Strategy and Politics

An Introduction to Game Theory

Emerson Niou, Peter C. Ordeshook

• Publisher: Routledge
• Year: 2015
• ISBN:
  9781317563112
• Edition: 1
• Topic: Politics & International Relations
• Subtopic: Politics
• Index: Politics & International Relations

Strategy and Politics: An Introduction to Game Theory is designed to introduce students with no background in formal theory to the application of game theory to modeling political processes. This accessible text covers the essential aspects of game theory while keeping the reader constantly in touch with why political science as a whole would benefit from considering this method. Examining the very phenomena that power political machineries—elections, legislative and committee processes, and international conflict, the book attempts to answer fundamental questions about their nature and function in a clear, accessible manner.

Included at the end of each chapter is a set of exercises designed to allow students to practice the construction and analysis of political models. Although the text assumes only an elementary-level training in algebra, students who complete a course around this text will be equipped to read nearly all of the professional literature that makes use of game theoretic analysis.

1 Politics as a Game

1.1 Decision Versus Game Theoretic Decision Making

Over twenty five hundred years ago, the Chinese scholar Sun Tzu, in The Art of War, proposed a codification of the general strategic character of armed conflict and, in the process, offered practical advice for securing military victory. His advice is credited, for example, with having greatly influenced Mao Zedong’s approach to conflict and the subtle tactics of revolution and the ways in which North Vietnam and the Viet Cong thwarted America’s military advantages. The formulation of general strategic principles—whether applied to war, parlor games such as Go, or politics—has long fascinated scholars. And regardless of context, the study of strategic principles is of interest because it grapples with fundamental facts of human existence—first, people’s fates are interdependent; second, this interdependence is characterized generally by conflicting goals; and, finally, as a consequence of the first two facts, conflicts such as war are not accidental but are the purposeful extension of a state’s or an individual’s motives and actions and must be studied in a rational way.

The Art of War is, insofar as we know, our first written record of the attempt to understand strategy and conflict in a coherent and general way. It is important, moreover, to recall that it was written at a time of prolonged conflict within an emerging China whereby the leaders of competing kingdoms possessed considerable experience not only in the explicit conduct of war, but also in diplomacy and strategic maneuver. As such, then, we should presume that it codifies the insights of an era skilled at strategy and tactics, including those of planning, deception and maneuver. This assumption, though, occasions a question: Although The Art of War was ostensibly written for the leader of a specific kingdom, what if all sides to a conflict have a copy of the book (or, equivalently, an advisor no less insightful than Sun Tzu)? How might our reading of Sun Tzu change if it is common knowledge that everyone studied The Art of War or its equivalent—where by “common knowledge” we mean that everyone knows that everyone has a copy of the book, everyone knows that everyone knows that everyone … and so on, ad infinitum. The assumption of common knowledge presumes that not only is each decision maker aware of the situation, but each is aware that the other is aware, each knows that the other knows, and so on and so forth, and after being told by Sun Tzu himself that the great trap to be avoided is underestimating the capabilities of one’s opponents, it seems imperative that the implementation of his advice proceed with the presumption that common knowledge applies.

In the case of The Art of War, taking account of the possibility that both sides of a conflict have a copy of the book differentiates the social from the natural sciences. In physics or chemistry, including their practical applications, one does not assume that the scientist or engineer confronts a benevolent or malevolent nature that acts strategically to deliberately assist or thwart one’s research or the application of natural laws as we understand them. Things might not function as designed, but only because our understanding or application of nature’s laws is imperfect. In the social sciences, on the other hand, especially in the domain of politics, it is typically the case that individuals must choose and act under the assumption that others are choosing and acting in reaction to one’s decisions or in anticipation of them, where those reactions can be either benevolent or malevolent.

Despite this fact, it is our experience that most readers of The Art of War implicitly or unconsciously (at least initially) take the view that the reader is the sole beneficiary of Sun Tzu’s advice—that one’s opponent is, much like nature, a “fixed target.” This might have been a valid assumption in 225 bc China in the absence of the internet, printing presses and Xerox machines, but it is no longer valid given the worldwide distribution of the book, including having it as required reading in business schools and military war colleges. So a more sophisticated student of Sun Tzu’s writings might suppose that one’s opponents have read the book as well, and might then reasonably assume that their opponents’ tactics and strategies conform to Sun Tzu’s guidance. But suppose we take things a step further and try to interpret an opponent’s actions not simply with the assumption that they’ve read the books with which we are familiar, but also that they know we are familiar with those books and that we are not only attempting to assess their tactics and strategies in light of the advice contained in The Art of War, but also that we are attempting to take into account the fact that they are attempting to take into account our familiarity with that advice.

If all of this sounds confusing, then referencing The Art of War as an introduction to this volume has served its purpose. Specifically, there are two general modes of decision making: Decision Making Under Risk and Game Theoretic Decision Making. In decision making under risk, one assumes, in effect, that although there may be inherent uncertainties associated with the consequences of one’s actions due to chance events and the actions of others, probabilities can be associated with those events and actions and the right choice is the one that yields the greatest expected return, where that return can be expressed in monetary terms, as psychological satisfaction or whatever. In this world, one assumes that other decision makers, including those who might be opposed to your goals, have, in effect, a limited view and do not respond to the assumption of common knowledge. In other words, just as the engineer or natural scientist does not assume that nature has the capacity for logical thought, the notion of common knowledge plays little to no role in decision making under risk since here one sees opponents as non-strategic “fixed targets” whose likely actions can be guessed at on the basis of, say, past patterns of behavior, bureaucratic rigidities or simple stupidity.

In game theoretic decision making, in contrast, one assumes that one’s opponents and other decision makers, in pursuit of their goals, take into account their knowledge of you, including the fact that you know that they know, etc. Other decision makers are no longer fixed targets. Now you must be concerned that, since they know you are aware of their past behaviors, they might try to confound your calculations by defecting in some way from whatever patterns their earlier decisions exhibit. And there is, moreover, an additional complication. Since in a game theoretic analysis we can also assume that they know you know their past history, they also know you know they might have an incentive to thwart your calculations by not changing past patterns of behavior at all. But, since you also know that they know that you know they might consider sticking to past patterns … and so on, ad infinitum once again.

Game theoretic decision making attempts to untangle such seemingly endless and convoluted thinking and in the process to define what it means to be rational in interactive decision contexts. This volume, then, attempts to lay out the rudiments of game theoretic analysis as it can be applied to situations we label “political.” Our specific objective, however, is not to provide a text on the mathematics of game theory. There are any number of excellent books available for that purpose, and the subject itself can be as dense as any branch of mathematics. Rather, our goal is to show that a game theoretic approach to understanding individual action is an essential component not only of being skillful at war, but also of understanding the less violent aspect of politics. However, rather than try to argue this point here, let us consider a series of examples that perhaps more clearly illustrate the difference between decision theoretic and game theoretic reasoning.

The Atomic Bomb and Japan: On the morning of August 6, 1945, a single plane (preceded by two weather reconnaissance aircraft), the Enola Gay, flew to and dropped its bomb on the city of Hiroshima. Ignoring the debate over whether this act was warranted or unwarranted with respect to the goal of ending a war, the question that concerns us here is: Why only one plane, which so easily could have been intercepted? The answer is that America’s strategic planners assumed that if the Enola Gay had been part of a fleet of bombers, the Japanese would have attempted to intercept the raid with its ground based fighters. A single plane, on the other hand, would be far less threatening and draw far less attention. That calculation turned out to be correct—based on earlier bomb raids over its cities, strategic planners correctly assessed Japan’s approach to air defense, and when the two scout planes turned back to the Pacific, city sirens sounded the “all clear” on the ground. The logic behind sending a single plane, then, on its deadly mission seems straightforward. But then, three days later, another solitary plane, Bockscar, flew to Nagasaki and dropped America’s second atomic bomb, and the question for us is: Did the same strategic calculation in choosing between a lone plane versus a plane imbedded in a fleet apply to Bockscar?

We do not know precisely what calculations were made in deciding to deliver the second bomb via another lone aircraft as opposed to a fleet. But certainly the calculation this time had to be different from the one that sent the Enola Gay on its way. In the case of the Enola Gay, America’s strategic planners could reasonably assume that the Japanese had no idea as to the destructiveness of its cargo and, thus, no reason to fear it any more than any previous lone aircraft over Japan. The response of Japan’s air defense command could be predicted with near certainty. But circumstances changed markedly once the Enola Gay delivered its payload. Now, presumably, there were those in Japan who knew the potential of a lone bomber, and the American decision to proceed as before had to be justified by a different calculation—one that took into account what the Japanese might now assume about lone bombers and how they might weigh that danger against the costs of scrambling interceptors against it. Might the Japanese assume that the United States wouldn’t be bold enough to again send a single bomber to drop any additional atomic bombs and instead would now try to disguise any subsequent use of its atomic arsenal by imbedding the plane carrying it in a fleet of bombers? In other words, America’s strategic planners now had to concern themselves with the possibility that Japan’s approach to air defense had changed in a complex way dictated by its best guess as to America’s guess about Japan’s response to the first bomb.

The decision to send a single plane to Hiroshima, then, was decision theoretic: Japan’s likely response to one plane versus many could be determined by its previous actions. All a strategic planner needs to do is to calculate the probability that Japan would try to intercept a single plane versus the likelihood that, if imbedded in a fleet, it would intercept the fleet and successfully shoot down the specific plane carrying a bomb. The decision to send only one plane to Nagasaki, in contrast, required an assessment of what Japan might have learned about the potential lethality of a single plane, whether Japan might assume the Americans would employ the same tactic a second time, how that tentative assessment might impact America’s tactical calculations, and how in turn Japan should respond to what it thinks America’s response would be to Japan’s reassessment of things. The decision to use a single bomber versus a fleet over Nagasaki, then, was a game theoretic one.

The Boston Marathon 2013: For a more contemporary example of decision versus game theoretic choice, consider the FBI’s move to release a department store security camera video of the two brothers who planted bombs at Boston’s 2013 marathon. As portrayed by the media, that decision was intended to elicit the public’s help in identifying the terrorists, and indeed the video was soon plastered across the internet’s social media. From this perspective, then, the FBI’s action appears to be a strictly decision theoretic move to increase the likelihood that their suspects would be recognized and identified. But suppose we give the FBI’s personnel more credit in assessing motives. Suppose they anticipated the released video going viral on the internet and knew the suspects would soon realize that their identities could not be kept hidden. Thus, if they planned any additional terrorist acts, both men knew they had better act quickly with little opportunity to plan carefully. In other words, suppose the FBI intended to “smoke out” their Russian suspects and induce them to be less careful than they might otherwise be if they assumed their identities could remain hidden for a time. It might have been the case, of course, that the two brothers knew the FBI was trying to smoke them out, but as committed jihadists, what choice did they have? Thus, by anticipating the terrorists’ response, the FBI can be said to have acted with a game theoretic understanding of things. And this is precisely what happened. A day or two after the bombing, at least one brother, seemingly oblivious to the fact that his identity would soon be known, was seen partying at the college he’d been attending. But following the video’s release, the two brothers, with bomb parts still unassembled in their apartment, tipped their hand by hijacking a car that led to a shoot-out with the police wherein one brother was killed and the other injured and captured soon thereafter.

Voters and Interest Groups in Three Candidate Elections: It isn’t always easy to decide how to vote in a three-candidate plurality rule (first-past-the-post) election. The problem here is the possibility of wasting one’s vote by casting a ballot for a candidate, however strongly preferred, who stands no chance of winning. If the candidates’ chances are unequal, it might be wise to vote for...

Table of contents

• Cover
• Title
• Copyright
• Contents
• 1 Politics as a Game
• 2 Extensive Forms, Voting Trees and Planning Ahead
• 3 The Strategic Form and Nash Equilibria
• 4 Zero-Sum Games with Spatial Preferences
• 5 The Prisoners’ Dilemma and Collective Action
• 6 Agendas and Voting Rules
• 7 Games with Incomplete Information
• 8 Cooperation and Coalitions
• Appendix
• Index