Game Theory Honoring Abraham Neyman's Scientific Achievements
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Embezzlement and Guilt Aversion Giuseppe Attanasi, Claire Rimbaud, Marie Claire Villeval
Embezzlement and Guilt Aversion Giuseppe Attanasi, Claire Rimbaud, Marie Claire Villeval To cite this version: Giuseppe Attanasi, Claire Rimbaud, Marie Claire Villeval. Embezzlement and Guilt Aversion. 2018. halshs-01779145 HAL Id: halshs-01779145 https://halshs.archives-ouvertes.fr/halshs-01779145 Preprint submitted on 26 Apr 2018 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. WP 1807 – April 2018 Embezzlement and Guilt Aversion Giuseppe Attanasi, Claire Rimbaud, Marie Claire Villeval Abstract: Donors usually need intermediaries to transfer their donations to recipients. A risk is that donations can be embezzled before they reach the recipients. Using psychological game theory, we design a novel three- player Embezzlement Mini-Game to study whether intermediaries suffer from guilt aversion and whether guilt aversion toward the recipient is stronger than toward the donor. Testing the predictions of the model in a laboratory experiment, we show that the proportion of guilt-averse intermediaries is the same irrespective of the direction of the guilt. However, structural estimates indicate that the effect of guilt on behaviour is higher when the guilt is directed toward the recipient. Keywords: Embezzlement, Dishonesty, Guilt Aversion, Psychological Game Theory, Experiment JEL codes: C91 Embezzlement and Guilt Aversion G. -
Lecture Notes
GRADUATE GAME THEORY LECTURE NOTES BY OMER TAMUZ California Institute of Technology 2018 Acknowledgments These lecture notes are partially adapted from Osborne and Rubinstein [29], Maschler, Solan and Zamir [23], lecture notes by Federico Echenique, and slides by Daron Acemoglu and Asu Ozdaglar. I am indebted to Seo Young (Silvia) Kim and Zhuofang Li for their help in finding and correcting many errors. Any comments or suggestions are welcome. 2 Contents 1 Extensive form games with perfect information 7 1.1 Tic-Tac-Toe ........................................ 7 1.2 The Sweet Fifteen Game ................................ 7 1.3 Chess ............................................ 7 1.4 Definition of extensive form games with perfect information ........... 10 1.5 The ultimatum game .................................. 10 1.6 Equilibria ......................................... 11 1.7 The centipede game ................................... 11 1.8 Subgames and subgame perfect equilibria ...................... 13 1.9 The dollar auction .................................... 14 1.10 Backward induction, Kuhn’s Theorem and a proof of Zermelo’s Theorem ... 15 2 Strategic form games 17 2.1 Definition ......................................... 17 2.2 Nash equilibria ...................................... 17 2.3 Classical examples .................................... 17 2.4 Dominated strategies .................................. 22 2.5 Repeated elimination of dominated strategies ................... 22 2.6 Dominant strategies .................................. -
The Monty Hall Problem in the Game Theory Class
The Monty Hall Problem in the Game Theory Class Sasha Gnedin∗ October 29, 2018 1 Introduction Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice? With these famous words the Parade Magazine columnist vos Savant opened an exciting chapter in mathematical didactics. The puzzle, which has be- come known as the Monty Hall Problem (MHP), has broken the records of popularity among the probability paradoxes. The book by Rosenhouse [9] and the Wikipedia entry on the MHP present the history and variations of the problem. arXiv:1107.0326v1 [math.HO] 1 Jul 2011 In the basic version of the MHP the rules of the game specify that the host must always reveal one of the unchosen doors to show that there is no prize there. Two remaining unrevealed doors may hide the prize, creating the illusion of symmetry and suggesting that the action does not matter. How- ever, the symmetry is fallacious, and switching is a better action, doubling the probability of winning. There are two main explanations of the paradox. One of them, simplistic, amounts to just counting the mutually exclusive cases: either you win with ∗[email protected] 1 switching or with holding the first choice. -
Stochastic Game Theory Applications for Power Management in Cognitive Networks
STOCHASTIC GAME THEORY APPLICATIONS FOR POWER MANAGEMENT IN COGNITIVE NETWORKS A thesis submitted to Kent State University in partial fulfillment of the requirements for the degree of Master of Digital Science by Sham Fung Feb 2014 Thesis written by Sham Fung M.D.S, Kent State University, 2014 Approved by Advisor , Director, School of Digital Science ii TABLE OF CONTENTS LIST OF FIGURES . vi LIST OF TABLES . vii Acknowledgments . viii Dedication . ix 1 BACKGROUND OF COGNITIVE NETWORK . 1 1.1 Motivation and Requirements . 1 1.2 Definition of Cognitive Networks . 2 1.3 Key Elements of Cognitive Networks . 3 1.3.1 Learning and Reasoning . 3 1.3.2 Cognitive Network as a Multi-agent System . 4 2 POWER ALLOCATION IN COGNITIVE NETWORKS . 5 2.1 Overview . 5 2.2 Two Communication Paradigms . 6 2.3 Power Allocation Scheme . 8 2.3.1 Interference Constraints for Primary Users . 8 2.3.2 QoS Constraints for Secondary Users . 9 2.4 Related Works on Power Management in Cognitive Networks . 10 iii 3 GAME THEORY|PRELIMINARIES AND RELATED WORKS . 12 3.1 Non-cooperative Game . 14 3.1.1 Nash Equilibrium . 14 3.1.2 Other Equilibriums . 16 3.2 Cooperative Game . 16 3.2.1 Bargaining Game . 17 3.2.2 Coalition Game . 17 3.2.3 Solution Concept . 18 3.3 Stochastic Game . 19 3.4 Other Types of Games . 20 4 GAME THEORETICAL APPROACH ON POWER ALLOCATION . 23 4.1 Two Fundamental Types of Utility Functions . 23 4.1.1 QoS-Based Game . 23 4.1.2 Linear Pricing Game . -
Incomplete Information I. Bayesian Games
Bayesian Games Debraj Ray, November 2006 Unlike the previous notes, the material here is perfectly standard and can be found in the usual textbooks: see, e.g., Fudenberg-Tirole. For the examples in these notes (except for the very last section), I draw heavily on Martin Osborne’s excellent recent text, An Introduction to Game Theory, Oxford University Press. Obviously, incomplete information games — in which one or more players are privy to infor- mation that others don’t have — has enormous applicability: credit markets / auctions / regulation of firms / insurance / bargaining /lemons / public goods provision / signaling / . the list goes on and on. 1. A Definition A Bayesian game consists of 1. A set of players N. 2. A set of states Ω, and a common prior µ on Ω. 3. For each player i a set of actions Ai and a set of signals or types Ti. (Can make actions sets depend on type realizations.) 4. For each player i, a mapping τi :Ω 7→ Ti. 5. For each player i, a vN-M payoff function fi : A × Ω 7→ R, where A is the product of the Ai’s. Remarks A. Typically, the mapping τi tells us player i’s type. The easiest case is just when Ω is the product of the Ti’s and τi is just the appropriate projection mapping. B. The prior on states need not be common, but one view is that there is no loss of generality in assuming it (simply put all differences in the prior into differences in signals and redefine the state space and si-mappings accordingly). -
Public Goods Agreements with Other-Regarding Preferences
NBER WORKING PAPER SERIES PUBLIC GOODS AGREEMENTS WITH OTHER-REGARDING PREFERENCES Charles D. Kolstad Working Paper 17017 http://www.nber.org/papers/w17017 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 May 2011 Department of Economics and Bren School, University of California, Santa Barbara; Resources for the Future; and NBER. Comments from Werner Güth, Kaj Thomsson and Philipp Wichardt and discussions with Gary Charness and Michael Finus have been appreciated. Outstanding research assistance from Trevor O’Grady and Adam Wright is gratefully acknowledged. Funding from the University of California Center for Energy and Environmental Economics (UCE3) is also acknowledged and appreciated. The views expressed herein are those of the author and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer- reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications. © 2011 by Charles D. Kolstad. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Public Goods Agreements with Other-Regarding Preferences Charles D. Kolstad NBER Working Paper No. 17017 May 2011, Revised June 2012 JEL No. D03,H4,H41,Q5 ABSTRACT Why cooperation occurs when noncooperation appears to be individually rational has been an issue in economics for at least a half century. In the 1960’s and 1970’s the context was cooperation in the prisoner’s dilemma game; in the 1980’s concern shifted to voluntary provision of public goods; in the 1990’s, the literature on coalition formation for public goods provision emerged, in the context of coalitions to provide transboundary pollution abatement. -
Experimental Evidence of Dictator and Ultimatum Games
games Article How to Split Gains and Losses? Experimental Evidence of Dictator and Ultimatum Games Thomas Neumann 1, Sabrina Kierspel 1,*, Ivo Windrich 2, Roger Berger 2 and Bodo Vogt 1 1 Chair in Empirical Economics, Otto-von-Guericke-University Magdeburg, Postbox 4120, 39016 Magdeburg, Germany; [email protected] (T.N.); [email protected] (B.V.) 2 Institute of Sociology, University of Leipzig, Beethovenstr. 15, 04107 Leipzig, Germany; [email protected] (I.W.); [email protected] (R.B.) * Correspondence: [email protected]; Tel.: +49-391-6758205 Received: 27 August 2018; Accepted: 3 October 2018; Published: 5 October 2018 Abstract: Previous research has typically focused on distribution problems that emerge in the domain of gains. Only a few studies have distinguished between games played in the domain of gains from games in the domain of losses, even though, for example, prospect theory predicts differences between behavior in both domains. In this study, we experimentally analyze players’ behavior in dictator and ultimatum games when they need to divide a monetary loss and then compare this to behavior when players have to divide a monetary gain. We find that players treat gains and losses differently in that they are less generous in games over losses and react differently to prior experiences. Players in the dictator game become more selfish after they have had the experience of playing an ultimatum game first. Keywords: dictator game; ultimatum game; gains; losses; equal split; experimental economics 1. Introduction Economists and social scientists have collected an increasing body of literature on the importance of other-regarding preferences for decision-making in various contexts [1]. -
(501B) Problem Set 5. Bayesian Games Suggested Solutions by Tibor Heumann
Dirk Bergemann Department of Economics Yale University Microeconomic Theory (501b) Problem Set 5. Bayesian Games Suggested Solutions by Tibor Heumann 1. (Market for Lemons) Here I ask that you work out some of the details in perhaps the most famous of all information economics models. By contrast to discussion in class, we give a complete formulation of the game. A seller is privately informed of the value v of the good that she sells to a buyer. The buyer's prior belief on v is uniformly distributed on [x; y] with 3 0 < x < y: The good is worth 2 v to the buyer. (a) Suppose the buyer proposes a price p and the seller either accepts or rejects p: If she accepts, the seller gets payoff p−v; and the buyer gets 3 2 v − p: If she rejects, the seller gets v; and the buyer gets nothing. Find the optimal offer that the buyer can make as a function of x and y: (b) Show that if the buyer and the seller are symmetrically informed (i.e. either both know v or neither party knows v), then trade takes place with probability 1. (c) Consider a simultaneous acceptance game in the model with private information as in part a, where a price p is announced and then the buyer and the seller simultaneously accept or reject trade at price p: The payoffs are as in part a. Find the p that maximizes the probability of trade. [SOLUTION] (a) We look for the subgame perfect equilibrium, thus we solve by back- ward induction. -
Endogenous Institutions and Game-Theoretic Analysis
Chapter 5 Endogenous Institutions and Game-theoretic Analysis Chapters 3 and 4 illustrate that restricting the set of admissible institutionalized beliefs is central to the way in which game theory facilitates the study of endogenous institutions. Durkheim (1950 [1895], p. 45) recognized the centrality of institutionalized beliefs, arguing that institutions are “all the beliefs and modes of behavior instituted by the collectivity.” But neither Durkheim nor his followers placed any analytic restrictions on what beliefs the collectivity could institute. Because beliefs are not directly observable, however, deductively restricting them, as game theory lets us do, is imperative. The only beliefs that can be instituted by the collectivity—that can be common knowledge—are those regarding equilibrium (self-enforcing) behavior. Furthermore, the behavior that these beliefs motivate should reproduce—not refute or erode—these beliefs. Game theory thus enables us to place more of the “responsibility for social order on the individuals who are part of that order” (Crawford and Ostrom 1995, p. 583). Rather than assuming that individuals follow rules, it provides an analytical framework within which it is possible to study the way in which behavior is endogenously generated—how, through their interactions, individuals gain the information, ability, and motivation to follow particular rules of behavior. It allows us to examine, for example, who applies sanctions and rewards that motivate behavior, how those who are to apply them learn or decide which ones to apply, why they do not shirk this duty, and why offenders do not flee to avoid sanctions. The empirical usefulness of the analytical framework of classical game theory is puzzling, however, because this theory rests on seemingly unrealistic assumptions about cognition, information and rationality. -
Deterministic and Stochastic Prisoner's Dilemma Games: Experiments in Interdependent Security
NBER TECHNICAL WORKING PAPER SERIES DETERMINISTIC AND STOCHASTIC PRISONER'S DILEMMA GAMES: EXPERIMENTS IN INTERDEPENDENT SECURITY Howard Kunreuther Gabriel Silvasi Eric T. Bradlow Dylan Small Technical Working Paper 341 http://www.nber.org/papers/t0341 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 August 2007 We appreciate helpful discussions in designing the experiments and comments on earlier drafts of this paper by Colin Camerer, Vince Crawford, Rachel Croson, Robyn Dawes, Aureo DePaula, Geoff Heal, Charles Holt, David Krantz, Jack Ochs, Al Roth and Christian Schade. We also benefited from helpful comments from participants at the Workshop on Interdependent Security at the University of Pennsylvania (May 31-June 1 2006) and at the Workshop on Innovation and Coordination at Humboldt University (December 18-20, 2006). We thank George Abraham and Usmann Hassan for their help in organizing the data from the experiments. Support from NSF Grant CMS-0527598 and the Wharton Risk Management and Decision Processes Center is gratefully acknowledged. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research. © 2007 by Howard Kunreuther, Gabriel Silvasi, Eric T. Bradlow, and Dylan Small. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Deterministic and Stochastic Prisoner's Dilemma Games: Experiments in Interdependent Security Howard Kunreuther, Gabriel Silvasi, Eric T. Bradlow, and Dylan Small NBER Technical Working Paper No. 341 August 2007 JEL No. C11,C12,C22,C23,C73,C91 ABSTRACT This paper examines experiments on interdependent security prisoner's dilemma games with repeated play. -
Stochastic Games with Hidden States∗
Stochastic Games with Hidden States¤ Yuichi Yamamoto† First Draft: March 29, 2014 This Version: January 14, 2015 Abstract This paper studies infinite-horizon stochastic games in which players ob- serve noisy public information about a hidden state each period. We find that if the game is connected, the limit feasible payoff set exists and is invariant to the initial prior about the state. Building on this invariance result, we pro- vide a recursive characterization of the equilibrium payoff set and establish the folk theorem. We also show that connectedness can be replaced with an even weaker condition, called asymptotic connectedness. Asymptotic con- nectedness is satisfied for generic signal distributions, if the state evolution is irreducible. Journal of Economic Literature Classification Numbers: C72, C73. Keywords: stochastic game, hidden state, connectedness, stochastic self- generation, folk theorem. ¤The author thanks Naoki Aizawa, Drew Fudenberg, Johannes Horner,¨ Atsushi Iwasaki, Michi- hiro Kandori, George Mailath, Takeaki Sunada, and Masatoshi Tsumagari for helpful conversa- tions, and seminar participants at various places. †Department of Economics, University of Pennsylvania. Email: [email protected] 1 1 Introduction When agents have a long-run relationship, underlying economic conditions may change over time. A leading example is a repeated Bertrand competition with stochastic demand shocks. Rotemberg and Saloner (1986) explore optimal col- lusive pricing when random demand shocks are i.i.d. each period. Haltiwanger and Harrington (1991), Kandori (1991), and Bagwell and Staiger (1997) further extend the analysis to the case in which demand fluctuations are cyclic or persis- tent. One of the crucial assumptions of these papers is that demand shocks are publicly observable before firms make their decisions in each period. -
Bounded Rationality in Bargaining Games: Do Proposers Believe That Responders Reject an Equal Split?
No. 11 UNIVERSITY OF COLOGNE WORKING PAPER SERIES IN ECONOMICS BOUNDED RATIONALITY IN BARGAINING GAMES: DO PROPOSERS BELIEVE THAT RESPONDERS REJECT AN EQUAL SPLIT? BEN GREINER Department of Economics University of Cologne Albertus-Magnus-Platz D-50923 Köln Germany http://www.wiso.uni-koeln.de Bounded Rationality in Bargaining Games: Do Proposers Believe That Responders Reject an Equal Split?∗ Ben Greiner† June 19, 2004 Abstract Puzzled by the experimental results of the ’impunity game’ by Bolton & Zwick (1995) we replicate the game and alter it in a systematic manner. We find that although almost nobody actually rejects an offered equal split in a bargaining game, proposers behave as if there would be a considerably large rejection rate for equal splits. This result is inconsistent with existing models of economic decision making. This includes models of selfish play- ers as well as models of social utility and reciprocity, even when combined with erroneous decision making. Our data suggests that subjects fail to foresee their opponent’s decision even for one step in our simple bargaining games. We consider models of bounded rational decision making such as rules of thumb as explanations for the observed behavioral pattern. Keywords: ultimatum game, dictator game, impunity game, social utility, bounded rationality JEL Classification: C72, C92, D3 ∗I thank Bettina Bartels, Hakan Fink and Ralica Gospodinova for research assistance, the Strategic Interaction Group at MPI Jena for comments and serving as pilot participants, especially Susanne B¨uchner, Sven Fischer, Katinka Pantz and Carsten Schmidt for support in the conduction of the experiment, and Werner G¨uth, Axel Ockenfels, Ro’i Zultan, participants at the European ESA Meeting in Erfurt and at the Brown Bag seminars in Jena and Cologne for discussions and valuable comments.