Game theory and exercises

Game Theory and Exercises Game Theory and Exercises introduces the main concepts of game theory, along with interactive exercises to aid readers’ learning and understanding Game theory is used to help players understand decisionmaking, risk-taking and strategy and the impact that the choices they make have on other players; and how the choices of those players, in turn, influence their own behaviour So, it is not surprising that game theory is used in politics, economics, law and management This book covers classic topics of game theory including dominance, Nash equilibrium, backward induction, repeated games, perturbed strategies, beliefs, perfect equilibrium, perfect Bayesian equilibrium and replicator dynamics It also covers recent topics in game theory such as level-k reasoning, best reply matching, regret minimization and quantal responses This textbook provides many economic applications, namely on auctions and negotiations It studies original games that are not usually found in other textbooks, including Nim games and traveller’s dilemma The many exercises and the inserts for students throughout the chapters aid the reader’s understanding of the concepts With more than 20 years’ teaching experience, Umbhauer’s expertise and classroom experience helps students understand what game theory is and how it can be applied to real life examples This textbook is suitable for both undergraduate and postgraduate students who study game theory, behavioural economics and microeconomics Gisèle Umbhauer is Associate Professor of Economics at the University of Strasbourg, France Routledge Advanced Texts in Economics and Finance Financial Econometrics Peijie Wang Macroeconomics for Developing Countries, 2nd edition Raghbendra Jha Advanced Mathematical Economics Rakesh Vohra Advanced Econometric Theory John S Chipman Understanding Macroeconomic Theory John M Barron, Bradley T Ewing and Gerald J Lynch Regional Economics Roberta Capello Mathematical Finance: Core Theory, Problems and Statistical Algorithms Nikolai Dokuchaev Applied Health Economics Andrew M Jones, Nigel Rice, Teresa Bago d’Uva and Silvia Balia â•⁄9 Information Economics Urs Birchler and Monika Bütler 10 Financial Econometrics (Second Edition) Peijie Wang 11 Development Finance Debates, Dogmas and New Directions Stephen Spratt 12 Culture and Economics On Values, Economics and International Business Eelke de Jong 13 Modern Public Economics, Second Edition Raghbendra Jha 14 Introduction to Estimating Economic Models Atsushi Maki 15 Advanced Econometric Theory John Chipman 16 Behavioral Economics Edward Cartwright 17 Essentials of Advanced Macroeconomic Theory Ola Olsson 18 Behavioral Economics and Finance Michelle Baddeley 19 Applied Health Economics, Second Edition Andrew M Jones, Nigel Rice, Teresa Bago d’Uva and Silvia Balia 20 Real Estate Economics A Point to Point Handbook Nicholas G Pirounakis 25 Strategic Entrepreneurial Finance From Value Creation to Realization Darek Klonowski 21 Finance in Asia Institutions, Regulation and Policy Qiao Liu, Paul Lejot and Douglas Arner 26 Computational Economics A concise introduction Oscar Afonso and Paulo Vasconcelos 22 Behavioral Economics, Second Edition Edward Cartwright 27 Regional Economics, Second Edition Roberta Capello 23 Understanding Financial Risk Management Angelo Corelli 28 Game Theory and Exercises Gisèle Umbhauer 24 Empirical Development Economics Måns Söderbom and Francis Teal with Markus Eberhardt, Simon Quinn and Andrew Zeitlin This page intentionally left blank Game Theory and Exercises Gisèle Umbhauer First published 2016 by Routledge Park Square, Milton Park, Abingdon, Oxon OX14 4RN by Routledge 711 Third Avenue, New York, NY 10017 Routledge is an imprint of the Taylor & Francis Group, an informa business © 2016 Gisèle Umbhauer The right of Gisèle Umbhauer to be identified as author of this work has been asserted by her in accordance with the Copyright, Designs and Patent Act 1988 All rights reserved No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data Umbhauer, Gisele Game theory and exercises / Gisele Umbhauer Game theory I Title HB144.U43 2015 519.3 dc23 2015020124 ISBN: 978-0-415-60421-5 (hbk) ISBN: 978-0-415-60422-2 (pbk) ISBN: 978-1-315-66906-9 (ebk) Typeset in Times New Roman and Bell Gothic by Saxon Graphics Ltd, Derby Dedication To my son Victor This page intentionally left blank Contents Acknowledgementsxix Introduction1 HOW TO BUILD A GAME INTRODUCTION5 STRATEGIC OR EXTENSIVE FORM GAMES? 1.1 Strategic/normal form games 1.1.1 Definition 1.1.2 Story strategic/normal form games and behavioural comments 1.1.3 All pay auction 12 1.2 Extensive form games 18 1.2.1 Definition 18 1.2.2 Story extensive form games and behavioural comments 20 1.2.3 Subgames 27 2 STRATEGIES 28 2.1 Strategies in strategic/normal form games 28 2.1.1 Pure strategies 28 2.1.2 Mixed strategies 28 2.2 Strategies in extensive form games 30 2.2.1 Pure strategies: a complete description of the behaviour 30 2.2.2 The Fort Boyard Sticks game and the Envelope game 31 2.2.3 Behavioural strategies 35 2.3 Strategic/normal form games and extensive form games: is there a difference? 36 INFORMATION AND UTILITIES 40 3.1 Perfect/imperfect information 40 3.1.1 A concept linked to the information sets 40 3.1.2 The prisoners’ disks game 41 3.2 Complete/incomplete information 43 3.2.1 Common knowledge: does it make sense? 43 45 3.2.2 Signalling games and screening games 3.3 Utilities 47 3.3.1 Taking risks into account 47 3.3.2 Which is the game you have in mind? 49 3.3.3 Fairness and reciprocity 49 3.3.4 Strategic feelings and paranoia 51 3.3.5 How to bypass utilities 52 CONCLUSION54 ix╇ ■ .. .Game Theory and Exercises Game Theory and Exercises introduces the main concepts of game theory, along with interactive exercises to aid readers’ learning and understanding Game theory. .. completely different games (the syndicate game and the chicken game) may have the same strategic structure Congestion games, coordination games, and battle of the sexes In a congestion game, two players... games, first price and second price all pay auction games, first price and second price wallet games, the traveller’s dilemma, the gift exchange game, the ultimatum game ) and I expose their