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Author: Edward Cartwright
Publisher:
ISBN:
Category : Economics
Languages : en
Pages : 46
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Author: Edward Cartwright
Publisher:
ISBN:
Category : Economics
Languages : en
Pages : 46
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Book Description
Author: Drew Fudenberg
Publisher: MIT Press
ISBN: 0262303760
Category : Business & Economics
Languages : en
Pages : 616
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Book Description
This advanced text introduces the principles of noncooperative game theory in a direct and uncomplicated style that will acquaint students with the broad spectrum of the field while highlighting and explaining what they need to know at any given point. This advanced text introduces the principles of noncooperative game theory—including strategic form games, Nash equilibria, subgame perfection, repeated games, and games of incomplete information—in a direct and uncomplicated style that will acquaint students with the broad spectrum of the field while highlighting and explaining what they need to know at any given point. The analytic material is accompanied by many applications, examples, and exercises. The theory of noncooperative games studies the behavior of agents in any situation where each agent's optimal choice may depend on a forecast of the opponents' choices. "Noncooperative" refers to choices that are based on the participant's perceived selfinterest. Although game theory has been applied to many fields, Fudenberg and Tirole focus on the kinds of game theory that have been most useful in the study of economic problems. They also include some applications to political science. The fourteen chapters are grouped in parts that cover static games of complete information, dynamic games of complete information, static games of incomplete information, dynamic games of incomplete information, and advanced topics.
Author: Mathieu Sylvestre
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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This work regards Nash equilibrium-seeking in multi-player finite games. We present a discrete-time algorithm that can be adapted to leverage two forms of side information - a local/global split in the utility structure, where we assume that each player can track the actions of its neighbors and knows the form of its local utility, and unplayed action payoff measurements, where we suppose that players may be capable of observing their hypothetical payoffs for some actions they didn't play - when it is available. We use stochastic approximation to prove that, under mild assumptions, the induced mixed strategies of all players convergence to a perturbed Nash equilibria in games where utilities satisfy certain negative monotonicity properties. We also analyze modifications of the proposed algorithm and prove associated results. All presented results are supported with simulations of certain representative games which illustrate that faster convergence can be obtained when side information is exploited.
Author: Aviad Rubinstein
Publisher:
ISBN:
Category :
Languages : en
Pages : 310
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Book Description
Nash equilibrium is the central solution concept in Game Theory. Since Nash's original paper in 1951, it has found countless applications in modeling strategic behavior of traders in markets, (human) drivers and (electronic) routers in congested networks, nations in nuclear disarmament negotiations, and more. A decade ago, the relevance of this solution concept was called into question by computer scientists~\cite{DGP, CDT}, who proved (under appropriate complexity assumptions) that {\em computing} a Nash equilibrium is an intractable problem. And if centralized, specially designed algorithms cannot find Nash equilibria, why should we expect distributed, selfish agents to converge to one? The remaining hope was that at least approximate Nash equilibria can be efficiently computed. Understanding whether there is an efficient algorithm for {\em approximate Nash equilibrium} has been the central open problem in this field for the past decade. In this thesis, we provide strong evidence that even finding an approximate Nash equilibrium is intractable. We prove several intractability theorems for different settings (two-player games and many-player games) and models (computational complexity, query complexity, and communication complexity). In particular, our main result is that under a plausible and natural complexity assumption (``Exponential Time Hypothesis for \PPAD''), there is no polynomial-time algorithm for finding an approximate Nash equilibrium in two-player games. The problem of approximate Nash equilibrium in a two-player game poses a unique technical challenge: it is a member of the class \PPAD, which captures the complexity of several fundamental total problems, i.e. problems that always have a solution; and it also admits a quasipolynomial ($\approx n^{\log n}$) time algorithm. Either property alone is believed to place this problem far below \NP-hard problems in the complexity hierarchy; having both simultaneously places it just above \P, at what can be called the frontier of intractability. Indeed, the tools we develop in this thesis to advance on this frontier are useful for proving hardness of approximation of several other important problems whose complexity lies between \P~and \NP: \begin{description} \item [Brouwer's fixed point] Given a continuous function $f$ mapping a compact convex set to itself, Brouwer's fixed point theorem guarantees that $f$ has a fixed point, i.e. $x$ such that $f(x) = x$. Our intractability result holds for the relaxed problem of finding an approximate fixed point, i.e. $x$ such that $f(x) \approx x$. \item [Market equilibrium] Market equilibrium is a vector of prices and allocations where the supply meets the demand for each good. %We consider the Arrow-Debreu model where agents are both sellers and buyers of goods. Our intractability result holds for the relaxed problem of finding an approximate market equilibrium, where the supply of each good approximately meets the demand. \item [CourseMatch (A-CEEI)] Approximate Competitive Equilibrium from Equal Income (A-CEEI) is the economic principle underlying CourseMatch, a system for fair allocation of classes to students (currently in use at Wharton, University of Pennsylvania). \item [Densest $k$-subgraph] Our intractability result holds for the following relaxation of the $k$-Clique problem: given a graph containing a $k$-clique, the algorithm has to find a subgraph over $k$ vertices that is ``almost a clique'', i.e. most of the edges are present. \item [Community detection] We consider a well-studied model of communities in social networks, where each member of the community is friends with a large fraction of the community, and each non-member is only friends with a small fraction of the community. \item [VC dimension and Littlestone dimension] The Vapnik-Chervonenkis (VC) dimension is a fundamental measure in learning theory that captures the complexity of a binary concept class. Similarly, the Littlestone dimension is a measure of complexity of online learning. \item [Signaling in zero-sum games] We consider a fundamental problem in signaling, where an informed signaler reveals private information about the payoffs in a two-player zero-sum game, with the goal of helping one of the players.
Author: Tim Roughgarden
Publisher: Cambridge University Press
ISBN: 1316781178
Category : Computers
Languages : en
Pages : 356
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Book Description
Computer science and economics have engaged in a lively interaction over the past fifteen years, resulting in the new field of algorithmic game theory. Many problems that are central to modern computer science, ranging from resource allocation in large networks to online advertising, involve interactions between multiple self-interested parties. Economics and game theory offer a host of useful models and definitions to reason about such problems. The flow of ideas also travels in the other direction, and concepts from computer science are increasingly important in economics. This book grew out of the author's Stanford University course on algorithmic game theory, and aims to give students and other newcomers a quick and accessible introduction to many of the most important concepts in the field. The book also includes case studies on online advertising, wireless spectrum auctions, kidney exchange, and network management.
Author: Konstantinos Daskalakis
Publisher:
ISBN:
Category :
Languages : en
Pages : 410
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Author: Drew Fudenberg
Publisher: MIT Press
ISBN: 9780262061940
Category : Business & Economics
Languages : en
Pages : 304
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Book Description
This work explains that equilibrium is the long-run outcome of a process in which non-fully rational players search for optimality over time. The models they e×plore provide a foundation for equilibrium theory and suggest ways for economists to evaluate and modify traditional equilibrium concepts.
Author: Yu Wu
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
The complexity of studying Nash equilibrium in large games often scales with the size of the system: as it increases, computing the exact Nash equilibrium can soon become intractable. However, when the number of players in the system approaches infinity and no individual player has a significant impact on the system, we can approximate the system by considering each single player no longer playing against other individual players but a single aggregation of all other players. In this paper, we apply this idea to study and approximate Nash equilibria in two large scale games. In part I, we consider a model of priced resource sharing that combines both queueing behavior and strategic behavior. We study a priority service model where a single server allocates its capacity to agents in proportion to their payment to the system, and users from different classes act to minimize the sum of their cost for processing delay and payment. As the exact processing time of this system is hard to compute and cannot be characterized in closed form, we introduce the concept of aggregate equilibrium to approximate the exact Nash equilibrium, by assuming each individual player plays against a common aggregate priority that characterizes the large system. We then introduce the notion of heavy traffic equilibrium as an alternative approximation of the Nash equilibrium, derived by considering the asymptotic regime where the system load approaches capacity. We show that both aggregate equilibrium and heavy traffic equilibrium are asymptotically exact in heavy traffic. We present some numerical results for both approximate equilibria, and discuss efficiency and revenue, and in particular provide a bound for the price of anarchy of the heavy traffic equilibrium. In part II, we study the reputation system of large scale online marketplace. We develop a large market model to study reputation mechanisms in online marketplaces. We consider two types of sellers: commitment sellers, who are intrinsically honest but may be unable to accurately describe items because of limited expertise; and strategic sellers, who are driven by a profit maximization motive. We focus on stationary equilibria for this dynamic market, in particular, on separating equilibria where strategic sellers are incentivized to describe the items they have for sale truthfully, and characterize the conditions under which such equilibria exist. We then complement our theoretical results with computational analysis and provide insights on the features of markets that may incentivize truthfulness in equilibrium.
Author: Guilherme Carmona
Publisher: World Scientific
ISBN: 9814390658
Category : Business & Economics
Languages : en
Pages : 153
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Book Description
The book aims at describing the recent developments in the existence and stability of Nash equilibrium. The two topics are central to game theory and economics and have been extensively researched. Recent results on existence and stability of Nash equilibrium are scattered and the relationship between them has not been explained clearly. The book will make these results easily accessible and understandable to researchers in the field. Book jacket.
Author: Frank L. Lewis
Publisher: John Wiley & Sons
ISBN: 1118453972
Category : Technology & Engineering
Languages : en
Pages : 498
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Book Description
Reinforcement learning (RL) and adaptive dynamic programming (ADP) has been one of the most critical research fields in science and engineering for modern complex systems. This book describes the latest RL and ADP techniques for decision and control in human engineered systems, covering both single player decision and control and multi-player games. Edited by the pioneers of RL and ADP research, the book brings together ideas and methods from many fields and provides an important and timely guidance on controlling a wide variety of systems, such as robots, industrial processes, and economic decision-making.
