Book of Abstracts
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Pareto Optimality in Coalition Formation
Pareto Optimality in Coalition Formation Haris Aziz NICTA and University of New South Wales, 2033 Sydney, Australia Felix Brandt∗ Technische Universit¨atM¨unchen,80538 M¨unchen,Germany Paul Harrenstein University of Oxford, Oxford OX1 3QD, United Kingdom Abstract A minimal requirement on allocative efficiency in the social sciences is Pareto op- timality. In this paper, we identify a close structural connection between Pareto optimality and perfection that has various algorithmic consequences for coali- tion formation. Based on this insight, we formulate the Preference Refinement Algorithm (PRA) which computes an individually rational and Pareto optimal outcome in hedonic coalition formation games. Our approach also leads to var- ious results for specific classes of hedonic games. In particular, we show that computing and verifying Pareto optimal partitions in general hedonic games, anonymous games, three-cyclic games, room-roommate games and B-hedonic games is intractable while both problems are tractable for roommate games, W-hedonic games, and house allocation with existing tenants. Keywords: Coalition Formation, Hedonic Games, Pareto Optimality, Computational Complexity JEL: C63, C70, C71, and C78 1. Introduction Ever since the publication of von Neumann and Morgenstern's Theory of Games and Economic Behavior in 1944, coalitions have played a central role within game theory. The crucial questions in coalitional game theory are which coalitions can be expected to form and how the members of coalitions should divide the proceeds of their cooperation. Traditionally the focus has been on the latter issue, which led to the formulation and analysis of concepts such as ∗Corresponding author Email addresses: [email protected] (Haris Aziz), [email protected] (Felix Brandt), [email protected] (Paul Harrenstein) Preprint submitted to Elsevier August 27, 2013 the core, the Shapley value, or the bargaining set. -
Learning and Equilibrium
Learning and Equilibrium Drew Fudenberg1 and David K. Levine2 1Department of Economics, Harvard University, Cambridge, Massachusetts; email: [email protected] 2Department of Economics, Washington University of St. Louis, St. Louis, Missouri; email: [email protected] Annu. Rev. Econ. 2009. 1:385–419 Key Words First published online as a Review in Advance on nonequilibrium dynamics, bounded rationality, Nash equilibrium, June 11, 2009 self-confirming equilibrium The Annual Review of Economics is online at by 140.247.212.190 on 09/04/09. For personal use only. econ.annualreviews.org Abstract This article’s doi: The theory of learning in games explores how, which, and what 10.1146/annurev.economics.050708.142930 kind of equilibria might arise as a consequence of a long-run non- Annu. Rev. Econ. 2009.1:385-420. Downloaded from arjournals.annualreviews.org Copyright © 2009 by Annual Reviews. equilibrium process of learning, adaptation, and/or imitation. If All rights reserved agents’ strategies are completely observed at the end of each round 1941-1383/09/0904-0385$20.00 (and agents are randomly matched with a series of anonymous opponents), fairly simple rules perform well in terms of the agent’s worst-case payoffs, and also guarantee that any steady state of the system must correspond to an equilibrium. If players do not ob- serve the strategies chosen by their opponents (as in extensive-form games), then learning is consistent with steady states that are not Nash equilibria because players can maintain incorrect beliefs about off-path play. Beliefs can also be incorrect because of cogni- tive limitations and systematic inferential errors. -
Game Theory Lecture Notes
Game Theory: Penn State Math 486 Lecture Notes Version 2.1.1 Christopher Griffin « 2010-2021 Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License With Major Contributions By: James Fan George Kesidis and Other Contributions By: Arlan Stutler Sarthak Shah Contents List of Figuresv Preface xi 1. Using These Notes xi 2. An Overview of Game Theory xi Chapter 1. Probability Theory and Games Against the House1 1. Probability1 2. Random Variables and Expected Values6 3. Conditional Probability8 4. The Monty Hall Problem 11 Chapter 2. Game Trees and Extensive Form 15 1. Graphs and Trees 15 2. Game Trees with Complete Information and No Chance 18 3. Game Trees with Incomplete Information 22 4. Games of Chance 24 5. Pay-off Functions and Equilibria 26 Chapter 3. Normal and Strategic Form Games and Matrices 37 1. Normal and Strategic Form 37 2. Strategic Form Games 38 3. Review of Basic Matrix Properties 40 4. Special Matrices and Vectors 42 5. Strategy Vectors and Matrix Games 43 Chapter 4. Saddle Points, Mixed Strategies and the Minimax Theorem 45 1. Saddle Points 45 2. Zero-Sum Games without Saddle Points 48 3. Mixed Strategies 50 4. Mixed Strategies in Matrix Games 53 5. Dominated Strategies and Nash Equilibria 54 6. The Minimax Theorem 59 7. Finding Nash Equilibria in Simple Games 64 8. A Note on Nash Equilibria in General 66 Chapter 5. An Introduction to Optimization and the Karush-Kuhn-Tucker Conditions 69 1. A General Maximization Formulation 70 2. Some Geometry for Optimization 72 3. -
PRICING and MODULARITY DECISIONS UNDER COMPETITION Feng Tao Hao Shao and Kinkeung Lai (Communicated by Stefan Wolfgang Pickl) 1
JOURNAL OF INDUSTRIAL AND doi:10.3934/jimo.2018152 MANAGEMENT OPTIMIZATION Volume 16, Number 1, January 2020 pp. 289{307 PRICING AND MODULARITY DECISIONS UNDER COMPETITION Feng Taoa aDepartment of Management Science and Engineering East China University of Science and Technology, Shanghai, 200237, China Hao Shaobc∗ and KinKeung Laide bShanghai University of International Business and Economics Gubei Road, 200336, Shanghai, China cShanghai Wage Intelligent Technology Co., Ltd dCollege of Economics, Shenzhen University, Shenzhen, China eInternational Business School, Shaanxi Normal University, Xian, China (Communicated by Stefan Wolfgang Pickl) Abstract. This paper considers price and modularity of competition between two firms with deterministic demand, in which demand is dependent on both the prices and the modularity levels determined by two firms. Bertrand com- petition and Stackelberg competition are formulated to derive the equilibrium solutions analytically. Because of the complexity, an intensive numerical study is conducted to investigate the impact of the sensitive parameters on equilib- rium prices and modularity levels, as well as optimal profits of the two firms. An important and interesting finding is that optimal profits of the two firms under both types of competition are decreasing with the modularity cost when the price and modularity sensitivities are low, where both firms are worse-off due to decrease of the modularity levels; but they are increasing when the price and modularity sensitivities are high, where both firms are better-off at the ex- pense of modular design. Our research reveals that Stackelberg game improves the modularity levels in most of the cases, though both firms perform better in Bertrand competition in these cases when jointly deciding the prices and modularity levels in the two firms. -
A New IFORS Journal Is Born!
Volume 16 | Number 1 | March 2021 | ISSN 2223-4373 International Federation of Operational Research Societies NEWS From the President What’s Inside 1 From the President A New IFORS journal is Born! Grazia Speranza Grazia Speranza <[email protected]> 2 From the Editor-in-Chief The International Transactions in Operational Sunity Shrestha Hada Research (ITOR) has been the flagship journal of IFORS since its launch in 1994. The journal has 2 OR Impact served the IFORS community for a number of years Transforming Food Production and with publishing the proceedings of conferences and Supply with OR/Analytics the biographies of key figures in the OR field, who now belong to the IFORS Hall of Fame (https://www. 6 OR and Development ifors.org/ifors-hall-of-fame/)The scientific editorial Disaster Mitigation: Leveraging world substantially evolved over time, furthermore Community Involvement to Improve the ITOR mission expanded and began to publish Water Access in sub-Saharan Africa high-quality scientific papers, capable of attracting citations. The initial goal for ITOR was to be indexed 9 Tutorial and then to increase the value of the key indicator of Integer Programming formulations the success of a journal, its impact factor. Thanks to the for the Vertex Coloring Problem commitment of the Editor-in-Chief, Celso Ribeiro, and the editorial board of the journal, year after year, ITOR has improved its impact factor (current 12 IFORS Award 2020 for OR in impact factor: 2.987 ) and has become one of the leading journals for the OR community. Development a) Optimal Investment Strategies In addition to a well-established flagship journal, a global society such as IFORS has to Minimize Flood Impact on Road the responsibility to introduce new ventures. -
On Dynamic Games with Randomly Arriving Players Pierre Bernhard, Marc Deschamps
On Dynamic Games with Randomly Arriving Players Pierre Bernhard, Marc Deschamps To cite this version: Pierre Bernhard, Marc Deschamps. On Dynamic Games with Randomly Arriving Players. 2015. hal-01377916 HAL Id: hal-01377916 https://hal.archives-ouvertes.fr/hal-01377916 Preprint submitted on 7 Oct 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. O n dynamic games with randomly arriving players Pierre Bernhard et Marc Deschamps September 2015 Working paper No. 2015 – 13 30, avenue de l’Observatoire 25009 Besançon France http://crese.univ-fcomte.fr/ CRESE The views expressed are those of the authors and do not necessarily reflect those of CRESE. On dynamic games with randomly arriving players Pierre Bernhard∗ and Marc Deschamps† September 24, 2015 Abstract We consider a dynamic game where additional players (assumed identi- cal, even if there will be a mild departure from that hypothesis) join the game randomly according to a Bernoulli process. The problem solved here is that of computing their expected payoff as a function of time and the number of players present when they arrive, if the strategies are given. We consider both a finite horizon game and an infinite horizon, discounted game. -
Loss of Commitment? an Evolutionary Analysis of BagwellS Example1
Loss of Commitment? An Evolutionary Analysis of Bagwells Example1 Jörg Oechssler2 Karl H. Schlag3 Department of Economics Economic Theory III Humboldt University, Berlin University of Bonn April, 1997 1 We wish to thank Wolfgang Leininger for starting this project by asking us about the relevance of noise for evolutionary predictions, and Wieland Müller and Larry Samuelson for contributing valuable comments. Financial support by the Deutsche Forschungsgemeinschaft through SFBs 303 and 373 is gratefully acknowledged. 2 Institut für Wirtschaftstheorie, Spandauer Str. 1, 10178 Berlin, Germany, FAX: +49302093-5619, Email: [email protected] 3 Adenauerallee 24-26, 53113 Bonn, Germany, Email: [email protected] bonn.de Abstract In a recent paper Bagwell (1995) pointed out that only the Cournot outcome, but not the Stackelberg outcome, can be supported by a pure Nash equilib- rium when actions of the Stackelberg leader are observed with the slightest error. The Stackelberg outcome, however, remains close to the outcome of a mixed equilibrium. We compare the predictions in various classes of evolutionary and learning processes in this game. Only the continuous best response dynamic uniquely selects the Stackelberg outcome under noise. All other dynamics analyzed allow for the Cournot equilibrium to be selected. In typical cases Cournot is the unique long run outcome even for vanishing noise in the signal. JEL classi cation numbers: C72, C73. Key words: imperfectly observable commitment, evolution, imitation, learn- ing, equilibrium selection. 1 Introduction In a recent paper Bagwell (1995) pointed out that a rst mover advantage in games depends crucially on the fact that the action taken by the rst mover is perfectly observable. -
The Logic of Costly Punishment Reversed: Expropriation of Free-Riders and Outsiders∗,†
The logic of costly punishment reversed: expropriation of free-riders and outsiders∗ ,† David Hugh-Jones Carlo Perroni University of East Anglia University of Warwick and CAGE January 5, 2017 Abstract Current literature views the punishment of free-riders as an under-supplied pub- lic good, carried out by individuals at a cost to themselves. It need not be so: often, free-riders’ property can be forcibly appropriated by a coordinated group. This power makes punishment profitable, but it can also be abused. It is easier to contain abuses, and focus group punishment on free-riders, in societies where coordinated expropriation is harder. Our theory explains why public goods are un- dersupplied in heterogenous communities: because groups target minorities instead of free-riders. In our laboratory experiment, outcomes were more efficient when coordination was more difficult, while outgroup members were targeted more than ingroup members, and reacted differently to punishment. KEY WORDS: Cooperation, costly punishment, group coercion, heterogeneity JEL CLASSIFICATION: H1, H4, N4, D02 ∗We are grateful to CAGE and NIBS grant ES/K002201/1 for financial support. We would like to thank Mark Harrison, Francesco Guala, Diego Gambetta, David Skarbek, participants at conferences and presentations including EPCS, IMEBESS, SAET and ESA, and two anonymous reviewers for their comments. †Comments and correspondence should be addressed to David Hugh-Jones, School of Economics, University of East Anglia, [email protected] 1 Introduction Deterring free-riding is a central element of social order. Most students of collective action believe that punishing free-riders is costly to the punisher, but benefits the community as a whole. -
Modeling Strategic Behavior1
Modeling Strategic Behavior1 A Graduate Introduction to Game Theory and Mechanism Design George J. Mailath Department of Economics, University of Pennsylvania Research School of Economics, Australian National University 1September 16, 2020, copyright by George J. Mailath. World Scientific Press published the November 02, 2018 version. Any significant correc- tions or changes are listed at the back. To Loretta Preface These notes are based on my lecture notes for Economics 703, a first-year graduate course that I have been teaching at the Eco- nomics Department, University of Pennsylvania, for many years. It is impossible to understand modern economics without knowl- edge of the basic tools of game theory and mechanism design. My goal in the course (and this book) is to teach those basic tools so that students can understand and appreciate the corpus of modern economic thought, and so contribute to it. A key theme in the course is the interplay between the formal development of the tools and their use in applications. At the same time, extensions of the results that are beyond the course, but im- portant for context are (briefly) discussed. While I provide more background verbally on many of the exam- ples, I assume that students have seen some undergraduate game theory (such as covered in Osborne, 2004, Tadelis, 2013, and Wat- son, 2013). In addition, some exposure to intermediate microeco- nomics and decision making under uncertainty is helpful. Since these are lecture notes for an introductory course, I have not tried to attribute every result or model described. The result is a somewhat random pattern of citations and references. -
A Game Theory Interpretation for Multiple Access in Cognitive Radio
1 A Game Theory Interpretation for Multiple Access in Cognitive Radio Networks with Random Number of Secondary Users Oscar Filio Rodriguez, Student Member, IEEE, Serguei Primak, Member, IEEE,Valeri Kontorovich, Fellow, IEEE, Abdallah Shami, Member, IEEE Abstract—In this paper a new multiple access algorithm for (MAC) problem has been analyzed using game theory tools cognitive radio networks based on game theory is presented. in previous literature such as [1] [2] [8] [9]. In [9] a game We address the problem of a multiple access system where the theory model is presented as a starting point for the Distributed number of users and their types are unknown. In order to do this, the framework is modelled as a non-cooperative Poisson game in Coordination Function (DCF) mechanism in IEEE 802.11. In which all the players are unaware of the total number of devices the DCF there are no base stations or access points which participating (population uncertainty). We propose a scheme control the access to the channel, hence all nodes transmit their where failed attempts to transmit (collisions) are penalized. In data frames in a competitive manner. However, as pointed out terms of this, we calculate the optimum penalization in mixed in [9], the proposed DCF game does not consider how the strategies. The proposed scheme conveys to a Nash equilibrium where a maximum in the possible throughput is achieved. different types of traffic can affect the sum throughput of the system. Moreover, in [10] it is assumed that the total number of players is known in order to evaluate the performance I. -
Recency, Records and Recaps: Learning and Non-Equilibrium Behavior in a Simple Decision Problem*
Recency, Records and Recaps: Learning and Non-equilibrium Behavior in a Simple Decision Problem* DREW FUDENBERG, Harvard University ALEXANDER PEYSAKHOVICH, Facebook Nash equilibrium takes optimization as a primitive, but suboptimal behavior can persist in simple stochastic decision problems. This has motivated the development of other equilibrium concepts such as cursed equilibrium and behavioral equilibrium. We experimentally study a simple adverse selection (or “lemons”) problem and find that learning models that heavily discount past information (i.e. display recency bias) explain patterns of behavior better than Nash, cursed or behavioral equilibrium. Providing counterfactual information or a record of past outcomes does little to aid convergence to optimal strategies, but providing sample averages (“recaps”) gets individuals most of the way to optimality. Thus recency effects are not solely due to limited memory but stem from some other form of cognitive constraints. Our results show the importance of going beyond static optimization and incorporating features of human learning into economic models. Categories & Subject Descriptors: J.4 [Social and Behavioral Sciences] Economics Author Keywords & Phrases: Learning, behavioral economics, recency, equilibrium concepts 1. INTRODUCTION Understanding when repeat experience can lead individuals to optimal behavior is crucial for the success of game theory and behavioral economics. Equilibrium analysis assumes all individuals choose optimal strategies while much research in behavioral economics -
Strong Stackelberg Reasoning in Symmetric Games: an Experimental
Strong Stackelberg reasoning in symmetric games: An experimental ANGOR UNIVERSITY replication and extension Pulford, B.D.; Colman, A.M.; Lawrence, C.L. PeerJ DOI: 10.7717/peerj.263 PRIFYSGOL BANGOR / B Published: 25/02/2014 Publisher's PDF, also known as Version of record Cyswllt i'r cyhoeddiad / Link to publication Dyfyniad o'r fersiwn a gyhoeddwyd / Citation for published version (APA): Pulford, B. D., Colman, A. M., & Lawrence, C. L. (2014). Strong Stackelberg reasoning in symmetric games: An experimental replication and extension. PeerJ, 263. https://doi.org/10.7717/peerj.263 Hawliau Cyffredinol / General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. 23. Sep. 2021 Strong Stackelberg reasoning in symmetric games: An experimental replication and extension Briony D. Pulford1, Andrew M. Colman1 and Catherine L. Lawrence2 1 School of Psychology, University of Leicester, Leicester, UK 2 School of Psychology, Bangor University, Bangor, UK ABSTRACT In common interest games in which players are motivated to coordinate their strate- gies to achieve a jointly optimal outcome, orthodox game theory provides no general reason or justification for choosing the required strategies.