This volume celebrating the 60th birthday of Béla Bollobás presents the state of the art in combinatorics.

The Underdog Theorem introduces a completely new idea that has been overlooked by every sports fan in the world. Written for the sports gambler and non-sports gambler alike, the Underdog Theorem presents specific, straightforward steps that can be used to predict events of every NFL season. The reader will learn how easy it is to repeat these steps on his own, year after year. The Underdog Theorem provides proof of the strategy's success over the past fourteen seasons. Other gambling books tell you about a strategy knowing that the roll of the dice or the deal of the cards can never be repeated, which frees the authors from ever being proven wrong (or right). There is only one NFL to bet on, only one outcome to every game, and only one Underdog Theorem.

Mathematics has been called the science of order. The subject is remarkably good for generalizing specific cases to create abstract theories. However, mathematics has little to say when faced with highly complex systems, where disorder reigns. This disorder can be found in pure mathematical arenas, such as the distribution of primes, the $3n+1$ conjecture, and class field theory. The purpose of this book is to provide examples--and rigorous proofs--of the complexity law: (1) discrete systems are either simple or they exhibit advanced pseudorandomness; (2) a priori probabilities often exist even when there is no intrinsic symmetry. Part of the difficulty in achieving this purpose is in trying to clarify these vague statements. The examples turn out to be fascinating instances of deep or mysterious results in number theory and combinatorics. This book considers randomness and complexity. The traditional approach to complexity--computational complexity theory--is to study very general complexity classes, such as P, NP and PSPACE. What Beck does is very different: he studies interesting concrete systems, which can give new insights into the mystery of complexity. The book is divided into three parts. Part A is mostly an essay on the big picture. Part B is partly new results and partly a survey of real game theory. Part C contains new results about graph games, supporting the main conjecture. To make it accessible to a wide audience, the book is mostly self-contained.

Contests are prevalent in many areas, including sports, rent seeking, patent races, innovation inducement, labor markets, scientific projects, crowdsourcing and other online services, and allocation of computer system resources. This book provides unified, comprehensive coverage of contest theory as developed in economics, computer science, and statistics, with a focus on online services applications, allowing professionals, researchers and students to learn about the underlying theoretical principles and to test them in practice. The book sets contest design in a game-theoretic framework that can be used to model a wide-range of problems and efficiency measures such as total and individual output and social welfare, and offers insight into how the structure of prizes relates to desired contest design objectives. Methods for rating the skills and ranking of players are presented, as are proportional allocation and similar allocation mechanisms, simultaneous contests, sharing utility of productive activities, sequential contests, and tournaments.

This systematic exposition and survey of mathematical economics emphasizes the unifying structures of economic theory.

“Much of what we experience in life results from a combination of skill and luck.” — From the Introduction The trick, of course, is figuring out just how many of our successes (and failures) can be attributed to each—and how we can learn to tell the difference ahead of time. In most domains of life, skill and luck seem hopelessly entangled. Different levels of skill and varying degrees of good and bad luck are the realities that shape our lives—yet few of us are adept at accurately distinguishing between the two. Imagine what we could accomplish if we were able to tease out these two threads, examine them, and use the resulting knowledge to make better decisions. In this provocative book, Michael Mauboussin helps to untangle these intricate strands to offer the structure needed to analyze the relative importance of skill and luck. He offers concrete suggestions for making these insights work to your advantage. Once we understand the extent to which skill and luck contribute to our achievements, we can learn to deal with them in making decisions. The Success Equation helps us move toward this goal by: • Establishing a foundation so we better understand skill and luck, and can pinpoint where each is most relevant • Helping us develop the analytical tools necessary to understand skill and luck • Offering concrete suggestions about how to take these findings and put them to work Showcasing Mauboussin’s trademark wit, insight, and analytical genius, The Success Equation is a must-read for anyone seeking to make better decisions—in business and in life.