Solution to 70 Paradoxes including “Prisoner’s Dilemma”


Book Description

This book solves many famous problems such as prisoner’s dilemma and half-fee litigation. The new academic viewpoints put forward in this book are: (1) The Pythagorean school and later generations’ proof that √2 is not a rational number is invalid. (2) A new definition is given to the concept of non-predicative definition, thus providing a logical justification for the legality of scientific concepts like function maximum. (3) Reconstruction of the theory of natural number provides an ultimate and reliable foundation for mathematics. Through the resolution of a large number of specific paradoxes, this book hopes that readers can establish a correct view that invalid reasoning is the cause of paradoxes, thus making it clear that the correct way to resolve paradoxes should be to find out the specific causes leading to invalid reasoning. This book can be used as a teaching reference book for general courses such as paradox, logic, game theory, economics, etc. Sales suggestions: Philosophy, logic, mathematics, game theory, economics.




Prisoner's Dilemma


Book Description

A masterful work of science writing that’s "both a fascinating biography of von Neumann, the Hungarian exile whose mathematical theories were building blocks for the A-bomb and the digital computer, and a brilliant social history of game theory and its role in the Cold War and nuclear arms race" (San Francisco Chronicle). Should you watch public television without pledging?...Exceed the posted speed limit?...Hop a subway turnstile without paying? These questions illustrate the so-called "prisoner's dilemma", a social puzzle that we all face every day. Though the answers may seem simple, their profound implications make the prisoner's dilemma one of the great unifying concepts of science. Watching players bluff in a poker game inspired John von Neumann—father of the modern computer and one of the sharpest minds of the century—to construct game theory, a mathematical study of conflict and deception. Game theory was readily embraced at the RAND Corporation, the archetypical think tank charged with formulating military strategy for the atomic age, and in 1950 two RAND scientists made a momentous discovery. Called the "prisoner's dilemma," it is a disturbing and mind-bending game where two or more people may betray the common good for individual gain. Introduced shortly after the Soviet Union acquired the atomic bomb, the prisoner's dilemma quickly became a popular allegory of the nuclear arms race. Intellectuals such as von Neumann and Bertrand Russell joined military and political leaders in rallying to the "preventive war" movement, which advocated a nuclear first strike against the Soviet Union. Though the Truman administration rejected preventive war the United States entered into an arms race with the Soviets and game theory developed into a controversial tool of public policy—alternately accused of justifying arms races and touted as the only hope of preventing them. Prisoner's Dilemma is the incisive story of a revolutionary idea that has been hailed as a landmark of twentieth-century thought.




The Game's Afoot! Game Theory in Myth and Paradox


Book Description

It all started with von Neumann and Morgenstern half a century ago. Their Theory of Games and Economic Behavior gave birth to a whole new area of mathematics concerned with the formal problems of rational decision as experienced by multiple agents. Now, game theory is all around us, making its way even into regular conversations. In the present book, Mehlmann presents mathematical foundations and concepts illustrated via social quandaries, mock political battles, evolutionary confrontations, economic struggles, and literary conflict. Most of the standard models - the prisoners' dilemma, the arms race, evolution, duels, the game of chicken, etc. - are here. Many non-standard examples are also here: the Legend of Faust, shootouts in the movies, the Madness of Odysseus, to name a few. The author uses familiar formulas, fables, and paradoxes to guide readers through what he calls the "hall of mirrors of strategic decision-making". His light-hearted excursion into the world of strategic calculation shows that even deep insights into the nature of strategic thought can be elucidated by games, puzzles and diversions. Originally written in German and published by Vieweg-Verlag, this AMS edition is a translation tailored for the English-speaking reader. It offers an intriguing look at myths and paradoxes through the lens of game theory, bringing the mathematics into sharper focus at the same time. This book is a must for those who wish to consider game theory from a different perspective: one that embraces science, literature, and real-life conflict. The Game's Afoot! would make an excellent book for an undergraduate course in game theory. It can also be used for independent study or as supplementary course reading. The connections to literature, films and everyday life also make it highly suitable as a text for a challenging course for non-majors. Its refreshing style and amusing combination of game theoretic analysis and cultural issues even make it appealing as recreational reading.




Paradoxes of Rationality and Cooperation


Book Description

This anthology, the first to bring together the most importantphilosophical essays on the paradoxes, analyses the concepts underlyingthe Prisoner's Dilemma and Newcomb's Problem and evaluates theproposed solutions. The relevant theories have been developed over thepast four decades in a variety of disciplines: mathematics, economics,psychology, political science, biology, and philosophy. And theproblems these paradoxes uncover can arise in many different forms: indebates over nuclear disarmament, labour-management disputes, maritalconflicts, Calvinist theology, and even in the evolution of diseasethrough the "cooperation" of microorganisms. Thepossibilities for application are virtually limitless.




Social Dilemmas


Book Description

Emphasizing real-world examples, Komorita and Parks illustrate both the theoretical and the ecological relevance of social dilemmas, focusing on "exchange theory" to explain how conflicts are resolved. This book is appropriate for students of psychology, political science, and sociology.




Paradoxes in Scientific Inference


Book Description

Paradoxes are poems of science and philosophy that collectively allow us to address broad multidisciplinary issues within a microcosm. A true paradox is a source of creativity and a concise expression that delivers a profound idea and provokes a wild and endless imagination. The study of paradoxes leads to ultimate clarity and, at the same time, indisputably challenges your mind. Paradoxes in Scientific Inference analyzes paradoxes from many different perspectives: statistics, mathematics, philosophy, science, artificial intelligence, and more. The book elaborates on findings and reaches new and exciting conclusions. It challenges your knowledge, intuition, and conventional wisdom, compelling you to adjust your way of thinking. Ultimately, you will learn effective scientific inference through studying the paradoxes.




Knowledge and Its Limits


Book Description

"Knowledge and Its Limits presents a systematic new conception of knowledge as a fundamental kind of mental state sensitive to the knower's environment. It makes a major contribution to the debate between externalist ad internalist philosophies of mind, and breaks radically with the epistemological tradition of analysing knowledge in terms of true belief. The theory casts light on a wide variety of philosophical issues: the problem of scepticism, the nature of evidence, probability and assertion, the dispute between realism and anti-realism and the paradox of the surprise examination. Williamson relates the new conception to structural limits on knowledge which imply that what can be known never exhausts what is true. The arguments are illustrated by rigorous models based on epistemic logic and probability theory. The result is a new way of doing epistemology for the twenty-first century."--BOOK JACKET.




Paradoxical Effects of Social Behavior


Book Description

In the history of science "paradoxes" are not only amusing puzzles and chal lenges to the human mind but also driving forces of scientific development. The notion of "paradox" is intimately related to the notion of "contradiction". Logi cal paradoxes allow for the derivation of contradictory propositions (e.g. "Rus sell's set of all sets not being members of themselves" or the ancient problem with propositions like "I am lying" 1), normative paradoxes deal with contradic tions among equally well accepted normative postulates (Arrow's "impossibility theorem", Sen's "Impossibility of a Paretian Liberal") and "factual" paradoxes refer to conflicts between conventional opinion based on an accepted empirical theory and contradictory empirical evidence (e.g. the "St. Petersburg paradox" or the "Allais paradox" in decision theory2). Paradoxes, either logical, normative or factual, also contradict our intui tions. The counter-intuitive property which seems to be a common feature of all paradoxes plays an important part in the empirical social sciences, particularly in the old research tradition of scrutinizing the unintended consequences of pur posive actions. Expectations based on naive theories ignoring interdependencies between individual actions are very often in conflict with "surprising" empirical evidence on collective results of social behavior. Examples are numerous reach ing from panic situations, the individual struggle for status gains resulting in collective deprivation, the less than optimal supply of collective goods etc. to global problems of the armament race and mismanagement of common resources.




Paradoxes in Probability Theory


Book Description

Paradoxes provide a vehicle for exposing misinterpretations and misapplications of accepted principles. This book discusses seven paradoxes surrounding probability theory. Some remain the focus of controversy; others have allegedly been solved, however the accepted solutions are demonstrably incorrect. Each paradox is shown to rest on one or more fallacies. Instead of the esoteric, idiosyncratic, and untested methods that have been brought to bear on these problems, the book invokes uncontroversial probability principles, acceptable both to frequentists and subjectivists. The philosophical disputation inspired by these paradoxes is shown to be misguided and unnecessary; for instance, startling claims concerning human destiny and the nature of reality are directly related to fallacious reasoning in a betting paradox, and a problem analyzed in philosophy journals is resolved by means of a computer program.​




Theory of Moves


Book Description

Steven J. Brams' Theory of Moves, though based on the classical theory of games, proposes changes in its rules to render it a truly dynamic theory. By postulating that players think ahead not just to the immediate consequences of making moves, but also to the consequences of countermoves to these moves, counter-countermoves, and so on, it extends the strategic analysis of conflicts into the more distant future. It elucidates the role that different kinds of power - moving, order and threat - may have on conflict outcomes, and it also shows how misinformation affects player choices. Applied to a series of cases drawn from politics, economics, sociology, fiction and the Bible, the theory provides not only a parsimonious explanation of their outcomes, but also shows why they unfolded as they did. This book, which assumes no prior knowledge of game theory or special mathematical background, will be of interest to scholars and students throughout the social sciences.