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.
This book is written for those seeking a decision theory appropriate for use in serious choices such as insurance. It employs stages of knowledge ahead to track satisfactions and dissatisfactions. From experimental and questionnaire data, people take into account such stages of knowledge ahead satisfactions and dissatisfactions. This means we must go beyond standard decision theories like expected utility or cumulative prospect theory.
This book provides insights that are useful for people with interests in Operations Research, statistics and econometrics. Each contribution offers a snapshot out from interesting topics. The relationships and interconnectivities between decisions and models from different economic fields lead to a better understanding of the modern field of Operations Research. The book focuses on modelling as an activity rather than on techniques and programming. Divided into three parts, part one provides decision theoretical models, part two provides several theoretical and empirical papers concerning statistics and econometrics. Finally, part three provides an up-to-date account of Operations Research.
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.
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