BRIEF HISTORY OF GAME THEORY

In the mid-twentieth century, Western civilization faced a triple crisis. Enlightenment philosophy was implicated in the rise of National Socialism and the failure to quarantine its potently destructive elements.¹³ Western insti­tutions of democracy and capitalism were brought to their knees by economic depression, fascism, totalitarianism, and communism.¹⁴ For four grueling years, the Allied powers promoting what was left of Enlightenment liberal values faced a military juggernaut with global dimensions.

Game theory and its corporeal creators were at the center of the unfolding drama, and none more so than the theory’s brainy powerhouse John von Neumann.¹⁶ A Hungarian Jew by birth and a mathematician by profession, von Neumann generated an axiomatized treatment of quantum mechanics in the 1930s. He reacted to anti-Semitic policies in the 1940s and simultaneously devised the mathematics of game theory. He was as aware as any of the potential emptiness of political promises and the possible ease with which self-evident rights of personhood and property could be rescinded.¹⁷ Von Neumann was central to the Manhattan Project and served on the select committee that determined the target cities of Hiroshima and Nagasaki.¹⁸ In 1944, von Neumann coauthored Theory of Games and Economic Behavior at the Princeton University Institute for Advanced Studies with the Austrian economist Oskar Morgenstern.

Game theory was the product of the most exalted mathematical minds of pre- WWII Europe. It grew amid the intense ferment over the philosophy of mathe­matics and its relationship to social theory.¹⁹ At the same time that the physics revolutions of relativity and quantum mechanics arrested determinism and reveries about Newtonian space-time, mathematicians wrestled with the source of certainty anchoring their discipline.

Rather than being just a body of mathematical expertise, game theory captured the mentality of competitive dueling exercised in parlor games and military combat. It was, in fact, Europe’s chess-playing culture, in which cham­pions displayed their intellectual supremacy not just over losers but also over the general public that provided the basis for von Neumann’s first academic paper on game theory. Masters played multiple concurrent games, blindfolded, against sighted opponents. The early nineteenth-century chess master and mathematician Emanuel Lasker viewed chess as exemplary of struggle and the science of strategy. The “perfect strategist” is free from emotion and will “calculate in advance... the optimal path... of the upcoming struggle.”²³

Von Neumann was also a chess player. His treatment is general, being applicable to all definable “games.” He likens his analysis to all manner of circumstances because “there is hardly a situation in daily life into which this

1 ⁸ Discussed in ibid., see also Richard Rhodes, Making of the Atomic Bomb (New York: Touchstone, 1986).

1 ⁹ See Leonard, von Neumann, 2010, especially his “Ethics and the Excluded Middle” chapter, 110-139.

²⁰ Kurt Godel, “Uber formal unentscheidbare Satze der Principia Mathematica und verwandter Systeme, I,” Monatshefte fur Mathematik und Physik (1931), 38, 173-198.

²¹ For a detailed discussion of the relationship between the hope for and abandonment of formal and causal determinism in Germany prior to World War II, see Paul Foreman, “Weimar Culture, Causality, and Quantum Theory, 1918-1927: Adaptation of German Physicists and Mathematicians to a Hostile Intellectual Environment,” Historical Studies of the Physical Sciences (1971), 3, 1-115. Apparently, von Neumann was not overly troubled by the collapse of the Hilbert program to axiomatize the foundations of mathematics.

²² Robert J. Leonard, “Creating a Context for Game Theory,” in Toward a History of Game Theory, ed. by E. Roy Weintraub (Duke University Press, 1993), 29-76.

²³ Leonard, quoting Lasker, von Neumann, 2010, at 14.

problem does not enter.”^[175] He explains, “It is easy to picture the forces strug­gling with each other in such a two-person game. The value of g(x,y) [person ι^,s (S1’s) winnings] is being tugged at from two sides, by S₁ who wants to maximize it, and by S₂ who wants to minimize it. S1 controls the variable x, S₂ controls variable y.”^[176] In this zero-sum context, von Neumann demonstrates that each player can select a strategy that will secure a minimum security threshold below which the other player cannot force him, an early expression of his “minimax” concept.

Whereas economists for almost three decades shunned game theory because of its recondite mathematics and zero-sum focus, the theory found fertile ground at the RAND Corporation, the military think tank where John von Neumann was a frequent consultant in the late 1940s.^[177] Game theory was applied to strategic problems as early as World War II. Von Neumann himself supplied the reasoning of his minimax theory to Philip Morse’s analysis of submarine detection in the English Channel.^[178] Abraham Wald applied von Neumann’s minimax theorem to statistical decision theory to develop a general­ized approach to games with a continua of strategies.^[179] Merrill Flood, one of the originators of the Prisoner’s Dilemma game along with Melvin Dresher, applied game theory to airborne attacks, authoring “Aerial Bombing Tactics: General Considerations” in 1944.^[180] Game theory’s initial application to warfare shows how well suited it is to analysis of strategic competition.

To apply game theory effectively, it was necessary to devise a metric of value to stand in as inter-agentively valid on par with money in an exchange economy. Flood’s investigation of this problem in his 1944 report anticipates the work done to appraise military worth at RAND during the early Cold War to pursue the science of strategy.^[181] At an early RAND meeting in 1948, von Neumann was present at a discussion of fighter aircraft dueling to which his minimax theorem was pertinent.^[182] Leonard notes, “Insofar as RAND was created to perpetuate operations research work of the kind applied during World War II, game theory was part of its raison d'etre.”³²

Von Neumann’s intellectual presence towered over RAND’s researchers.³³ Game theory was applied to aerial attacks and nuclear strikes. Ed Paxson addressed “Games of Tactics.” Richard Bellman analyzed “A Bomber-Fighter Duel,” “ Application of Theory Games to Identification of Friend and Foe,” and “Games Involving Bluffing.”³⁴ The list of such papers stands as testimony to the ready application of game theory to warfare: “Local Defense of Targets of Equal Value,” “Optimal Tactics in a Multistrike Air Campaign,” “Optimal Timing in Missile Launching: A Game Theoretic Analysis,” and “A Game Theory Analysis of Tactical Air War.” Melvin Dresher wrote the text Games of Strategy: Theory and Applications, which had appeared as a classified manual for Air Force staff in the decade prior to its 1963 publication.³⁵ Leonard observes that “at the early stages, game-theoretic models were thought likely to be useful in solving tactical military problems to be encountered in a war with the USSR.”³⁶

RATIONAL DETERRENCE AND GAME THEORY’S ASCENDANCE

The exceptional nature of nuclear warfare calls for a nonempirical science prior to any experience of nations sparring with weapons of mass destruction 1000 times more powerful than the US atomic bombs Fat Man and Little Boy that annihilated Hiroshima and Nagasaki.

(Santa Monica, CA: RAND Corporation, 1948), September 3, 1948, discussed in Leonard, von Neumann, 2010, 295.

³² Leonard, von Neumann, 2010, at 298.

³³ Ibid., 300-301.

³⁴ Ibid., 310.

³⁵ Ibid.; Melvin Dresher, Games of Strategy (Upper Saddle River, NJ: Prentice Hall, 1963).

³⁶ Leonard, von Neumann, 2010, 298.

³⁷ Civilian analysts with no prior military experience pushed aside seasoned military officers in leadership roles; see Amadae, Rationalizing Capitalist Democracy, 2003, 27-85. For an enga­ging and illuminating analysis of the abstract yet unethical character of rational decision and deterrence theory, see Philip Green, Deadly Logic: The Theory of Nuclear Deterrence (Columbus: Ohio State University Press, 1966), especially 118-128 and 213-254.

³⁸ Herman Kahn, On Thermonuclear War (Princeton, NJ: Princeton University Press, 1960), 162. RobertJervis recognizes this point, observing, “All the fundamental ideas about nuclear strategy came from civilians, and their dominance probably helps explain the break with much previous thinking. Nuclear weapons also seemed so stark as to lend themselves to abstract analysis, and the match with the recently developed game theory was very attractive, although critics argued The story of Robert S. McNamara’s ascent to the office of the US Secretary of Defense under John F. Kennedy’s celebrated administration is told and retold with unremitting enthusiasm.³⁹ Like the civilian strategists whom McNamara appointed to work under him, the new Secretary of Defense could boast of analytic expertise, but no experience in the realm of military affairs.

The direct implication of this new reality was that “the civilian experts have made great inroads” into the formerly closed military strategy war room:

They have overwhelmed the military in the quality and quantity of their contributions to the literature of the subject; no one would now think of turning to the writings of retired officers rather than to the standard academic treatments of deterrence, limited war, or arms control, for illumination of the problems of the nuclear age.⁴¹

Bull enunciates the displacement of military staff at war colleges by these civilian defense intellectuals and notes that “most prominently in the United States, the civilian strategists have entered the citadels of power and have prevailed over military advisers on major issues of policy.”⁴² Fortunately, the empirical experience with nuclear warfare did not increase. In 1977, political scientist Jack L. Snyder observed that this lack of experience continually led to an emphasis on deductive game theoretic analysis. The burden of proof thus fell on any strategist proposing an alternative to the “generic rational man” codified by game theory because “it is well known that the established strategy of deterrence in the United States is explicitly based upon the rational theory of decision.”⁴³ Alluding to Thomas Schelling’s corpus and the approach it

that this influence was malign.” “Security Studies: Ideas, Policy, and Politics,” in The Evolution ofPolitical Knowledge: Democracy, Autonomy, and Conflict in Comparative and International Politics, ed. Edward D. Mansfield and Richard Sisson (Ohio State University Press, 2004), 100­126, at 109.

³⁹ David Halberstam, The Best and the Brightest (New York: Ballantine Books, 1993); Fred Kaplan, Wizards of Armageddon (Stanford University Press, 1983); Gregg F. Herken, Counsels of War (New York: Knopf, 1985); Deborah Shapley, Promise and Power: The Life and Times of Robert McNamara (Boston: Little, Brown 1993); Stephen W. Twing, Myths, Models and US Foreign Policy: The Cultural Shaping of Three Cold Warriors (London: Lynne Rienner, 1998), 145-186; Amadae, Rationalizing Capitalist Democracy, 2003, 27-82.

⁴⁰ Hedley Bull, “Strategic Studies and Its Critics,” World Politics (1968), 20:4, 593-603, at 594-595.

⁴¹ Ibid., 594.

⁴² Ibid.

⁴³ Jack L. Snyder, “The Soviet Strategic Culture: Implications for Limited Nuclear Operations,” RAND Report R-2154-AF, September 1977, especially 4. Second quote is John Steinbruner, “Beyond Rational Deterrence: The Struggle for a New Concept,” World Politics (1976) 28:2 223-245 at 225. inspired, Snyder makes clear that “the current U.S. selective-options policy is an intellectual offspring of the distinctively Western notions about deterrence, coercive diplomacy, and war.”⁴⁴ Thus, in theι960s and early 1970s, the rational actor model was initially embraced in the domain of national security.

Observers acknowledged that military strategy as it was developed first at RAND and subsequently within the Pentagon evolved as a hybrid of decision and game theory, systems analysis, operations research, and computerized command structures.⁴⁵ Bernard Brodie, Herman Kahn, Morton Kaplan, Glenn Synder, Daniel Ellsberg, Walter Kaufman, Albert Wohlstetter, Henry Kissinger, Oskar Morgenstern, Malcolm Hoag, Thomas Schelling, and James R. Schlesinger were prominent defense analysts. Of these theorists, Schelling, Morgenstern, Kahn, Kaplan, Synder, Hoag, and Ellsberg drew on game theory. Discussing their work, Frank Zagare observes, “In time, the theore­tical edifice they created came to be seen as the Rosetta stone of nuclear theory,” and remained so into the 1990s.⁴⁶ Robert Jervis notes that this “second wave” of deterrence theory “soon became conventional wisdom.”⁴⁷ Thomas Schelling would be awarded the 2005 Nobel Prize for economics for his work “enhancing our understanding of conflict and cooperation through

⁴⁴ Ibid., 18.

⁴⁵ See Robert Leonard, “ Creating a Context for Game Theory,” 1992, 29-76; Philip Mirowski, Machine Dreams (Cambridge: Cambridge University Press, 2002), 184-190. See also William Thomas, Rational Action: The Sciences of Policy in Britain and America, 1940­1960 (Cambridge, MA: MIT Press, 2015). Robert Jervis observes subjects of inquiry labeled security studies were elevated in “standing, legitimacy, and [had] a claim on national resources and priorities,” “Security Studies,” 2004, 106; in response to this essay, Thomas Schelling adds that “Jervis states that ‘seeing security studies as being created at the end of World War II is very much a simplification, but one with some validity.’ I would have said, ‘not very much of a simplification,’” “Academics, Decision Makers, and Security Policy during the Cold War: A Comment on Jervis,” in The Evolution of Political Knowledge: Democracy, Autonomy, and Conflict in Comparative and International Politics, ed. Edward D. Mansfield and Richard Sisson (Columbus: Ohio State University Press, 2004), 137-139, ^at 137.

⁴⁶ Frank C. Zagare, “Classic Deterrence Theory: A Critical Assessment,” International Interactions: Empirical and Theoretical Research in International Relations (1996) 21:4, 365­387, at 366, 376. Schelling flatly rejects the independent significance of game theory in the development of security studies, in his “Academics, Decision Makers, and Security Policy during the Cold War: A Comment on Jervis,” in The Evolution of Political Knowledge: Democracy, Autonomy, and Conflict in Comparativeand International Politics, 2004,137-139, at 138-139. However, in correspondence to me, Robert Jervis notes that “this is quite contrary to what he [Schelling] told me in several conversations.” Jervis adds that the core ideas of the two nuclear security positions of assured destruction and pro-nuclear use were articulated by Bernard Brodie, The Absolute Weapon (New York: Harcourt Brace, 1946) and William Liscum Borden, There Will Be No Time (New York: Macmillan, 1946).

⁴⁷ RobertJervis, “Deterrence Theory Revisited,” World Politics (1979) 31:2, 89-324, at 289; see also Morgan, “New Directions in Deterrence Theory,” 1986. game-theory analysis.”^[183] By 1963, Schelling’s research directly helped secure the nuclear policy rationale for “assured destruction,” later derided as “mutual assured destruction,” or MAD, by its detractors.^[184] Assured destruc­tion typified the McNamara doctrine that shaped US nuclear strategy from 1963 until 1973, when RAND alumnus James R. Schlesinger became Secretary of Defense under President Richard M. Nixon.

Following Schelling’s 1960 treatment in “Reciprocal Fear of Surprise Attack,” defense analysts routinely viewed the nuclear arms race as a Prisoner’s Dilemma.^[185] Reviewing E. S. Quade’s Analysis for Military Decisions, F. M. Scherer worried about the over-reliance on the Prisoner’s Dilemma model that uncritically accepts the proposition that the Soviets hope to annihilate America, and vice versa.^[186] Scherer laments that

On the whole, however, there is too little concern for the fact that strategic deterrence, decisions to develop new weapons technologies, and arms races are typically Prisoner’s Dilemma games, in which minimax is a notoriously bad strategy. The deeply pessimistic Weltanschauung of this work is characterized most vividly by [Albert] Wohlstetter’s asser­tion that the Soviets’ “fondest desires” include launching a successful surprise nuclear attach against the United States. No one can prove such pessimism is wholly unwarranted, but the expected value of the world’s survival game almost certainly suffers if we continue pursuing a minimax approach to the problems of deterrence, arms control, and disarmament. All might benefit if military systems analysts spent less time worrying how we can make the best of the worst our rivals may do, and more time inventing ways of cooperating to avoid new self-defeating steps in the perfection and spread of mass-destruction weapons.^[187]

In this prescient quote, Scherer astutely sets forth the main argument of Prisoners of Reason: the embrace of the game theoretic mentality creates a self-fulfilling pro­phecy, as worst-case planning builds the institutional infrastructure for a dystopian world. In his opinion, game theory itself seems to drive a mutually suboptimal outcome and leads strategists to view the Soviet Union as “the enemy.”^[188]

KAHN’S DEFENSE OF NUCLEAR USE THEORY (NUTS)

When analyzing Herman Kahn’s pro-nuclear-use stance, one must begin with an understanding of the state of the American military capability by the mid-1950s. Not only had the Americans successfully detonated the world’s first thermonuclear warhead in 1952 and exploded a fully functional hydrogen bomb in 1954, but under Project Vista orchestrated during the Korean War, the United States developed the atomic cannon, atomic mortar, and atomic mine.^[189] During the WWII campaign against Germany, the United States had rejected the British military policy of the aerial bombing of cities to produce massive civilian casualties. Yet in the Pacific theater, the United States had adopted a city bombing policy even prior to the detonation of the atomic bombs over Hiroshima and Nagasaki, which produced 120,000 and 80,000 casualties, respectively. Early US Cold War policy likewise planned to target cities and their inhabitants with hydrogen bombs. This strategic stance was consistent with General Curtis LeMay’s leadership over the Strategic Air Command and underwrote President Eisenhower’s policy of massive retaliation to respond “massively, at times and places of our choosing” to any provocation deemed worthy of substantial reaction.^[190] Notably, during these early days of the Cold War, when the United States enjoyed unparalleled military supremacy, some of President Eisenhower’s high-level national security advisors recom­mended initiating preemptive nuclear war against the USSR to prevent the Soviets from developing thermonuclear weapons of their own. Schelling’s pro­tracted analysis of the reciprocal fear of surprise attack and Kahn’s proposal to maintain escalation dominance were thus responsive to the state of 1950s military science, technology, and strategic policy.

Herman Kahn (1922-1983) was a nuclear physicist who worked at the University of California Lawrence Livermore Laboratory and helped create the hydrogen bomb. His 600-page On Thermonuclear War (1960), prepared from his countless lectures, provides excruciating analysis of the logistical exercise of fighting and winning a nuclear war. Kahn aspired to achieve the gravitas and legendary quality of Prussian military strategist Carl von Clausewitz’s classic On War.^[191] He was an early employee of the RAND Corporation, joining the military think tank in 1947. He thrived on RAND’s exploitation of gaps: the bomber gap, the missile gap, and the vulnerability gap. Fred Kaplan’s description of the grandiloquent physicist’s ponderous tome is unsurpassed for its fidelity: “It was a massive, sweeping, disorganized volume, presented as if a giant vacuum cleaner had swept through the corridors of RAND, sucking up every idea, concept, metaphor and calculation that anyone in the strategic community had conjured up over the previous decade.”^[192] Still, the text became a best seller and incited the imaginations of both fellow strategists and the public. Kahn’s position would become known as nuclear utilization target selection (NUTS, sometimes spelled out as Nuclear Use Theorie[S] in the 1980s). Kahn’s approach represented one side of the nuclear strategy debate, articulated in Robert McNamara’s 1962 “no-cities” “flexible response” policy, then subsequently in Lyndon Johnson’s Foster panel, Richard Nixon’s Schlesinger doctrine codified in NSDM-242, Gerald Ford’s Team B Report, Jimmy Carter’s Presidential Directives 59, and Ronald Reagan’s Direct Guidance.^[193] Brashly promulgating rationalist strategy, On Thermonuclear War represents what would become the essence of the NUTS position: the attempt to achieve military superiority, even at the risk of instigating a hard-fought arms race punctuated with the incentive for preemptive war and the continual worry of an unstoppable escalation into an endless arms buildup and spasm warfare.^[194]

Kahn’s On Thermonuclear War is consistent with Albert Wohlstetter’s 1959 “Delicate Balance of Terror” and the 1957 Gaither Report in urging the United States to shore up any vulnerabilities in its Strategic Air Command and develop a coherent plan to prevail in any conceivable military showdown with the Russians.^[195] Building his case for analytic deterrence theory, Kahn reminds readers that because “there is no one with experience in the conduct of thermo­nuclear war... we must depend on hypotheses, i.e., paper studies.”^[196] He announced the “technical break through” at the RAND Corporation in the science of warfare, of which game theory was one component. In On

figure 3. Nuclear Chicken Game Matrix

Thermonuclear War, Kahn set the precedent of referring to nuclear deterrence, or brinkmanship, as a “Chicken game,” drawing on the writings of the pre­eminent philosopher and renowned pacifist Bertrand Russell.⁶² In the nuclear Chicken game, the US, in striving for its first choice of supremacy (DC), will settle for mutual cooperation (CC) or even surrender (CD), rather than accept mutual annihilation (DD) (Figures 3 and 4).

This nuclear Chicken game plays an important role in the ongoing debate between proponents of NUTS and advocates of MAD. Both groups view nuclear deterrence as a form of coercive bargaining best reflected by this game.⁶³

² Bertrand Russell, Common Sense and Nuclear Warfare (New York: Simon & Schuster, 1959). For discussion, see Lackey, “American Debate,” 1987,19-20. Russell was not only a pacifist and a famous philosopher, but his commentary on the morality of nuclear weapons also had significant impact. Russell makes the case that nuclear war cannot serve any aim of purposive agency and is immoral besides; consequently, it must be a common goal to end the likelihood that nuclear warfare could occur. Russell’s position is in opposition to that which would prevail over the US military.

⁶³ How to resolve the question of strategic bargaining so as not to be the loser in a perpetual contest of wills was central to the debate between MAD and NUTS. On Chicken games and bargaining, see Jervis, “Deterrence Theory Revisited,” 1979, 291-92; Glaser, “Why Do Strategists Disagree,” 1989, at 145. For commentary, see also Patrick James and Frank Harvey, “The Most Dangerous Game: Superpower Rivalry in International Crises, 1948-1985,” Journal of Politics (1992), 54:1, 25-53. Note that Herbert Gintis argues that the Chicken game explains the origin of property rights, Bounds of Reason: Game Theory and the Unification of the Behavioral Sciences (Princeton NJ: Princeton University Press, 2009).

figure 4. Nuclear Chicken Game Diagram

Once the mutual threat of assured destruction is achieved, the initial concession to the Prisoner’s Dilemma payoff matrix of each seeking unilateral defection and strategic domination remains: each side prefers to sucker the other, even though, of course, both seek to avoid mutual destruction. Thus, the key difference is that in the Chicken game, both agents would choose their own unilateral cooperation paired with the other’s unilateral defection rather than face mutual annihilation.

Kahn outlines and advocates for three types of deterrence: (1) passive, or the ability to marshal a second strike against the aggressor; (2) active, or first-strike capability; and (3) “tit-for-tat.”⁶4 The third, which is also referred to as a graduated, or flexible, response, represents the centerpiece of the NUTS policy. Its central idea is to command the ability to respond, not in kind, but with a strategy of “escalation dominance” to trump any aggressive move made by the opposition. Achieving (3) made it difficult to avoid (2), or at a minimum being perceived to seek first-strike capability. By contrast, as will become apparent ahead, Schelling’s position on deterrence recognizes the need to be able to signal the threat of counteraction but focuses on the ability to marshal a destructive second strike that does not mimic the first strike.

In 1965, Kahn published his sequel, On Escalation: Metaphors and Scenarios.⁶⁵ In it, he defines escalation as “an increase in the level of conflict in [an] international situation.”⁶⁶ He provides an analysis of the step-by-step

⁴ Kahn, On Thermonuclear War, i960, at 282.

⁶⁵ Herman Kahn, On Escalation: Metaphors and Scenarios (New York: Praeger, 1965).

⁶⁶ See Freedman, Evolution of Nuclear Strategy, 1981, 210; Kahn also wrote Thinking about the Unthinkable (New York: Horizon Press, 1962).

qualitative growth of force up the “escalation ladder.” His ladder has 44 rungs; nuclear exchange is initiated at the 15th rung, and he prescribes 30 ways to wield nuclear bombs.^[197] The book’s articulation of the logic of “escalation dominance” anticipated the late twentieth-century US military mandate of “full spectrum dominance.”^[198] This strategy recommends pressing one’s mili­tary advantage on any level of the escalation ladder on which one enjoys an asymmetric advantage. Kahn explains, “This is the capacity, all other things being equal, to enable the side possessing [escalation dominance]... to enjoy marked advantages in a given region of the escalation ladder.”^[199] In Freedman’s words, “Thus success through escalation dominance depended on a favorable asymmetry of capabilities.”^[200] Ideally, one would enjoy such asymmetric advan­tage on each rung of the escalation ladder or at least be able to control events such that the conflict is concluded on a rung over which one dominates. Kahn addresses the possibility of “eruption” into full-scale thermonuclear war, which seems to be an inevitable consequence of climbing the escalation ladder.^[201] He refers to the final rung on the ladder as “spasm war,” indicating a total loss of control and thought. The sexual connotation was not foreign to Kahn who lectured high-level SAC officers on “wargasm.”^[202] NUTS breaks with the classic liberal security posture of reciprocal noninterference by resting security on the achievement of dominance; its deterrence can only be asymmetrical.^[203]

Schelling’s defense of mutual assured destruction (mad)

President Eisenhower’s nuclear strategy of massive retaliation signified that the Strategic Air Command was already prepared to devastate Russia to a “smok­ing, radiating ruin in about two hours.”^[204] By 1955, this strategy began to receive scrutiny in view of its potential immorality and inefficacy. At this time, as a RAND analyst and US Department of Defense consultant, Kahn had access to military information not generally available to the American public, and his On Thermonuclear War frightened the lay public into recognizing the dangers and realities of nuclear confrontation.^[205] Pointedly, US superior military might had done nothing to prevent or stop the Soviets from invading Hungary in 1956. All that a massive retaliating strike was bound to secure was the Soviet’s nuclear devastation of Western Europe, and even potentially the United States itself.

Eisenhower’s aversion to budget deficits led him to reject building up con­ventional forces, and he left office with his Single Integrated Operational Plan (SIOP), a war plan of simultaneous massive nuclear retaliation against all Soviet (and Chinese) cities, in place. This strategic reality, coupled with the Soviet’s newly acquired thermonuclear capability, set the stage for a two-decade policy debate between advocates of mutual deterrence and proponents of flexible response, counterforce, and escalation dominance. Hence, the Cold War chal­lenge, based on achieving a bipolar strategic deadlock in which neither side could reasonably afford to wage nuclear war, stood in place.

Unlike Kahn, Schelling played an active role in McNamara’s Department of Defense.^[206] The Kennedy administration had come to office arguing that Eisenhower was weak on defense. McNamara’s first move, which he brought to public attention with his famous public speech in Ann Arbor, Michigan, in June 1962, was to introduce the new SIOP 63, set to take effect the following year, predicated on maintaining “Flexible Response.”^[207] McNamara was attempting to respond to the perceived weaknesses of Eisenhower’s massive retaliation: the immorality of targeting innocent civilians, and the lack of credibility of only being able to achieve efficacy at the price of suicide. Flexible Response worked by responding to a less-than-all-out attack against the United States with a less-than-all-out-attack against the Soviet Union and targeting harder to hit military installations and forces rather than simply attacking vulnerable and large cities.^[208] Although this policy was ostensibly more moral for targeting weapons systems instead of people, counterforce weapons could be used in a first-strike assault. Therefore, this strategy was inherently destabilizing because it put the Soviets in the position of worrying about preemptive attack and how to secure their own second-strike capability. Nor was it more certain that this new form of flexible deterrent threat of retaliation was any less suicidal that Eisenhower’s because there was no guar­antee that escalation could be capped.^[209]

Secretary of Defense Robert S. McNamara’s 1963 reconstitution of US nuclear strategy along Flexible Response lines and his subsequent backpedaling to assured destruction made it possible to recognize Thomas Schelling’s con­tributions to what would become the then-prevailing conceptual framework for organizing military capability and posture.^[210] Schelling’s essay “Diplomacy of Violence,” in which he directly responds to McNamara’s 1962 Ann Arbor address, as well as his essays “The Reciprocal Fear of Surprise Attack” and “Surprise Attack and Disarmament” set forth his view that the nuclear standoff resembles a Prisoner’s Dilemma situation and his resolution of this otherwise mutually disastrous scenario with the deterrent policy of assured destruction.^[211]

According to Schelling, two unprecedented features of nuclear war forever altered the nature of warfare. First, concurring with Bernard Brodie’s 1950s estimation, he held that the primary characteristic of nuclear war is that it makes coercive force more effective as bargaining leverage to deter or compel specific behavior; nuclear weapons are not useful for achieving the military defeat of one’s enemy. Second, he argued that nuclear weapons make it possible to exert a phenomenal threat of human destruction even without the power to stand as the military victor of a conquest.^[212] Fully on board with strategic rationality, Schelling insisted that the ability to inflict pain was a significant attribute of bargaining. If the other is persuaded by coercive threats of punish­ment, then the application of physical harm need not be imposed. The brute force of physical domination is thus replaced by carefully calibrated threats measured against the other’s expected gain from prospective choices of action: “The threat of pain tries to structure someone’s motives, while brute force tries to overcome his strength.” Schelling concludes, “Unhappily, the power to hurt is often communicated by some performance of it... It is the expectation of more violence that gets the wanted behavior, if the power to hurt can get it at all.”^[213]

Notwithstanding Schelling’s seeming pessimism that the grand power of nuclear weapons signaled a military stalemate because neither side could gain by using them, he was sanguine that these weapons could be deployed to one’s advantage through coercive bargaining:

The power to hurt is nothing new in warfare, but for the United States modern technol­ogy has drastically enhanced the strategic importance of pure, unconstructive, unacqui- sitive pain and damage, whether used against us or in our own defense. This in turn enhances the importance of war and threats of war as techniques of influence, not of destruction; of coercion and deterrence, not of conquest and defense; of bargaining and intimidation... War no longer looks like just a contest of strength. War and the brink of war are more a contest of nerve and risk-taking than of pain and endurance.

Schelling, like Kahn, accepts that with deterrence in place, superpowers will face each other in a Chicken game contest of nerves. He observes that “military strategy can no longer be thought of... as the science of military victory.” War is better regarded as “the art of coercion, intimidation and deterrence.” He therefore concludes, “military strategy... has become the diplomacy of violence.”^[214] Schelling’s diplomacy of violence embedded in a nuclear stalemate held out the hope of retaining military control and international stature by wielding nuclear threats. Schelling advocated the use of a demonstration explo­sion of a nuclear device during the Berlin crisis, “over an isolated place in Russia like the island of Novaya Zemlya,” as an attempt to show that the United States would retaliate if the Soviets did not back down.^[215] Therefore, although the strategist did not endorse escalation dominance because it is inherently self­defeating, still he did support a flexible use of nuclear weapons in what he hoped would be limited war to maintain deterrent brinkmanship.^[216]

“The Reciprocal Fear of Surprise Attack” and “Surprise Attack and Disar­mament” initiated the convention of analyzing the fear of nuclear preemption in terms of a Prisoner’s Dilemma.^[217] Schelling begins by applying a Stag Hunt, or Assurance Game, to a standoff between a homeowner and a burglar, each of whom wants a peaceable resolution without escalation to a shooting incident.^[218] In game theory, a Stag Hunt has two possible equilibrium outcomes in which neither actor can alone improve on his payoff by selecting a different course of action: mutual cooperation and mutual defection. Figures 5 and 6 present a matrix and graphic depiction of the Stag Hunt game. Using von Neumann’s reasoning, some argue that choosing to defect is always superior in a Stag Hunt because this choice at least achieves the maximin outcome of a hare for certain rather than the slim pickings that would be available after attempting to cooperate but being stood up by the other actor.

Schelling introduces the idea that each is uncertain about the preferences of the other, whether he seeks a peaceable solution or prefers to shoot the other, and similarly worries that the other may incorrectly guess his own intent. Introducing an 80 percent likelihood that one believes the other is a predator and multiplying the cardinal utility matrix of the Stag Hunt by the anticipated likelihood of each act, Schelling demonstrates that the Stag Hunt transforms

figure 5. Stag Hunt Game Matrix

figure 6. Stag Hunt Game Diagram

into a Prisoner’s Dilemma, in which the row actor is better off defecting than cooperating no matter what the other side does (DC>CC and DD>CD) (Figure 7). Schelling’s transformation of an Assurance Game into a Prisoner’s Dilemma as a function of probability is a crucial moment in the analytic development of game theory, nuclear security, and the future use of the PD game to model actors’ hopes to achieve security. It set a precedent for suggesting

figure 7. Schelling’s Prisoner’s Dilemma Payoff Matrix Derived from Stag Hunt

that one’s sufficient doubt about the other’s intention warrants adopting the preferences of an aggressor. Doves must become hawks in self-defense.^[219]

The reciprocal fear of surprise attack emerges in an environment character­ized by a high degree of suspicion and large preemptive incentives. It is a situation captured by a one-shot PD, in which both sides must defect regardless of what the other does. Because the only route to security lies in offensive action, even pure security seekers must assume the worst of others and act like aggres­sors. The assumed impossibility of signaling one’s own benign intentions com­bined with the staggering costs of guessing wrong about the intentions and future actions of the other explains how unpredictability can lead to aggressive behavior and preemptive wars that no one wants.^[220]

States operating in an uncertain environment of large first-strike advantages confront the same problem faced by two gunslingers in a small town lacking a capable sheriff. Both gunslingers may prefer a bargain whereby each leaves the other alone, but neither can credibly commit not to shoot the other in the back.^[221]

figure 8. MAD Payoff Matrix

figure 9. MAD Payoff Diagram

Assured destruction solves this problem by eliminating all preemptive incentives. The key is for both superpowers to possess a survivable second-strike force that can wreak unacceptable damage on the other. If, for instance, the two gunslingers now only have slow-acting bullets that take minutes to work, a shootout makes no sense for either side, for it has become tantamount to mutual suicide (Figures 8 and 9). In Figure 9, even if the US initially cooperates and receives the USSR's preemptive first strike, its second strike counterforce ensures the USSR's destruction.

Schelling addresses the considerations of the incentive to strike a preemptive blow in self-defense in “Surprise Attack and Disarmament.” It is in this essay that Schelling outlines the philosophy underlying Assured Destruction: “The innovation in the surprise-attack approach... has to do with what scheme is designed to protect and what armaments it takes for granted. An anti-surprise­attack scheme has as its purpose not just to make attack more difficult but to reduce or to eliminate the advantage of striking first.”^[222] In essence, if the advantage of striking first is entirely reduced by the opposition’s reserve of devastating second-strike force power, then neither side will be inclined to attack first. This eventuality depends entirely on the United States and the USSR building weapons that cannot be mistaken for first-strike forces designed to destroy military targets. Therefore, “schemes to avert surprise attack have as their most immediate objective the safety of weapons rather than the safety of people,” rejecting Herman Kahn’s type II deterrence.^[223] The other nation’s weapons must remain sacrosanct so that its leaders feel secure in being able to marshal a devastating counterattack at the first sign of being assaulted. Submarine forces are ideal for this, because they are difficult to detect and destroy, and they can maintain a counterstrike capability targeted at vulnerable population centers.

Schelling speaks in terms of the logic of stalemate, for even if one side could mount an attack that could knock out the other in a devastating blow subvert­ing their counter-strike ability, the opposition would only have the heightened incentive to strike first. In the language of the Prisoner’s Dilemma game that Schelling argues captures the problem of the reciprocal fear of surprise attack, the capability of second-strike reprisal serves to alter the payoff for a unilateral attack to that of mutual devastation signifying the inherent impossibility of obtaining dominance. Schelling and Kahn differ in their appraisals of nuclear strategy: whereas the latter holds out the hope for achieving nuclear supremacy, the former espouses the belief that because the capability for mutual devastation has already been achieved, the best that can be hoped for is a stable “balance of terror.”^[224]

Persuaded by Schelling’s logic, Robert McNamara capped the US nuclear arsenal at 400 megatons of explosive potential, regarding this as sufficient to achieve a devastating counter strike in case the Soviets launched a preemptive attack. Harkening back to Eisenhower’s administration, McNamara used a i960 military study called WSEG-50, which advocated for a policy of “finite deter­rence” through city destruction.^[225] He officially announced his reformulated strategy to President Lyndon B. Johnson two weeks after John F. Kennedy’s assassination, calling it “assured destruction.”^[226] It rested on a calculation of the destructive force of megatons of explosive power arrayed at the Soviets in terms of “industry destroyed” and “population destroyed.”^[227] McNamara’s crucial insight was that after a certain amount of money has been allocated to building the US stockpile of nuclear warheads for land-based ICBMs (intercontinental ballistic missiles) and strategic bombing, in addition to deployment on undetectable submarines, any more allocation of funds could not significantly increase the destructive force already unleashed because there would be few if any remaining targets, including cities, industry, or military sites.

McNamara’s move was twofold. First, he set the rhetoric of US defense policy in terms of deterrent city busting versus counterforce capability, there­fore diminishing the readiness with which the United States might be perceived as clandestinely seeking first-strike power.^[228] Second, he maneuvered to deter­mine precisely how much destructive power was sufficient to deter the Soviets from attacking the United States, and thus exactly how large the US missile arsenal needed to be. His civilian defense rationalists put the number at 400 megatons, which guaranteed that after a Soviet first-strike on US territory, there would be sufficient counter-strike potential to kill 30 percent of the Soviet population and half of its industrial base.^[229] Even though this policy resembled President Eisenhower’s strategy of massive retaliation, to the liberal wing of the defense rationalists, it seemed reasonable because they found it “very hard to believe that any country would deliberately accept the certainty of severe retaliatory damage in preference to the uncertain prospect of being the victim of a first strike.”^[230] Whereas McNamara equipped each arm of the US military triad of air, land, and sea with 400 megatons of destructive capacity to build redundancy into the US defenses, Schelling argued for a minimum deterrent restricted to submarine missiles that are virtually impossible to detect and destroy but have less accurate targeting capability and thus cannot be mistaken for preemptive weapons.^[231]

Schelling’s ideas were severely tested in the Vietnam War. The war itself, organized in terms of escalating bouts of punitive damage on the country’s civilian population, provided an empirical case study of Schelling’s idea of diplomatic violence through the threat of pain.^[232] This war, interpreted by US officials as a crucial stand against communism and Soviet imperialism, became a test case for maintaining American credibility. Schelling had written that in Chicken-style diplomacy, maintaining one’s credibility is key, for once it is challenged, it will forever be possible to be out-maneuvered. All the US nuclear forces, on 24-hour deterrent alert, were apparently useless in controlling the outcome of the Vietnam War.