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Game Theory 101: The Rationality of War William Spaniel Copyright William Spaniel 2012-2014. All rights reserved. About the Author William Spaniel is a PhD candidate in political science at the University of Rochester, creator of the popular YouTube series Game Theory 101, and founder of gametheory101.com. You can email him at [email protected] or follow him on Twitter @gametheory101. Acknowledgements I thank Hein Goemans, Ryan Jaimes, Benjamin Laughlin, Varsha Nair, Maria Salas, Mary Ellen Spaniel, Zachary Taylor, and my students from PSC/IR 106 in the spring semesters of 2012 and 2013 at the University of Rochester for their comments as I compiled this book. It goes without saying that my teachers influenced the way I think about the strategic aspects of international relations. I learned the politics of international relations from Erik Gartzke, Hein Goemans, Ethan Hollander, Bethany Lacina, Victor Magagna, Branislav Slantchev, and Randall Stone. I learned game theory from Branislav Slantchev, John Duggan, Mark Fey, and Avidit Acharya. Thanks to them, this book makes coherent sense. Table of Contents PREFACE: WAR IN THE COURT CHAPTER 1: WHY WAR? 1.1: H D W U W ? OW O E NDERSTAND AR 1.2: O B UTLINE OF THE OOK CHAPTER 2: WAR’S INEFFICIENCY PUZZLE 2.1: T A M HE LGEBRAIC ODEL 2.2: T G M HE EOMETRIC ODEL 2.3: T G T M HE AME HEORETICAL ODEL 2.4: W I P ? HAT S THE UZZLE 2.5: F R URTHER EADING CHAPTER 3: PREVENTIVE WAR 3.1: G M P T ROWING ORE OWERFUL OVER IME 3.2: C H G HOOSING OW TO ROW 3.3: D P W A E ? OES REVENTIVE AR CTUALLY XIST 3.4: F R URTHER EADING CHAPTER 4: PRIVATE INFORMATION AND INCENTIVES TO MISREPRESENT 4.1: U P NCERTAINTY ABOUT OWER 4.2: M A D UTUALLY SSURED ESTRUCTION 4.3: I M S NCENTIVES TO ISREPRESENT AND IGNALING 4.4: T C P HE ONVERGENCE ROCESS 4.5: U R NCERTAINTY ABOUT ESOLVE 4.6: U M E NCERTAINTY IN THE ODERN RA 4.7: F R URTHER EADING CHAPTER 5: ISSUE INDIVISIBILITY 5.1: I I SSUE NDIVISIBILITY 5.2: S P I L IDE AYMENTS AND SSUE INKAGE 5.3: P I OWER NDIVISIBILITY 5.4: F R URTHER EADING CHAPTER 6: PREEMPTIVE WAR 6.1: P W C P REEMPTIVE AR AS A OORDINATION ROBLEM 6.2: W I P W I ? HEN S REEMPTIVE AR NEVITABLE 6.3: F S A O M IRST TRIKE DVANTAGES IN THER ODELS 6.4: F R URTHER EADING CHAPTER 7: THINKING STRATEGICALLY ABOUT WAR MORE FROM WILLIAM SPANIEL Preface: War in the Court Image you run a small ice cream shop. The building that you own has a slight quirk to it: the sidewalk outside is an inch lower than the floor inside. Every now and then, customers trip on their way into the store. However, you do not see an easy way to fix the problem, and so life continues a bit unevenly. One day, things turn ugly. A customer’s toe catches the lip of the doorway, and his head smashes against the floor. Fortunately, he makes a full recovery; unfortunately, he is now suing you for $100,000 to pay for his medical bills and compensate for his suffering. You consult your lawyer on the best course of action. She advises you on the inherent uncertainty about these types of cases. You will win 50% of the time, she tells you, because the actual outcome of the lawsuit will depend on the judge and the makeup of the jury. Either way, you will have to pay her $10,000 to represent you at the trial. The plaintiff’s attorney is giving him the same information. Jury trials are random, and he will only win 50% of the time. But regardless, his attorney’s fees amount to $5,000. Three outcomes seem plausible. First, one of you could immediately concede the case. If you do so, you must pay $100,000 to the plaintiff; if he does so, the charges drop, and you can go back to running your business in peace. Second, you could go to trial and let the jury decide whether you were at fault for the accident. Finally, the two of you could settle out of court. You would pay the plaintiff some amount of money, and he would be legally bound to drop the suit. Which of these outcomes should we actually expect in practice? We should quickly dismiss an immediate concession from either side. Think about how much you would expect to pay if the case went to court. 50% of the time, you will win and pay nothing. 50% of the time, you will lose and have to pay $100,000. Therefore, in expectation, you will lose $50,000 at trial. After factoring in the $10,000 cost of your attorney, the total bill will average out to $60,000. That is a lot less than paying $100,000 up front. It would be equally bizarre for the plaintiff to concede the suit. If he goes to trial, he wins $100,000 half the time and wins nothing the rest of the time. Therefore, he expects the jury to award him $50,000 on average. Deducting his attorney’s fees, his expected profit comes out to $45,000. That $45,000 is much better than walking away with nothing. However, a trial is a silly outcome as well. Consider any settlement offer in which you give at least $45,000 to the plaintiff but no more than $60,000. For example, suppose the offer is $50,000, take-it-or-leave-it. Should he accept that offer? Of course—he only earns $45,000 for the trial, which is $5,000 less than accepting the settlement. What about you? It is the same story—you will lose $60,000 if you go to trial but the settlement saves you $10,000. Thus, the settlement leaves both parties better off than had they gone to court. Consequently, it would be extremely odd for this case to go to trial. Put differently, a [lawsuit/war] is inefficient. [Lawyers’ fees/People dying and buildings destroyed] create costs. As such, the [plaintiff and defendant/two countries] can sign [an out of court settlement/peace treaty] that distributes the [money/territory] at stake in a manner that reflects their relatively likelihood of winning [at trial/on the battlefield]. Everyone ends up happy, since neither side can [insist on a trial/declare war] and expect to do better. If you turn on a television, you will hear a thousand different reasons countries go to war with one another. Very few of these tell us why those actors would choose such a costly means to resolve their differences when bargaining, in theory, would make both sides happier. This book will provide an explanation, without resorting to trivial claims of irrational behavior or personal greed. On the contrary, war can occur between two perfectly intelligent and sane actors who are only looking out for the best interests of their countries. Chapter 1: Why War? The winter of 2003 was an interesting time. George W. Bush, then President of the United States, was mounting a very public campaign for a war in Iraq. I was only 16 at the time and could only recount three wars: the Gulf War (barely), the Kosovo War, and the War in Afghanistan. Yet I knew that the diplomatic process had never been so transparent. Day in and day out, Bush or someone from his administration was on television, selling the war to the American public, America’s allies, and the United Nations. Thanks to the advent of the 24/7 news cycle following the September 11 attacks, diplomacy was omnipresent. We all know how it ended. The Bush administration convinced a majority of the American public to support the war. A large number of other countries also volunteered to support the U.S.—though not the ones necessary to obtain a United Nations Security Council resolution in support of the war. Five years later, Iraq was a mess, the average American regretted the war, and the United States’ miscues had made the country a pariah in the international realm. What went wrong? In retrospect, the Iraq War was a complete debacle. It cost the United States thousands lives and almost a trillion dollars. And the principally publicized purpose of the war—to rid Iraq of weapons of mass destruction—turned out to be a complete non-issue. The war seemed senseless. However, even as a teenager, I wondered whether the Iraq War was inevitable. Although political pundits were quick to point to personal biases in the Bush administration, the mistakes ran deeper. One person was not to blame here. The American public, as a whole, bought into the war, as did the other governments that lent their support. And while it is easy to second guess decisions with perfect retrospect, the fear of an Iraq with weapons of mass destruction was palpable at the time. Iraq tried to reassure the West, but the United States did not buy it. After all, regardless of whether Iraq was actually building weapons,