied aspects (in Finance, Production, Transportation and Market Games). A contribution on Minimax Theorem (by Ken Binmore) and a brief history of early Game Theory (by Gianfranco Gambarelli and Guillermo Owen) are also enclosed.