DOCSLIB.ORG

Lecturenotesongametheory

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Lecturenotesongametheory Lecture Notes on Game Theory Theory and Examples Xiang Sun November 2, 2017 ii Contents Acknowledgement vii 1 Introduction 1 1.1 Timeline of the main evolution of game theory ................................ 1 1.2 Nobel prize laureates .............................................. 16 1.3 Potential Nobel prize winners ......................................... 19 1.4 Rational behavior ................................................ 20 1.5 Common knowledge .............................................. 20 2 Strategic games with complete information 23 2.1 Strategic games ................................................. 23 2.2 Nash equilibrium ................................................ 24 2.3 Examples .................................................... 25 2.4 Existence of a Nash equilibrium ........................................ 42 2.5 Symmetric games ................................................ 43 2.6 Strictly competitive games (zero-sum games) ................................. 44 2.7 Contest ..................................................... 45 2.8 Strategic games with discontinuous payoff functions ............................. 47 3 Bayesian games 49 3.1 Bayes’ rule (Bayes’ theorem) .......................................... 49 3.2 Bayesian games ................................................. 50 3.3 Examples .................................................... 54 3.4 Bilateral trading (Double auction) ....................................... 66 3.5 Providing a public good under incomplete information ........................... 71 i Contents ii 3.6 Comments on Bayesian games ......................................... 71 4 Auction 75 4.1 Preliminary ................................................... 75 4.2 The symmetric model ............................................. 77 4.3 Second-price sealed-bid auction ........................................ 77 4.4 First-price sealed-bid auction ......................................... 78 4.5 Revenue comparison .............................................. 86 4.6 Reserve prices ................................................. 88 4.7 The revenue equivalence principle ....................................... 91 4.8 All-pay auction ................................................. 92 4.9 Third-price auction ............................................... 93 4.10 Uncertain number of bidders ......................................... 95 5 Mixed-strategy Nash equilibrium 97 5.1 Mixed-strategy Nash equilibrium ....................................... 97 5.2 Examples .................................................... 99 5.3 Interpretation of mixed-strategy Nash equilibrium .............................. 102 5.3.1 Purification .............................................. 103 6 Correlated equilibrium 109 6.1 Motivation ................................................... 109 6.2 Correlated equilibrium ............................................. 110 6.3 Examples .................................................... 113 7 Rationalizability 117 7.1 Rationalizability ................................................ 117 7.2 Iterated elimination of never-best response .................................. 121 7.3 Iterated elimination of strictly dominated actions .............................. 122 7.4 Examples .................................................... 125 7.5 Iterated elimination of weakly dominated actions .............................. 128 8 Knowledge model 131 8.1 A model of knowledge ............................................. 131 8.2 Common knowledge .............................................. 136 8.3 Common prior ................................................. 137 Contents iii 8.4 “Agree to disagree” is impossible ........................................ 138 8.5 No-trade theorem ............................................... 140 8.6 Speculation ................................................... 141 8.7 Characterization of the common prior assumption .............................. 143 8.8 Unawareness .................................................. 145 9 Interactive epistemology 147 9.1 Epistemic conditions for Nash equilibrium .................................. 147 9.2 Epistemic foundation of rationalizability ................................... 150 9.3 Epistemic foundation of correlated equilibrium ............................... 151 9.4 The electronic mail game ............................................ 151 10 Extensive games with perfect information 155 10.1 Extensive games with perfect information .................................. 155 10.2 Subgame perfect equilibrium ......................................... 157 10.3 Examples .................................................... 160 10.4 Three notable games .............................................. 167 10.5 Iterated elimination of weakly dominated strategies ............................. 169 10.6 Forward induction ............................................... 170 11 Bargaining games 173 11.1 A bargaining game of alternating offers .................................... 173 11.2 Bargaining games with finite horizon ..................................... 174 11.3 Bargaining games with infinite horizon .................................... 175 11.4 Properties of subgame perfect equilibria in Rubinstein bargaining games .................. 178 11.5 Bargaining games with cost .......................................... 179 11.6 n-person bargaining games .......................................... 179 12 Repeated games 183 12.1 Infinitely repeated games ............................................ 183 12.2 Trigger strategy equilibrium .......................................... 188 12.3 Tit-for-tat strategy equilibrium ........................................ 193 12.4 Folk theorem .................................................. 194 12.5 Nash-threats folk theorem ........................................... 195 12.6 Perfect folk theorem .............................................. 196 12.7 Finitely repeated games ............................................ 199 Contents iv 13 Extensive games with imperfect information 201 13.1 Extensive games with imperfect information ................................. 201 13.2 Mixed and behavioral strategies ........................................ 203 13.3 Subgame perfect equilibrium ......................................... 206 13.4 Perfect Bayesian equilibrium .......................................... 212 13.5 Sequential equilibrium ............................................. 217 13.6 Trembling hand perfect equilibrium ...................................... 221 14 Information economics 1: signaling 223 14.1 Adverse selection ................................................ 223 14.2 Signaling .................................................... 226 14.3 Job-market signaling .............................................. 238 14.4 Cheap talk ................................................... 240 14.4.1 The model with two types ....................................... 242 14.4.2 The model with three types ...................................... 244 14.4.3 The model with a continuum of types ................................ 244 14.4.4 Optimal communication mechanism (the commitment case) .................... 248 14.5 Bayesian persuasion .............................................. 252 14.5.1 Example ................................................ 252 14.5.2 A model of Bayesian persuasion ................................... 254 14.5.3 Simplified problem .......................................... 256 14.5.4 Optimal information structure .................................... 257 14.6 Optimal information disclosure ........................................ 260 15 Information economics 2: screening 261 15.1 The principal-agent model ........................................... 261 15.1.1 Complete information ......................................... 262 15.1.2 Incomplete information ........................................ 265 15.1.3 The revelation principle ........................................ 269 15.1.4 General utility function for the agent ................................. 270 15.1.5 Nonresponsiveness .......................................... 271 15.2 Pricing a single indivisible good ........................................ 272 15.3 Nonlinear pricing ............................................... 275 15.3.1 The model with two types ....................................... 276 15.3.2 The model with a continuum of types ................................ 280 Contents v 15.4 Insurance .................................................... 282 15.5 Sequential screening .............................................. 282 15.5.1 A motivating example ......................................... 283 15.5.2 Optimal menu of refund contracts: two-type case .......................... 283 15.5.3 Sequential screening: general type case ................................ 287 15.5.4 Optimal selling mechanism ...................................... 290 16 Information economics 3: moral hazard 291 16.1 The principle-agent problem .......................................... 291 16.2 Complete information ............................................. 293 16.3 Incomplete information with risk-neutral agent ............................... 294 16.4 Incomplete information with limited liability ................................. 295 16.5 Incomplete information with risk-averse agent ................................ 296 16.6 n levels of performance ...........................................
Load more

Recommended publications
  • Game Theory- Prisoners Dilemma Vs Battle of the Sexes EXCERPTS
    Lesson 14. Game Theory 1 Lesson 14 Game Theory c 2010, 2011 ⃝ Roberto Serrano and Allan M. Feldman All rights reserved Version C 1. Introduction In the last lesson we discussed duopoly markets in which two firms compete to sell a product. In such markets, the firms behave strategically; each firm must think about what the other firm is doing in order to decide what it should do itself. The theory of duopoly was originally developed in the 19th century, but it led to the theory of games in the 20th century. The first major book in game theory, published in 1944, was Theory of Games and Economic Behavior,byJohnvon Neumann (1903-1957) and Oskar Morgenstern (1902-1977). We will return to the contributions of Von Neumann and Morgenstern in Lesson 19, on uncertainty and expected utility. Agroupofpeople(orteams,firms,armies,countries)areinagame if their decision problems are interdependent, in the sense that the actions that all of them take influence the outcomes for everyone. Game theory is the study of games; it can also be called interactive decision theory. Many real-life interactions can be viewed as games. Obviously football, soccer, and baseball games are games.Butsoaretheinteractionsofduopolists,thepoliticalcampaignsbetweenparties before an election, and the interactions of armed forces and countries. Even some interactions between animal or plant species in nature can be modeled as games. In fact, game theory has been used in many different fields in recent decades, including economics, political science, psychology, sociology, computer science, and biology. This brief lesson is not meant to replace a formal course in game theory; it is only an in- troduction.
    [Show full text]
  • Prisoners of Reason Game Theory and Neoliberal Political Economy
    C:/ITOOLS/WMS/CUP-NEW/6549131/WORKINGFOLDER/AMADAE/9781107064034PRE.3D iii [1–28] 11.8.2015 9:57PM Prisoners of Reason Game Theory and Neoliberal Political Economy S. M. AMADAE Massachusetts Institute of Technology C:/ITOOLS/WMS/CUP-NEW/6549131/WORKINGFOLDER/AMADAE/9781107064034PRE.3D iv [1–28] 11.8.2015 9:57PM 32 Avenue of the Americas, New York, ny 10013-2473, usa Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning, and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781107671195 © S. M. Amadae 2015 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2015 Printed in the United States of America A catalog record for this publication is available from the British Library. Library of Congress Cataloging in Publication Data Amadae, S. M., author. Prisoners of reason : game theory and neoliberal political economy / S.M. Amadae. pages cm Includes bibliographical references and index. isbn 978-1-107-06403-4 (hbk. : alk. paper) – isbn 978-1-107-67119-5 (pbk. : alk. paper) 1. Game theory – Political aspects. 2. International relations. 3. Neoliberalism. 4. Social choice – Political aspects. 5. Political science – Philosophy. I. Title. hb144.a43 2015 320.01′5193 – dc23 2015020954 isbn 978-1-107-06403-4 Hardback isbn 978-1-107-67119-5 Paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet Web sites referred to in this publication and does not guarantee that any content on such Web sites is, or will remain, accurate or appropriate.
    [Show full text]
  • Repeated Games
    REPEATED GAMES 1 Early PD experiments In 1950, Merrill Flood and Melvin Dresher (at RAND) devised an experiment to test Nash’s theory about defection in a two-person prisoners’ dilemma. Experimental Design – They asked two friends to play the PD 100 times. – They measured the success of Nash’s equilibrium concept by counting the number of times the players chose {D;D}. 2 Flood and Dresher’s results Player 1 cooperated in 68 rounds Player 2 cooperated in 78 rounds Both cooperated in 60 of last 89 rounds Flood Dresher Nash 3 Flood and Dresher’s results Player 1 cooperated in 68 rounds Player 2 cooperated in 78 rounds Both cooperated in 60 of last 89 rounds Wait a Ha! That jerk I can’tI’mOh a be Ha! Nash second... Nash was genius...%&@#!wrong! was wrong! wrong! Flood Dresher Nash 4 Nash’s response “If this experiment were conducted with various different players rotating the competition and with no information given to a player of what choices the others have been making until the end of all trials, then the experimental results would have been quite different, for this modification of procedure would remove the interaction between the trials.” 5 Nash’s response “The flaw in this experiment as a test of equilibrium point theory is that the experiment really amounts to having the players play one large multimove game. One cannot...think of the thing as a sequence of independent games...there is too much interaction.” In other words, Nash said that repeating the game changes the game itself.
    [Show full text]
  • A Beautiful Math : John Nash, Game Theory, and the Modern Quest for a Code of Nature / Tom Siegfried
    A BEAUTIFULA BEAUTIFUL MATH MATH JOHN NASH, GAME THEORY, AND THE MODERN QUEST FOR A CODE OF NATURE TOM SIEGFRIED JOSEPH HENRY PRESS Washington, D.C. Joseph Henry Press • 500 Fifth Street, NW • Washington, DC 20001 The Joseph Henry Press, an imprint of the National Academies Press, was created with the goal of making books on science, technology, and health more widely available to professionals and the public. Joseph Henry was one of the founders of the National Academy of Sciences and a leader in early Ameri- can science. Any opinions, findings, conclusions, or recommendations expressed in this volume are those of the author and do not necessarily reflect the views of the National Academy of Sciences or its affiliated institutions. Library of Congress Cataloging-in-Publication Data Siegfried, Tom, 1950- A beautiful math : John Nash, game theory, and the modern quest for a code of nature / Tom Siegfried. — 1st ed. p. cm. Includes bibliographical references and index. ISBN 0-309-10192-1 (hardback) — ISBN 0-309-65928-0 (pdfs) 1. Game theory. I. Title. QA269.S574 2006 519.3—dc22 2006012394 Copyright 2006 by Tom Siegfried. All rights reserved. Printed in the United States of America. Preface Shortly after 9/11, a Russian scientist named Dmitri Gusev pro- posed an explanation for the origin of the name Al Qaeda. He suggested that the terrorist organization took its name from Isaac Asimov’s famous 1950s science fiction novels known as the Foun- dation Trilogy. After all, he reasoned, the Arabic word “qaeda” means something like “base” or “foundation.” And the first novel in Asimov’s trilogy, Foundation, apparently was titled “al-Qaida” in an Arabic translation.
    [Show full text]
  • Game Theory and Its Practical Applications
    University of Northern Iowa UNI ScholarWorks Presidential Scholars Theses (1990 – 2006) Honors Program 1997 Game theory and its practical applications Angela M. Koos University of Northern Iowa Let us know how access to this document benefits ouy Copyright ©1997 Angela M. Koos Follow this and additional works at: https://scholarworks.uni.edu/pst Part of the Other Economics Commons Recommended Citation Koos, Angela M., "Game theory and its practical applications" (1997). Presidential Scholars Theses (1990 – 2006). 100. https://scholarworks.uni.edu/pst/100 This Open Access Presidential Scholars Thesis is brought to you for free and open access by the Honors Program at UNI ScholarWorks. It has been accepted for inclusion in Presidential Scholars Theses (1990 – 2006) by an authorized administrator of UNI ScholarWorks. For more information, please contact [email protected]. Game Theory and its Practical Applications A Presidential Scholar Senior Thesis University of Northern Iowa by Angela M. Koos Spring 1997 Dr. Ken Brown, 7 Dfrte Thesis and Major Advisor ,~-,, Dr. Ed Rathmell, Date Chair of Presidential Scholars Board Table of Contents Section Page(s) I. Historical Overview 1 I.A. Early Contributions to Game Theory 1 - 3 LB. John von Neumann, the RAND Corporation, and the Arms Race 3 - 7 LC. John Nash 7 - 8 I.D. Other Contributions to Game Theory 9 II. Defining Game Theory 9 - 12 II.A. Formal Representations of Games 12 - 13 II.A. I. Extensive Form 13 - 24 II.A.2. Normal Form 24 - 25 III. The Minimax Theorem 25 - 26 III.A. Preliminary Comments 26 - 27 III.B. The Theorem 27 - 28 IV.
    [Show full text]
  • Why Is Behavioral Game Theory a Game for Economists? the Concept of Beliefs in Equilibrium∗
    Why is behavioral game theory a game for economists? The concept of beliefs in equilibrium∗ Michiru Nagatsu Chiara Lisciandray May 7, 2021 Abstract The interdisciplinary exchange between economists and psychologists has so far been more active and fruitful in the modifications of Expected Util- ity Theory than in those of Game Theory. We argue that this asymmetry may be explained by economists' specific way of doing equilibrium analysis of aggregate-level outcomes in their practice, and by psychologists' reluctance to fully engage with such practice. We focus on the notion of belief that is em- bedded in economists' practice of equilibrium analysis, more specifically Nash equilibrium, and argue that its difference from the psychological counterpart is one of the factors that makes interdisciplinary exchange in behavioral game theory more difficult. 1 Introduction One of the most influential texts published in the behavioral and social sciences in the first half of the twentieth century was, according to many, Von Neumann and Morgenstern's (vNM) Theory of Games and Economic Behavior (1944). Not only did the book lay the foundation of game theory, which has become the essential research tool in contemporary economics, it also influenced several other disciplines beyond economics, from political science to linguistics and biology. Two of the most important contributions of Theory of Games and Economic Be- havior to economics are the axiomatic derivation of expected utility (in the second edition of 1947) and the minimax solution to zero-sum games. John Nash general- ized vNM's existence proof of equilibrium in non-zero-sum games in 1951, thereby ∗To appear in Egashira, Taishido, Hands and M¨aki(eds.) (2018) A Genealogy of Self-interest in Economics (Springer).
    [Show full text]
  • Algorithmic Collusion in the Digital Single Market
    This is a repository copy of EU Competition Policy: Algorithmic Collusion in the Digital Single Market. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/160267/ Article: Stewart-Moreno, Alexander (2020) EU Competition Policy: Algorithmic Collusion in the Digital Single Market. York Law Review, 1. pp. 49-82. 10.15124/yao-y99rnjtm Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. [email protected] https://eprints.whiterose.ac.uk/ EU Competition Policy: Algorithmic Collusion in the Digital Single Market Alexander Stewart-Moreno Abstract E-commerce promises a digital environment with ‘more perfect’ market characteristics. Although consumers may benefit from digital efficiencies, firms’ exploitation of such benefits may require new policy to regulate in line with the European Commission’s Digital Single Market Strategy. Price-setting algorithms are central to this dichotomy, as faster and more transparent pricing strategies could conceivably maintain algorithmic price-fixing cartels – which Article 101 of the Treaty on the Functioning of the European Union may prove inadequate in tackling.
    [Show full text]
  • Chronology of Game Theory
    Chronology of Game Theory http://www.econ.canterbury.ac.nz/personal_pages/paul_walker/g... Home | UC Home | Econ. Department | Chronology of Game Theory | Nobel Prize A Chronology of Game Theory by Paul Walker September 2012 | Ancient | 1700 | 1800 | 1900 | 1950 | 1960 | 1970 | 1980 | 1990 | Nobel Prize | 2nd Nobel Prize | 3rd Nobel Prize | 0-500AD The Babylonian Talmud is the compilation of ancient law and tradition set down during the first five centuries A.D. which serves as the basis of Jewish religious, criminal and civil law. One problem discussed in the Talmud is the so called marriage contract problem: a man has three wives whose marriage contracts specify that in the case of this death they receive 100, 200 and 300 respectively. The Talmud gives apparently contradictory recommendations. Where the man dies leaving an estate of only 100, the Talmud recommends equal division. However, if the estate is worth 300 it recommends proportional division (50,100,150), while for an estate of 200, its recommendation of (50,75,75) is a complete mystery. This particular Mishna has baffled Talmudic scholars for two millennia. In 1985, it was recognised that the Talmud anticipates the modern theory of cooperative games. Each solution corresponds to the nucleolus of an appropriately defined game. 1713 In a letter dated 13 November 1713 Francis Waldegrave provided the first, known, minimax mixed strategy solution to a two-person game. Waldegrave wrote the letter, about a two-person version of the card game le Her, to Pierre-Remond de Montmort who in turn wrote to Nicolas Bernoulli, including in his letter a discussion of the Waldegrave solution.
    [Show full text]
  • Several Remarks on the Role of Certain Positional
    Foundations of Management, Vol. 8 (2016), ISSN 2080-7279 DOI: 10.1515/fman-2016-0022 289 SEVERAL REMARKS ON THE ROLE OF CERTAIN POSITIONAL AND SOCIAL GAMES IN THE CREATION OF THE SELECTED STATISTICAL AND ECONOMIC APPLICATIONS Ewa DRABIK Warsaw University of Technology, Faculty of Management, Warsaw, Poland e-mail: [email protected] Abstract: The game theory was created on the basis of social as well as gambling games, such as chess, poker, baccarat, hex, or one-armed bandit. The aforementioned games lay solid foundations for analogous mathematical models (e.g., hex), artificial intelligence algorithms (hex), theoretical anal- ysis of computational complexity attributable to various numerical problems (baccarat), as well as illustration of several economic dilemmas particularly in the case where the winner takes every- thing (e.g., noughts and crosses). A certain gambling games, such as a horse racing, may be successful- ly applied to verify a wide spectrum of market mechanism, for example, market effectiveness or customer behavior in light of incoming information regarding a specific product. One of a lot appli- cations of the slot machine (one-armed bandit) is asymptotically efficient allocation rule, which was as- signed by T.L. Lai and H. Robbins (1985). In the next years, the rule was developed by another and was named a multi-armed. The aim of the paper is to discuss these social games along with their potential mathematical models, which are governed by the rules predominantly applicable to the social and natural sciences. Key words: positional games, social games, gambling games, one-armed bandit, chess. 1 Introduction Melvin Dresher working at RAND in 1950), gender discrimination game, chicken game, or Colonel Blot- The humanity has been accompanied by gambling to game were created.
    [Show full text]
  • Members of the American Academy of Arts and Sciences, 1780-2019 -- S
    S Saari, Donald Gene (1940-) Sabatini, David Domingo (1931-) Sabine, Wallace Clement (1868-1919) Election: 2004, Fellow Election: 1980, Fellow Election: 1894, Fellow Affiliation at election: University of Affiliation at election: New York Affiliation at election: Harvard University California, Irvine University School of Medicine Residence at election: Cambridge, MA Residence at election: Irvine, CA Residence at election: New York, NY Career description: Physicist; Educator; Career description: Mathematician; Career description: Cell biologist; Academic administrator Economist; Educator Biochemist; Educator Current affiliation: Same Current affiliation: Same Sabloff, Jeremy Arac (1944-) Election: 1999, Fellow Saariaho, Kaija A. (1952-) Sabean, David Warren (1939-) Affiliation at election: University of Election: 2012, FHM Election: 2000, Fellow Pennsylvania Affiliation at election: Paris, France Affiliation at election: University of Residence at election: Philadelphia, PA Residence at election: Paris, France California, Los Angeles Career description: Archaeologist; Career description: Musician (composer) Residence at election: Los Angeles, CA Educator; Museum administrator Current affiliation: Same Career description: Historian; Educator Current affiliation: Santa Fe Institute Current affiliation: Same Sabra, Abdelhamid Ibrahim (1924-2013) Election: 1975, Fellow Affiliation at election: Harvard University Residence at election: Cambridge, MA Career description: Historian; Educator Sachar, Abram Leon (1899-1993) Election: 1951, Fellow
    [Show full text]
  • Learning with Bandit Feedback in Potential Games
    Learning with Bandit Feedback in Potential Games Johanne Cohen LRI-CNRS, Université Paris-Sud,Université Paris-Saclay, France [email protected] Amélie Héliou LIX, Ecole Polytechnique, CNRS, AMIBio, Inria, Université Paris-Saclay [email protected] Panayotis Mertikopoulos Univ. Grenoble Alpes, CNRS, Inria, LIG, F-38000, Grenoble, France [email protected] Abstract This paper examines the equilibrium convergence properties of no-regret learning with exponential weights in potential games. To establish convergence with mini- mal information requirements on the players’ side, we focus on two frameworks: the semi-bandit case (where players have access to a noisy estimate of their payoff vectors, including strategies they did not play), and the bandit case (where players are only able to observe their in-game, realized payoffs). In the semi-bandit case, we show that the induced sequence of play converges almost surely to a Nash equilibrium at a quasi-exponential rate. In the bandit case, the same result holds for "-approximations of Nash equilibria if we introduce an exploration factor " > 0 that guarantees that action choice probabilities never fall below ". In particular, if the algorithm is run with a suitably decreasing exploration factor, the sequence of play converges to a bona fide Nash equilibrium with probability 1. 1 Introduction Given the manifest complexity of computing Nash equilibria, a central question that arises is whether such outcomes could result from a dynamic process in which players act on empirical information on their strategies’ performance over time. This question becomes particularly important when the players’ view of the game is obstructed by situational uncertainty and the “fog of war”: for instance, when deciding which route to take to work each morning, a commuter is typically unaware of how many other commuters there are at any given moment, what their possible strategies are, how to best respond to their choices, etc.
    [Show full text]
  • Global Kidney Exchange: Analysis and Background Papers from the Perspective of the Right to Health
    University of Denver Digital Commons @ DU Anthropology: Undergraduate Student Scholarship Department of Anthropology 12-2017 Global Kidney Exchange: Analysis and Background Papers from the Perspective of the Right to Health Alejandro Cerón University of Denver Kiaryce Bey University of Denver Kelly Bonk University of Denver Ellie Carson University of Denver Emilia Chapa UnivFollowersity this of and Denv additionaler works at: https://digitalcommons.du.edu/anthropology_student Part of the International Public Health Commons, Medical Humanities Commons, and the Social and See next page for additional authors Cultural Anthropology Commons Recommended Citation Cerón, Alejandro; Bey, Kiaryce; Bonk, Kelly; Carson, Ellie; Chapa, Emilia; Cohen, Louisa; Crockford, Katie; Cuda, Rachel; Injac, Sebastian; Kirby, Kajsa; Leon-Alvarez, Daniela; Looney, Mackenzie; McBeth, Kendall; Pham, Winnie; Smith, Rose; Soltero Gutierrez, Margarita; Sugura, Katherine; Yu, Alexander; and Lazier, Flinn, "Global Kidney Exchange: Analysis and Background Papers from the Perspective of the Right to Health" (2017). Anthropology: Undergraduate Student Scholarship. 3. https://digitalcommons.du.edu/anthropology_student/3 This work is licensed under a Creative Commons Attribution 4.0 License. This Book is brought to you for free and open access by the Department of Anthropology at Digital Commons @ DU. It has been accepted for inclusion in Anthropology: Undergraduate Student Scholarship by an authorized administrator of Digital Commons @ DU. For more information, please contact
    [Show full text]