Game Theory Solution Explaination
Publicly-available solutions for
AN INTRODUCTION TO GAME THEORY
Publicly-available solutions for
AN INTRODUCTION TO GAME THEORY
M ARTIN J. O SBORNE
University of Toronto
Copyright © 2005 by Martin J. Osborne All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Martin J. Osborne. This manual was typeset by the author, who is greatly indebted to Donald Knuth A (TEX), Leslie Lamport (L TEX), Diego Puga (mathpazo), Christian Schenk (MiKTEX), Ed Sznyter (ppctr), Timothy van Zandt (PSTricks), and others, for generously making superlative software freely available. The main font is 10pt Palatino.
Version 5: 2005-10-7
Contents
Preface 1
xi
Introduction 1 Exercise 5.3 (Altruistic preferences) 1 Exercise 6.1 (Alternative representations of preferences)
1
2
Nash Equilibrium 3 Exercise 16.1 (Working on a joint project) 3 Exercise 17.1 (Games equivalent to the Prisoner’s Dilemma) 3 Exercise 20.1 (Games without conflict) 3 Exercise 31.1 (Extension of the Stag Hunt) 4 Exercise 34.1 (Guessing two-thirds of the average) 4 Exercise 34.3 (Choosing a route) 5 Exercise 37.1 (Finding Nash equilibria using best response functions) 6 Exercise 38.1 (Constructing best response functions) 6 Exercise 38.2 (Dividing money) 7 Exercise 41.1 (Strict and nonstrict Nash equilibria) 7 Exercise 47.1 (Strict equilibria and dominated actions) 8 Exercise 47.2 (Nash equilibrium and weakly dominated actions) 8 Exercise 50.1 (Other Nash equilibria of the game modeling collective decision-making) 8 Exercise 51.2 (Symmetric strategic games) 9 Exercise 52.2 (Equilibrium for pairwise interactions in a single population) 9 Nash Equilibrium: Illustrations 11 Exercise 58.1 (Cournot’s duopoly game with linear inverse demand and different unit costs) 11 Exercise 60.2 (Nash equilibrium of
AN INTRODUCTION TO GAME THEORY
Publicly-available solutions for
AN INTRODUCTION TO GAME THEORY
M ARTIN J. O SBORNE
University of Toronto
Copyright © 2005 by Martin J. Osborne All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Martin J. Osborne. This manual was typeset by the author, who is greatly indebted to Donald Knuth A (TEX), Leslie Lamport (L TEX), Diego Puga (mathpazo), Christian Schenk (MiKTEX), Ed Sznyter (ppctr), Timothy van Zandt (PSTricks), and others, for generously making superlative software freely available. The main font is 10pt Palatino.
Version 5: 2005-10-7
Contents
Preface 1
xi
Introduction 1 Exercise 5.3 (Altruistic preferences) 1 Exercise 6.1 (Alternative representations of preferences)
1
2
Nash Equilibrium 3 Exercise 16.1 (Working on a joint project) 3 Exercise 17.1 (Games equivalent to the Prisoner’s Dilemma) 3 Exercise 20.1 (Games without conflict) 3 Exercise 31.1 (Extension of the Stag Hunt) 4 Exercise 34.1 (Guessing two-thirds of the average) 4 Exercise 34.3 (Choosing a route) 5 Exercise 37.1 (Finding Nash equilibria using best response functions) 6 Exercise 38.1 (Constructing best response functions) 6 Exercise 38.2 (Dividing money) 7 Exercise 41.1 (Strict and nonstrict Nash equilibria) 7 Exercise 47.1 (Strict equilibria and dominated actions) 8 Exercise 47.2 (Nash equilibrium and weakly dominated actions) 8 Exercise 50.1 (Other Nash equilibria of the game modeling collective decision-making) 8 Exercise 51.2 (Symmetric strategic games) 9 Exercise 52.2 (Equilibrium for pairwise interactions in a single population) 9 Nash Equilibrium: Illustrations 11 Exercise 58.1 (Cournot’s duopoly game with linear inverse demand and different unit costs) 11 Exercise 60.2 (Nash equilibrium of
References: The page numbers on which the references are cited are given in brackets after each item. Nagel, Rosemarie (1995), “Unraveling in guessing games: an experimental study”, American Economic Review 85, 1313–1326. [8] Ochs, Jack (1995), “Coordination problems”, in Handbook of experimental economics (John H. Kagel and Alvin E. Roth, eds.), 195–251. Princeton: Princeton University Press. [6] Shubik, Martin (1982), Game theory in the social sciences. Cambridge, MA: MIT Press. [55] Van Huyck, John B., Raymond C. Battalio, and Richard O. Beil (1990), “Tacit coordination games, strategic uncertainty, and coordination failure”, American Economic Review 80, 234–248. [6] 89