Regularity Theory for Mean-Field Game Systems PDF Download

Author: Diogo A. Gomes
Publisher: Springer
ISBN: 3319389343
Category : Mathematics
Languages : en
Pages : 165

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Book Description
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.

Author: John Wall Barger
Publisher:
ISBN: 9781989287095
Category : Suffering
Languages : en
Pages : 0

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Book Description
Poetry. THE MEAN GAME--John Wall Barger's fourth book-length entry in what might be called, collectively, a savage comedy--bristles with allegories that explore human cruelty and suffering. Gathering narratives that feel both ancient and modern, Barger forges an apocalyptic vision without sacrificing poetry's underlying sense of joy, humour and revelation. Part comic book translated from a dead language, and part nightmare dreamscape, THE MEAN GAME is a must-read from one of Canada's most kinetic writers.

Author: Alain Bensoussan
Publisher: Springer Science & Business Media
ISBN: 1461485088
Category : Science
Languages : en
Pages : 132

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Book Description
​Mean field games and Mean field type control introduce new problems in Control Theory. The terminology “games” may be confusing. In fact they are control problems, in the sense that one is interested in a single decision maker, whom we can call the representative agent. However, these problems are not standard, since both the evolution of the state and the objective functional is influenced but terms which are not directly related to the state or the control of the decision maker. They are however, indirectly related to him, in the sense that they model a very large community of agents similar to the representative agent. All the agents behave similarly and impact the representative agent. However, because of the large number an aggregation effect takes place. The interesting consequence is that the impact of the community can be modeled by a mean field term, but when this is done, the problem is reduced to a control problem. ​

Author: Yves Achdou
Publisher: Springer Nature
ISBN: 3030598373
Category : Mathematics
Languages : en
Pages : 316

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Book Description
This volume provides an introduction to the theory of Mean Field Games, suggested by J.-M. Lasry and P.-L. Lions in 2006 as a mean-field model for Nash equilibria in the strategic interaction of a large number of agents. Besides giving an accessible presentation of the main features of mean-field game theory, the volume offers an overview of recent developments which explore several important directions: from partial differential equations to stochastic analysis, from the calculus of variations to modeling and aspects related to numerical methods. Arising from the CIME Summer School "Mean Field Games" held in Cetraro in 2019, this book collects together lecture notes prepared by Y. Achdou (with M. Laurière), P. Cardaliaguet, F. Delarue, A. Porretta and F. Santambrogio. These notes will be valuable for researchers and advanced graduate students who wish to approach this theory and explore its connections with several different fields in mathematics.

Author: Simon Sinek
Publisher: Penguin
ISBN: 0735213526
Category : Business & Economics
Languages : en
Pages : 272

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Book Description
From the New York Times bestselling author of Start With Why and Leaders Eat Last, a bold framework for leadership in today’s ever-changing world. How do we win a game that has no end? Finite games, like football or chess, have known players, fixed rules and a clear endpoint. The winners and losers are easily identified. Infinite games, games with no finish line, like business or politics, or life itself, have players who come and go. The rules of an infinite game are changeable while infinite games have no defined endpoint. There are no winners or losers—only ahead and behind. The question is, how do we play to succeed in the game we’re in? In this revelatory new book, Simon Sinek offers a framework for leading with an infinite mindset. On one hand, none of us can resist the fleeting thrills of a promotion earned or a tournament won, yet these rewards fade quickly. In pursuit of a Just Cause, we will commit to a vision of a future world so appealing that we will build it week after week, month after month, year after year. Although we do not know the exact form this world will take, working toward it gives our work and our life meaning. Leaders who embrace an infinite mindset build stronger, more innovative, more inspiring organizations. Ultimately, they are the ones who lead us into the future.

Author: Reginald A. Banez
Publisher: Springer Nature
ISBN: 3030869059
Category : Computers
Languages : en
Pages : 184

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Book Description
This book covers the basic theory of mean field game (MFG) and its applications in wireless networks. It starts with an overview of the current and future state-of-the-art in 5G and 6G wireless networks. Then, a tutorial is presented for MFG, mean-field-type game (MFTG), and prerequisite fields of study such as optimal control theory and differential games. This book also includes a literature survey of MFG-based research in wireless network technologies such as ultra-dense networks (UDNs), device-to-device (D2D) communications, internet-of-things (IoT), unmanned aerial vehicles (UAVs), and mobile edge networks (MENs). Several applications of MFG and MFTG in UDNs, social networks, and multi-access edge computing networks (MECNs) are introduced as well. Applications of MFG covered in this book are divided in three parts. The first part covers three single-population MFG research works or case studies in UDNs including ultra-dense D2D networks, ultra-dense UAV networks, and dense-user MECNs. The second part centers on a multiple-population MFG (MPMFG) modeling of belief and opinion evolution in social networks. It focuses on a recently developed MPMFG framework and its application in analyzing the behavior of users in a multiple-population social network. Finally, the last part concentrates on an MFTG approach to computation offloading in MECN. The computation offloading algorithms are designed for energy- and time-efficient offloading of computation-intensive tasks in an MECN. This book targets advanced-level students, professors, researchers, scientists, and engineers in the fields of communications and networks. Industry managers and government employees working in these same fields will also find this book useful.

Author: Neil Strauss
Publisher: Harper Collins
ISBN: 0062130110
Category : Biography & Autobiography
Languages : en
Pages : 466

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Book Description
Hidden somewhere, in nearly every major city in the world, is an underground seduction lair. And in these lairs, men trade the most devastatingly effective techniques ever invented to charm women. This is not fiction. These men really exist. They live together in houses known as Projects. And Neil Strauss, the bestselling author and journalist, spent two years living among them, using the pseudonym Style to protect his real-life identity. The result is one of the most explosive and controversial books of the last decade—guaranteed to change the lives of men and transform the way women understand the opposite sex forever. On his journey from AFC (average frustrated chump) to PUA (pick-up artist) to PUG (pick-up guru), Strauss not only shares scores of original seduction techniques but also has unforgettable encounters with the likes of Tom Cruise, Britney Spears, Paris Hilton, Heidi Fleiss, and Courtney Love. And then things really start to get strange—and passions lead to betrayals lead to violence. The Game is the story of one man's transformation from frog to prince to prisoner in the most unforgettable book of this generation.

Author: Nassim Nicholas Taleb
Publisher: Random House
ISBN: 0425284638
Category : Philosophy
Languages : en
Pages : 305

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Book Description
#1 NEW YORK TIMES BESTSELLER • A bold work from the author of The Black Swan that challenges many of our long-held beliefs about risk and reward, politics and religion, finance and personal responsibility In his most provocative and practical book yet, one of the foremost thinkers of our time redefines what it means to understand the world, succeed in a profession, contribute to a fair and just society, detect nonsense, and influence others. Citing examples ranging from Hammurabi to Seneca, Antaeus the Giant to Donald Trump, Nassim Nicholas Taleb shows how the willingness to accept one’s own risks is an essential attribute of heroes, saints, and flourishing people in all walks of life. As always both accessible and iconoclastic, Taleb challenges long-held beliefs about the values of those who spearhead military interventions, make financial investments, and propagate religious faiths. Among his insights: • For social justice, focus on symmetry and risk sharing. You cannot make profits and transfer the risks to others, as bankers and large corporations do. You cannot get rich without owning your own risk and paying for your own losses. Forcing skin in the game corrects this asymmetry better than thousands of laws and regulations. • Ethical rules aren’t universal. You’re part of a group larger than you, but it’s still smaller than humanity in general. • Minorities, not majorities, run the world. The world is not run by consensus but by stubborn minorities imposing their tastes and ethics on others. • You can be an intellectual yet still be an idiot. “Educated philistines” have been wrong on everything from Stalinism to Iraq to low-carb diets. • Beware of complicated solutions (that someone was paid to find). A simple barbell can build muscle better than expensive new machines. • True religion is commitment, not just faith. How much you believe in something is manifested only by what you’re willing to risk for it. The phrase “skin in the game” is one we have often heard but rarely stopped to truly dissect. It is the backbone of risk management, but it’s also an astonishingly rich worldview that, as Taleb shows in this book, applies to all aspects of our lives. As Taleb says, “The symmetry of skin in the game is a simple rule that’s necessary for fairness and justice, and the ultimate BS-buster,” and “Never trust anyone who doesn’t have skin in the game. Without it, fools and crooks will benefit, and their mistakes will never come back to haunt them.”

Author: René Carmona
Publisher: Springer
ISBN: 3319564366
Category : Mathematics
Languages : en
Pages : 712

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Book Description
This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the master equation, a partial differential equation satisfied by the value function of the game over the space of probability measures. Existence of viscosity and classical solutions are proven and used to study asymptotics of games with finitely many players. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.

Author: Ian Bogost
Publisher: Basic Books
ISBN: 0465096506
Category : Science
Languages : en
Pages : 290

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Book Description
How filling life with play-whether soccer or lawn mowing, counting sheep or tossing Angry Birds -- forges a new path for creativity and joy in our impatient age Life is boring: filled with meetings and traffic, errands and emails. Nothing we'd ever call fun. But what if we've gotten fun wrong? In Play Anything, visionary game designer and philosopher Ian Bogost shows how we can overcome our daily anxiety; transforming the boring, ordinary world around us into one of endless, playful possibilities. The key to this playful mindset lies in discovering the secret truth of fun and games. Play Anything, reveals that games appeal to us not because they are fun, but because they set limitations. Soccer wouldn't be soccer if it wasn't composed of two teams of eleven players using only their feet, heads, and torsos to get a ball into a goal; Tetris wouldn't be Tetris without falling pieces in characteristic shapes. Such rules seem needless, arbitrary, and difficult. Yet it is the limitations that make games enjoyable, just like it's the hard things in life that give it meaning. Play is what happens when we accept these limitations, narrow our focus, and, consequently, have fun. Which is also how to live a good life. Manipulating a soccer ball into a goal is no different than treating ordinary circumstances- like grocery shopping, lawn mowing, and making PowerPoints-as sources for meaning and joy. We can "play anything" by filling our days with attention and discipline, devotion and love for the world as it really is, beyond our desires and fears. Ranging from Internet culture to moral philosophy, ancient poetry to modern consumerism, Bogost shows us how today's chaotic world can only be tamed-and enjoyed-when we first impose boundaries on ourselves.