Balanced Silverman Games on General Discrete Sets
Balanced Silverman Games on General Discrete Sets

Author: Gerald A. Heuer

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 149

ISBN-13: 3642956637

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A Silverman game is a two-person zero-sum game defined in terms of two sets S I and S II of positive numbers, and two parameters, the threshold T > 1 and the penalty v > 0. Players I and II independently choose numbers from S I and S II, respectively. The higher number wins 1, unless it is at least T times as large as the other, in which case it loses v. Equal numbers tie. Such a game might be used to model various bidding or spending situations in which within some bounds the higher bidder or bigger spender wins, but loses if it is overdone. Such situations may include spending on armaments, advertising spending or sealed bids in an auction. Previous work has dealt mainly with special cases. In this work recent progress for arbitrary discrete sets S I and S II is presented. Under quite general conditions, these games reduce to finite matrix games. A large class of games are completely determined by the diagonal of the matrix, and it is shown how the great majority of these appear to have unique optimal strategies. The work is accessible to all who are familiar with basic noncooperative game theory.

General Equilibrium with Increasing Returns
General Equilibrium with Increasing Returns

Author: Antonio Villar

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 172

ISBN-13: 3662004577

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This is a book on general equilibrium in which firms are allowed to exhibit increasing returns to scale (more precisely, in which the convexity of production sets is not assumed). As such, it provides a full fledged general equilibrium model and analyzes the chief questions concerning existence and optimality. Increasing returns is a topic which many economists find it to be simultaneously very imponant, very difficult and very discouraging. It is very important because it refers to a well established technological phenomenon which is essentially incompatible with the functioning of competitive markets. It is very difficult because the standard concepts and tools for the analysis fail (in particular, the supply mappings are not well defined). It is very discouraging because the available models do not seem to solve the basic questions: Normative models where nonconvex firms follow marginal pricing do not achieve efficient outcomes, and positive models cannot incorporate monopolistic competition as a way of defming the behavior of those firms with increasing returns to scale. I would like to think that this monograph will contribute to show that "the increasing returns question" is neither too difficult nor too discouraging. Concerning the difficulty, it will be shown that the analysis can be carried out with essentially the same tools as those applicable to the standard competitive model. As for the relevance of the results available, let me point out the following.

Search Games and Other Applications of Game Theory
Search Games and Other Applications of Game Theory

Author: Andrey Garnaev

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 157

ISBN-13: 3642573045

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This book is on applications of game theory. The title of this book is not "Game Theory and its Applications" because it does not construct a general theory for considered games. The book contains a lot of examples of applica tion of game theory together with the background of those games considered and a list of unsolved problems. Also we consider only the game where the optimal strategies of the players are found in closed form. This book is an attempt to carryon the approach developed in nice books "Search Games" by Gal and "Geometric Games and their Applications" by Ruckle. The first chapter of this book supplies the required definitions and theorems from game theory. The second chapter deals with discrete search games where both players act simultaneously: the games of protection of a channel from infiltration of a submarine, the submarine versus helicopter game, the matrix search games and others. The third chapter considers the game where the players allocate their contin uous efforts. In these games players face up an alternative either not to come into contest if the cost of efforts seems too high, or come into it. In the last case the player have to decide how much resources they can afford to spend. The allocation models of search, antiballistic protection and marketing are investigated.

Adjustment Processes for Exchange Economies and Noncooperative Games
Adjustment Processes for Exchange Economies and Noncooperative Games

Author: Antoon van den Elzen

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 155

ISBN-13: 3642481337

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This monograph is a treatise on adjustment processes. We consider price adjustment processes in exchange economies and strategy adjustment processes in noncooperative games. In the most simple version of an exchange economy, i.e. a pure exchange economy, there exist markets on which prices are determined by the demand and supply created by a finite number of consumers willing to exchange their initial endowments in order to maximize their utilities. An equilibrium situation is attained if, for some price vector, demand equals supply in all markets. Starting from a situation not being an equi librium an adjustment process reaches an equilibrium via adaptations of prices. The advantage of the adjustment processes we will present in this monograph is that they exist and converge under far weaker assumptions than existing processes. The second subject concerns the problem of finding Nash equilibria in noncooperative games. A Nash equilibrium is a situation from which no player can improve his position by unilaterally changing his strategy. We present a new algorithm for finding such equilibria. The sequence of stra tegy vectors generated by the algorithm can be interpreted as the path followed by a strategy adjustment process.

Focal Points in Framed Games
Focal Points in Framed Games

Author: Andre Casajus

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 142

ISBN-13: 3642511120

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Go to, let us go down, and there confound their language, that they may not understand one another's speech. So the LORD scattered them abroad from thence upon the face of all the earth: and they left off to built the city. (Genesis 11.7-8) 1.1 Static Focal Points 1.1.1 Coordination In real life, people quite often face situations in which they prefer to act in the same way, but they are not particular about the concrete way of acting. Some examples are given below: Credit cards: Buyers want to possess the credit cards potential sellers do accept. Also, sellers wish to have contracted the credit card company the credit cards of which potential customers usually carry along. For both, basically, it is all the same which credit card this is. What matters is that both choices coincide. Communication, information transmission: The transmission of in formation requires that the signals used have the same meaning to both the sender and the receiver. But it is inessential which signal has a certain mean ing. In verbal communication, this basically means that the people involved use the same (natural) language, though even then some ambiguities remain. Things are a bit more difficult for non-verbal communication, for example data transmission between computers-both sides have to use the same or compatible protocols. Again, what matters is the protocols to be the same for both sides.

Silverman’s Game
Silverman’s Game

Author: Gerald A. Heuer

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 295

ISBN-13: 3642468195

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The structure of a Silverman game can be explained very quickly: Each of two players independently selects a number out of a prede termined set, not necessarily the same one for both of them. The higher number wins unless it is at least k times as high as the other one; if this is the case the lower number wins. The game ends in a draw if both numbers are equal. k is a constant greater than 1. The simplicity of the rules stimulates the curiosity of the the orist. Admittedly, Silverman games do not seem to have a direct applied significance, but nevertheless much can be learnt from their study. This book succeeds to give an almost complete overview over the structure of optimal strategies and it reveals a surprising wealth of interesting detail. A field like game theory does not only need research on broad questions and fundamental issues, but also specialized work on re stricted topics. Even if not many readers are interested in the subject matter, those who are will appreciate this monograph.

Litigation and Settlement in a Game with Incomplete Information
Litigation and Settlement in a Game with Incomplete Information

Author: Wolfgang Ryll

Publisher: Springer Science & Business Media

Published: 1996-07-12

Total Pages: 188

ISBN-13: 9783540613046

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The book investigates a two-person game of litigation and settlement with incomplete information on one side. The experimental design allows investigation of how subjects solve the bargaining problem. A prominence level analysis is applied to the data and suggests that subjects tend to choose "round" numbers. It is shown that there exists a correlation between machiavellianism and subjects' adjustment behaviour in the game. The learning behaviour is discussed extensively. Plaintiffs' acceptance limits polarize at the beginning of the second play. A model of learning direction theory applied to explain subjects's behaviour over the course of the game.

Dynamic Preferences, Choice Mechanisms, and Welfare
Dynamic Preferences, Choice Mechanisms, and Welfare

Author: Ludwig von Auer

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 227

ISBN-13: 3642588794

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For most economic aspects of human behaviour, static deci sion models provide an insufficient description. More specifically, they ignore the fact that preferences may change over time and that at each point of time current preferences depend on aspects which are associated with the past or the future. The neglect of these phenomena may lead to results which have little in com mon with real life. Dynamic decision models were developed in order to cope with these complications. Spurred by the availability of new mathematical tools such as optimal control theory and dynamic programming, dynamic utility models mushroomed over the last two decades. Various frameworks were developed featuring dif ferent restrictions on the way agents form preferences in an in tertemporal environment. Unfortunately, no systematic reappraisal of this literature ex ists. The survey provided in part I of this thesis attempts to fill in this gap. It introduces a comprehensive classification sys tem which allows for a coherent organization of all studies of intertemporal choice under certainty and complete information. 2 1. Introduction The latter implies that the individual knows in advance all fu ture preferences and choice possibilities. In this survey we show that all dynamic utility models can be viewed as special cases of the class of universal utility mod els. It is therefore desirable to investigate intertemporal decision making in terms of this least restrictive framework. Accordingly, all findings of part II of this thesis are derived for the class of universal utility models.

Empirical Vector Autoregressive Modeling
Empirical Vector Autoregressive Modeling

Author: Marius Ooms

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 397

ISBN-13: 3642487920

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1. 1 Integrating results The empirical study of macroeconomic time series is interesting. It is also difficult and not immediately rewarding. Many statistical and economic issues are involved. The main problems is that these issues are so interrelated that it does not seem sensible to address them one at a time. As soon as one sets about the making of a model of macroeconomic time series one has to choose which problems one will try to tackle oneself and which problems one will leave unresolved or to be solved by others. From a theoretic point of view it can be fruitful to concentrate oneself on only one problem. If one follows this strategy in empirical application one runs a serious risk of making a seemingly interesting model, that is just a corollary of some important mistake in the handling of other problems. Two well known examples of statistical artifacts are the finding of Kuznets "pseudo-waves" of about 20 years in economic activity (Sargent (1979, p. 248)) and the "spurious regression" of macroeconomic time series described in Granger and Newbold (1986, §6. 4). The easiest way to get away with possible mistakes is to admit they may be there in the first place, but that time constraints and unfamiliarity with the solution do not allow the researcher to do something about them. This can be a viable argument.

Dynamic Timing Decisions Under Uncertainty
Dynamic Timing Decisions Under Uncertainty

Author: Nguyen M. Hung

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 201

ISBN-13: 3642515088

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Jay Forrester's Economic Dynamics was published in 1971 and The Limits to Growth by Dennis Meadows and his associates appeared a year later. The publication of those two books gave rise to twenty years of intense research into the economics of exhaustible resources, research which everywhere has had a substantial impact both on public debate and on academic curricula. And now, just as that line of research is losing steam, economists are focussing on problems associated with the degradation of the natural environment, problems which call for models which, in their formal structure, are quite similar to those already developed in resource economics. This is therefore an appropriate moment for the appearance of a thorough exposition of the economics of exhaustible resources. For that is what Nguyen Manh Hung and Nguyen Van Quyen have provided. Their splendid new book covers equally well the older Hotelling-inspired theory of cake-eating and the economics of search and R&D designed to uncover new and cheaper sources of supply. It provides an entree to the whole subject of resource economics, as well as many new discoveries which will be of interest to experienced researchers.