Machine Learning, Game Theory, and Mechanism Design for a Networked World A
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Evolutionary Game Theory: ESS, Convergence Stability, and NIS
Evolutionary Ecology Research, 2009, 11: 489–515 Evolutionary game theory: ESS, convergence stability, and NIS Joseph Apaloo1, Joel S. Brown2 and Thomas L. Vincent3 1Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, Nova Scotia, Canada, 2Department of Biological Sciences, University of Illinois, Chicago, Illinois, USA and 3Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, Arizona, USA ABSTRACT Question: How are the three main stability concepts from evolutionary game theory – evolutionarily stable strategy (ESS), convergence stability, and neighbourhood invader strategy (NIS) – related to each other? Do they form a basis for the many other definitions proposed in the literature? Mathematical methods: Ecological and evolutionary dynamics of population sizes and heritable strategies respectively, and adaptive and NIS landscapes. Results: Only six of the eight combinations of ESS, convergence stability, and NIS are possible. An ESS that is NIS must also be convergence stable; and a non-ESS, non-NIS cannot be convergence stable. A simple example shows how a single model can easily generate solutions with all six combinations of stability properties and explains in part the proliferation of jargon, terminology, and apparent complexity that has appeared in the literature. A tabulation of most of the evolutionary stability acronyms, definitions, and terminologies is provided for comparison. Key conclusions: The tabulated list of definitions related to evolutionary stability are variants or combinations of the three main stability concepts. Keywords: adaptive landscape, convergence stability, Darwinian dynamics, evolutionary game stabilities, evolutionarily stable strategy, neighbourhood invader strategy, strategy dynamics. INTRODUCTION Evolutionary game theory has and continues to make great strides. -
Potential Games. Congestion Games. Price of Anarchy and Price of Stability
8803 Connections between Learning, Game Theory, and Optimization Maria-Florina Balcan Lecture 13: October 5, 2010 Reading: Algorithmic Game Theory book, Chapters 17, 18 and 19. Price of Anarchy and Price of Staility We assume a (finite) game with n players, where player i's set of possible strategies is Si. We let s = (s1; : : : ; sn) denote the (joint) vector of strategies selected by players in the space S = S1 × · · · × Sn of joint actions. The game assigns utilities ui : S ! R or costs ui : S ! R to any player i at any joint action s 2 S: any player maximizes his utility ui(s) or minimizes his cost ci(s). As we recall from the introductory lectures, any finite game has a mixed Nash equilibrium (NE), but a finite game may or may not have pure Nash equilibria. Today we focus on games with pure NE. Some NE are \better" than others, which we formalize via a social objective function f : S ! R. Two classic social objectives are: P sum social welfare f(s) = i ui(s) measures social welfare { we make sure that the av- erage satisfaction of the population is high maxmin social utility f(s) = mini ui(s) measures the satisfaction of the most unsatisfied player A social objective function quantifies the efficiency of each strategy profile. We can now measure how efficient a Nash equilibrium is in a specific game. Since a game may have many NE we have at least two natural measures, corresponding to the best and the worst NE. We first define the best possible solution in a game Definition 1. -
California Institute of Technology
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Caltech Authors - Main DIVISION OF THE HUM ANITIES AND SO CI AL SCIENCES CALIFORNIA INSTITUTE OF TECHNOLOGY PASADENA, CALIFORNIA 91125 IMPLEMENTATION THEORY Thomas R. Palfrey � < a: 0 1891 u. "')/,.. () SOCIAL SCIENCE WORKING PAPER 912 September 1995 Implementation Theory Thomas R. Palfrey Abstract This surveys the branch of implementation theory initiated by Maskin (1977). Results for both complete and incomplete information environments are covered. JEL classification numbers: 025, 026 Key words: Implementation Theory, Mechanism Design, Game Theory, Social Choice Implementation Theory* Thomas R. Palfrey 1 Introduction Implementation theory is an area of research in economic theory that rigorously investi gates the correspondence between normative goals and institutions designed to achieve {implement) those goals. More precisely, given a normative goal or welfare criterion for a particular class of allocation pro blems (or domain of environments) it formally char acterizes organizational mechanisms that will guarantee outcomes consistent with that goal, assuming the outcomes of any such mechanism arise from some specification of equilibrium behavior. The approaches to this problem to date lie in the general domain of game theory because, as a matter of definition in the implementation theory litera ture, an institution is modelled as a mechanism, which is essentially a non-cooperative game. Moreover, the specific models of equilibrium behavior -
Descartes' Influence in Shaping the Modern World-View
R ené Descartes (1596-1650) is generally regarded as the “father of modern philosophy.” He stands as one of the most important figures in Western intellectual history. His work in mathematics and his writings on science proved to be foundational for further development in these fields. Our understanding of “scientific method” can be traced back to the work of Francis Bacon and to Descartes’ Discourse on Method. His groundbreaking approach to philosophy in his Meditations on First Philosophy determine the course of subsequent philosophy. The very problems with which much of modern philosophy has been primarily concerned arise only as a consequence of Descartes’thought. Descartes’ philosophy must be understood in the context of his times. The Medieval world was in the process of disintegration. The authoritarianism that had dominated the Medieval period was called into question by the rise of the Protestant revolt and advances in the development of science. Martin Luther’s emphasis that salvation was a matter of “faith” and not “works” undermined papal authority in asserting that each individual has a channel to God. The Copernican revolution undermined the authority of the Catholic Church in directly contradicting the established church doctrine of a geocentric universe. The rise of the sciences directly challenged the Church and seemed to put science and religion in opposition. A mathematician and scientist as well as a devout Catholic, Descartes was concerned primarily with establishing certain foundations for science and philosophy, and yet also with bridging the gap between the “new science” and religion. Descartes’ Influence in Shaping the Modern World-View 1) Descartes’ disbelief in authoritarianism: Descartes’ belief that all individuals possess the “natural light of reason,” the belief that each individual has the capacity for the discovery of truth, undermined Roman Catholic authoritarianism. -
Econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible
A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Banerjee, Abhijit; Weibull, Jörgen W. Working Paper Evolution and Rationality: Some Recent Game- Theoretic Results IUI Working Paper, No. 345 Provided in Cooperation with: Research Institute of Industrial Economics (IFN), Stockholm Suggested Citation: Banerjee, Abhijit; Weibull, Jörgen W. (1992) : Evolution and Rationality: Some Recent Game-Theoretic Results, IUI Working Paper, No. 345, The Research Institute of Industrial Economics (IUI), Stockholm This Version is available at: http://hdl.handle.net/10419/95198 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten Nutzungsrechte. may exercise further usage rights as specified in the indicated licence. www.econstor.eu Ind ustriens Utred n i ngsi nstitut THE INDUSTRIAL INSTITUTE FOR ECONOMIC AND SOCIAL RESEARCH A list of Working Papers on the last pages No. -
Quantum Logical Causality, Category Theory, and the Metaphysics of Alfred North Whitehead
Quantum Logical Causality, Category Theory, and the Metaphysics of Alfred North Whitehead Connecting Zafiris’ Category Theoretic Models of Quantum Spacetime and the Logical-Causal Formalism of Quantum Relational Realism Workshop Venue: Swiss Federal Institute of Technology (ETH) Chair for Philosophy (building RAC) Raemistrasse 36, 8001 Zurich Switzerland January 29 – 30, 2010 I. Aims and Motivation Recent work in the natural sciences—most notably in the areas of theoretical physics and evolutionary biology—has demonstrated that the lines separating philosophy and science have all but vanished with respect to current explorations of ‘fundamental’ questions (e.g., string theory, multiverse cosmologies, complexity-emergence theories, the nature of mind, etc.). The centuries-old breakdown of ‘natural philosophy’ into the divorced partners ‘philosophy’ and ‘science,’ therefore, must be rigorously re- examined. To that end, much of today’s most groundbreaking scholarship in the natural sciences has begun to include explicit appeals to interdisciplinary collaboration among the fields of applied natural sciences, mathematics and philosophy. This workshop will be dedicated to the question of how a philosophical-metaphysical theory can be fruitfully applied to basic conceptualizations in the natural sciences. More narrowly, we will explore the process oriented metaphysical scheme developed by philosopher and mathematician Alfred North Whitehead (1861-1947) and Michael Epperson’s application of this scheme to recent work in quantum mechanics, and the relation of these to Elias Zafiris’s category theoretic model of quantum event structures. Our aim is to give participants from various fields of expertise (see list below) the opportunity to exchange their specialized knowledge in the context of a collaborative exploration of the fundamental questions raised by recent scholarship in physics and mathematics. -
Collusion Constrained Equilibrium
Theoretical Economics 13 (2018), 307–340 1555-7561/20180307 Collusion constrained equilibrium Rohan Dutta Department of Economics, McGill University David K. Levine Department of Economics, European University Institute and Department of Economics, Washington University in Saint Louis Salvatore Modica Department of Economics, Università di Palermo We study collusion within groups in noncooperative games. The primitives are the preferences of the players, their assignment to nonoverlapping groups, and the goals of the groups. Our notion of collusion is that a group coordinates the play of its members among different incentive compatible plans to best achieve its goals. Unfortunately, equilibria that meet this requirement need not exist. We instead introduce the weaker notion of collusion constrained equilibrium. This al- lows groups to put positive probability on alternatives that are suboptimal for the group in certain razor’s edge cases where the set of incentive compatible plans changes discontinuously. These collusion constrained equilibria exist and are a subset of the correlated equilibria of the underlying game. We examine four per- turbations of the underlying game. In each case,we show that equilibria in which groups choose the best alternative exist and that limits of these equilibria lead to collusion constrained equilibria. We also show that for a sufficiently broad class of perturbations, every collusion constrained equilibrium arises as such a limit. We give an application to a voter participation game that shows how collusion constraints may be socially costly. Keywords. Collusion, organization, group. JEL classification. C72, D70. 1. Introduction As the literature on collective action (for example, Olson 1965) emphasizes, groups often behave collusively while the preferences of individual group members limit the possi- Rohan Dutta: [email protected] David K. -
Electronic Commerce (Algorithmic Game Theory) (Tentative Syllabus)
EECS 547: Electronic Commerce (Algorithmic Game Theory) (Tentative Syllabus) Lecture: Tuesday and Thursday 10:30am-Noon in 1690 BBB Section: Friday 3pm-4pm in EECS 3427 Email: [email protected] Instructor: Grant Schoenebeck Office Hours: Wednesday 3pm and by appointment; 3636 BBBB Graduate Student Instructor: Biaoshuai Tao Office Hours: 4-5pm Friday in Learning Center (between BBB and Dow in basement) Introduction: As the internet draws together strategic actors, it becomes increasingly important to understand how strategic agents interact with computational artifacts. Algorithmic game theory studies both how to models strategic agents (game theory) and how to design systems that take agent strategies into account (mechanism design). On-line auction sites (including search word auctions), cyber currencies, and crowd-sourcing are all obvious applications. However, even more exist such as designing non- monetary award systems (reputation systems, badges, leader-boards, Facebook “likes”), recommendation systems, and data-analysis when strategic agents are involved. In this particular course, we will especially focus on information elicitation mechanisms (crowd- sourcing). Description: Modeling and analysis for strategic decision environments, combining computational and economic perspectives. Essential elements of game theory, including solution concepts and equilibrium computation. Design of mechanisms for resource allocation and social choice, for example as motivated by problems in electronic commerce and social computing. Format: The two weeks will be background lectures. The next half of the class will be seminar style and will focus on crowd-sourcing, and especially information elicitation mechanisms. Each class period, the class will read a paper (or set of papers), and a pair of students will briefly present the papers and lead a class discussion. -
As Recursive Self-Prediction: Does a Deterministic Mechanism Reduce Responsibility?
1 'Free Will' as Recursive Self-Prediction: Does a Deterministic Mechanism Reduce Responsibility? George Ainslie 11,09 To appear in Poland, Jeffrey and Graham, George, Addiction and Responsibility. MIT This material is the result of work supported with resources and the use of facilities at the Department of Veterans Affairs Medical Center, Coatesville, PA, USA. Advances in brain imaging have revealed more and more about the physical basis of motivated behavior, making the age-old dispute about free will and moral responsibility increasingly salient. Science seems to be delineating chains of causality for feelings, choices, and even beliefs; but if all mental life is strictly caused by prior events, and those by still earlier events in a chain extending back before birth, how can individuals be held responsible for their actions? Most people feel that they originate their actions (Nadelhoffer et.al., 2005) and will readily give opinions about whether particular circumstances make an action blameworthy or not (Monterosso et.al., 2005); but when philosophers take the chain of causality explicitly into account they generally distance themselves from these direct introspections, holding for instance that blame is just a way of assuaging instinctive resentment (Strawson, 1962/2003) or a threat to manipulate people’s motives (Dennett, 1984, pp. 131-172). I come to this subject with a behavioral science rather than a philosophy background, but the free will dispute looks to this outsider like something that recent empirical findings might resolve. The dispute is age old because of a fundamental conundrum. We insist on the truth of each of two propositions, the compatibility of which is far from obvious, perhaps absurd: 1. -
Informational Size and Incentive Compatibility
Econometrica, Vol. 70, No. 6 (November, 2002), 2421–2453 INFORMATIONAL SIZE AND INCENTIVE COMPATIBILITY By Richard McLean and Andrew Postlewaite1 We examine a general equilibrium model with asymmetrically informed agents. The presence of asymmetric information generally presents a conflict between incentive com- patibility and Pareto efficiency. We present a notion of informational size and show that the conflict between incentive compatibility and efficiency can be made arbitrarily small if agents are of sufficiently small informational size. Keywords: Incentive compatibility, mechanism design, incomplete information. 1 introduction The incompatibility of Pareto efficiency and incentive compatibility is a central theme in economics and game theory. The issues associated with this incompatibility are particularly important in the design of resource allocation mechanisms in the presence of asymmetrically informed agents where the need to acquire information from agents in order to compute efficient outcomes and the incentives agents have to misrepresent that information for personal gain come into conflict. Despite a large literature that focuses on these issues, there has been little work aimed at understanding those situations in which informational asymmetries are quantitatively important. Virtually every transaction is characterized by some asymmetry of information: any investor who buys or sells a share of stock generally knows something rel- evant to the value of the share that is not known to the person on the other side of the transaction. In order to focus on more salient aspects of the problem, many models (rightly) ignore the incentive problems associated with informa- tional asymmetries in the belief that, for the problem at hand, agents are “infor- mationally small.” However, few researchers have investigated the circumstances under which an analysis that ignores these incentive problems will yield results similar to those obtained when these problems are fully accounted for. -
Game Theory 2021
More Mechanism Design Game Theory 2021 Game Theory 2021 Ulle Endriss Institute for Logic, Language and Computation University of Amsterdam Ulle Endriss 1 More Mechanism Design Game Theory 2021 Plan for Today In this second lecture on mechanism design we are going to generalise beyond the basic scenario of auctions|as much as we can manage: • Revelation Principle: can focus on direct-revelation mechanisms • formal model of direct-revelation mechanisms with money • incentive compatibility of the Vickrey-Clarke-Groves mechanism • other properties of VCG for special case of combinatorial auctions • impossibility of achieving incentive compatibility more generally Much of this is also (somewhat differently) covered by Nisan (2007). N. Nisan. Introduction to Mechanism Design (for Computer Scientists). In N. Nisan et al. (eds.), Algorithmic Game Theory. Cambridge University Press, 2007. Ulle Endriss 2 More Mechanism Design Game Theory 2021 Reminder Last time we saw four auction mechanisms for selling a single item: English, Dutch, first-price sealed-bid, Vickrey. The Vickrey auction was particularly interesting: • each bidder submits a bid in a sealed envelope • the bidder with the highest bid wins, but pays the price of the second highest bid (unless it's below the reservation price) It is a direct-revelation mechanism (unlike English and Dutch auctions) and it is incentive-compatible, i.e., truth-telling is a dominant strategy (unlike for Dutch and FPSB auctions). Ulle Endriss 3 More Mechanism Design Game Theory 2021 The Revelation Principle Revelation Principle: Any outcome that is implementable in dominant strategies via some mechanism can also be implemented by means of a direct-revelation mechanism making truth-telling a dominant strategy. -
Pleksiglass Som Lokke Mat Og Mulighet Plexiglas As a Lure And
Pleksiglass som lokke mat og mulighet Pleksiglass som lokke mat og mulighet Plexiglas as a lure and Plexiglas potential By Liam Gillick Den britiske kunstneren Liam Gillick har gjerne The British artist Liam Gillick is often associated as a lure and blitt forbundet med den relasjonelle estetikken, with relational aesthetics, which emphasises the som la vekt på betrakteren som medskaper av ver- contribution of the viewer to an artwork and tends ket, og som ofte handlet om å tilrettelegge steder to focus on defining places and situations for social og situasjoner for sosial interaksjon. Men i mot- interaction. But in contrast to artists like Rirkrit setning til kunstnere som Rirkrit Tiravanija, som Tiravanija, who encourages audience-participation inviterte publikum til å samtale over et måltid, in a meal or a conversation, Gillick’s scenarios do gir ikke Gillicks scenarier inntrykk av å være laget not seem constructed for human activity. Instead, for menneskelig aktivitet. Installasjonene hans i his installations of Plexiglas and aluminium are potential pleksiglass og aluminium handlere snarere om concerned with the analysis of structures and types å analysere sosiale strukturer og organisasjons- of social organisation, and with the exploration of måter, og undersøke de romlige forutsetningene the spatial conditions for human interaction. Rec- for menneskelig interaksjon. Inspirert av hans ognising Gillick’s carefully considered relationship reflekterte forhold til materialene han jobber to the materials he uses, we invited him to write By med, ba vi ham skrive om sin interesse for pleksi- about his interest in Plexiglas, a material he has glass, et materiale han har arbeidet med i over 30 år.