GAMES FOR BUSINESS AND ECONOMICS ROY/GARDNER Indiana University Nachrichtentechnische BibliotHek TUD Inv.-Nr.: /S.JOtUM- John Wiley & Sons, Inc. 5" New York Chichester Brisbane Toronto Singapore
Contents Part I Basic Game Theory I 1 An Introduction to Games and Their Theory 3 1.1 What Is a Game? S 1.2 What Is Game Theory, and Why? 6 1.3 One-Person Games with Perfect Information 8 1.4 Utility 13 1.5 One-Person Games with Imperfect Information 17 1.6 The Three Attitudes toward Risk 20 1.7 Two-Person Games with Perfect Information 23 1.8 Games like Chess 26 1.9 Extensive Form, Normal Form, and Coalition Function Form 28 2 Two-Person Games 36 2.1 Zero-Sum Games and Constant-Sum Games 37 2.2 Competitive Advantage 40 2.3 One-Card Stud Poker 41 2.4 Solutions of Two-Person, Zero-Sum Games 45 2.5 Two-Person, Variable-Sum Games 48 2.6 A Sufficient Condition for Solving Variable-Sum Games 49 2.7 Cigarette Advertising on Television 51 2.8 Two-Person Games with Many Strategies 53 2.9 Existence of Equilibrium 55 Appendix Winning at Blackjack 59 3 Mixed Strategies and Mixed Strategy Equilibrium 67 3.1 Mixed Strategies 68 3.2 Computing Mixed Strategy Equilibria in 2 x 2 Games 70 xii
3.3 Mixed Strategies and Bluffing: Liar's Poker 74 3.4 Mixed Strategy Equilibria of Coordination Games and Coordination Problems 78 3.5 Asymmetrical Mixed Strategy Equilibria 79 3.6 Everyday Low Prices 81 Appendix Bluffing in One-Card Stud Poker 86 4 n-person Games in Normal Form 93 4.1 Fundamental Differences with Three Players: The Spoiler 94 4.2 Competitive Advantage and Market Niche with Three Players 4.3 Three-Player Versions of Video System Coordination, Let's Make a Deal, and Cigarette Television Advertising 99 4.4 Stonewalling Watergate 102 4.5 Symmetry and Games with Many Players 104 4.6 Solving Symmetrical Games with Many Strategies 106 4.7 The Tragedy of the Commons 108 Appendix Tragedy of the Commons in the Laboratory 113 5 Noncooperative Market Games in Normal Form 118 5.1 Quantity Competition between Two Firms 119 5.2 Cournot Competition, Two Firms, Many Strategies 121 5.3 Cournot Variations, Including Many Firms 124 5.4 Are Coffee Prices Going Up? 127 5.5 Price Competition between Two Firms 129 5.6 Bertrand Variations 133 5.7 Market Games with Differentiated Products 134 5.8 Bertrand Competition among Differentiated Products in the Cigarette Industry 138 Appendix Uniqueness of Equilibrium 141 Part II Games with Sequential Structure 145 6 Credibility and Subgame Perfect Equilibrium 147 6.1 Subgames and Their Equilibria 148 6.2 Maintaining Credibility via Subgame Perfection 153 6.3 Credible Threats and Promises 154 6.4 Reluctant Volunteers: Conscription in the American Civil War, 1862-65 157 6.5 Mutually Assured Destruction 159 6.6 Credible Quantity Competition: Cournot-Stackelberg Equilibrium 164 6.7 Credible Price Competition: Bertrand-Stackelberg Equilibrium 167 6.8 Differentiated Products 168
6.9 This Offer Is Good for a Limited Time Only 170 Appendix Ultimatums in the Laboratory 173 7 Repeated Games 176 7.1 Strategies and Payoffs for Games Played Twice 177 7.2 Two-Person, Zero-Sum Games Played More Than Once 180 7.3 Variable-Sum Games with a Single Equilibrium, Played Twice 181 7.4 OPEC Drops Quotas 184 7.5 Variable-Sum Games with Multiple Equilibria, Played Finitely Many Times 186 7.6 Infinitely Repeated Games: Strategies and Payoffs 191 7.7 Infinitely Repeated Cournot Market Games 194 7.8 Price Leadership in the Ready-to-Eat Cereals Industry 200 8 Evolutionary Stability and Bounded Rationality 204 8.1 How Boundedly Rational Players Play Games 205 8.2 ESS for 2x2 Symmetrical Games 209 8.3 Frogs Call for Mates 215 8.4 ESS for 2x2 Asymmetrical Games 219 8.5 Fast Learning with a Finite Number of Players 225 8.6 The Evolution of Video Games 229 Appendix Evolution in the Laboratory 233 Part III Games with Imperfect Information 237 9 Signaling Games and Sequential Equilibrium 239 9.1 Two-Player Signaling Games 240 9.2 Sequential Equilibrium: Pure Strategies 243 9.3 Sequential Equilibrium: Mixed Strategies 251 9.4 The Market for Lemons 254 9.5 Costly Commitment as a Signaling Device 257 9.6 Repeated Signaling and Track Records 259 9.7 Barbarians at the Gate 266 10 Games between a Principal and an Agent 271 10.1 Principal Versus Agent: Perfect Information 272 10.2 Principal Versus Agent: Subgame Perfect Equilibrium 274 10.3 Principal Versus Agent: Imperfect Information 280 10.4 Depositor Versus S&L 286 10.5 Principal Versus Agent When Attitudes toward Risk Differ 288
Contents 10.6 Principal Versus Agent with Two Types of Agents 291 10.7 Compensating Corporate Executives 294 11 Auctions 299 11.1 Sealed-Bid Auctions with Complete Information 300 11.2 Second-Price Auctions 305 11.3 Individual Private-Value Auctions 307 11.4 Auctioning Off Failed Thrifts 311 11.5 Common-Value Auctions 314 11.6 Bidding for Offshore Oil 319 Appendix Auctions in the Laboratory 322 Part IV Games Involving Bargaining 325 12 Two-Person Bargains 327 12.1 Bargaining Games 328 12.2 Asymmetries and the Nash Bargaining Solution 331 12.3 Bankruptcy I: Independence of Irrelevant Alternatives and the Nash Bargaining Solution 336 12.4 Bankruptcy II: Monotonicity and the Kalai-Smorodinsky Solution 339 12.5 MCI and BT Make a Deal 342 12.6 Sequential Bargaining with Perfect Information 343 12.7 Sequential Bargaining with Imperfect Information 346 12.8 United States-Japan Trade Negotiations 348 Appendix Bargaining in the Laboratory 352 13 Arbitration 357 13.1 Conventional Arbitration 358 13.2 A Random, but Not Arbitrary, Arbitrator 362 13.3 Conventional Grievance Arbitration 364 13.4 Fred Witney, Professional Arbitrator 371 13.5 Final Offer Arbitration 373 13.6 Final Offer Arbitration in Major League Professional Baseball 377 14 n-person Bargaining and the Core 382 14.1 n-person Bargaining Games 383 14.2 Solutions for n-person Bargaining Games in Coalition Function Form 384 14.3 n-person Bankruptcy Games 389 14.4 The Bank of Credit and Commerce International Goes Bust 393 XV
14.5 The Coalition Function When Intermediate Coalitions Have Power 395 14.6 The Core of a Game in Coalition Function Form 397 14.7 Sharing Defense Burdens 401 14.8 Bosnian Peace Plans 404 Part V Games, Markets, and Politics 411 15 Two-Sided Markets and Matching Games 413 15.1 Two-sided Markets: The Fundamentals 414 15.2 The Coalition Function of a Two-Sided Market Game 418 15.3 The Core of a Two-Sided Market Game 420 15.4 Limitations on Core Equivalence 423 15.5 Barbarians at the Gate II: The Core 427 15.6 Two-Sided Matching Games 430 15.7 Matching Games in Coalition Form 432 15.8 Sorority Rush 434 16 Voting Games 439 16.1 Two-Candidate Voting Games with a Discrete Issue Spectrum 440 16.2 Two-Candidate Voting Games with a Continuous Issue Spectrum 443 16.3 MultiCandidate Voting Games 447 16.4 Multicandidate Presidential Elections, 1824 1992 451 16.5 Positional Voting Rules 453 16.6 Voting Games in Coalition Function Form 455 16.7 Measuring Power 457 16.8 Expanding the United Nations Security Council 460 Suggestions for Further Readings 468 Games List 470 Index 471