Schelling, Von Neumann, and the Event That Didn't Occur
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Games 2014, 5, 53-89; doi:10.3390/g5010053 OPEN ACCESS games ISSN 2073-4336 www.mdpi.com/journal/games Article Schelling, von Neumann, and the Event that Didn’t Occur Alexander J. Field Department of Economics, Santa Clara University, Santa Clara, CA 95053, USA; E-Mail: [email protected]; Tel.: +1-408-554-4348 Received: 19 August 2013; in revised form: 10 December 2013 / Accepted: 31 January 2014 / Published: 25 February 2014 Abstract: Thomas Schelling was recognized by the Nobel Prize committee as a pioneer in the application of game theory and rational choice analysis to problems of politics and international relations. However, although he makes frequent references in his writings to this approach, his main explorations and insights depend upon and require acknowledgment of its limitations. One of his principal concerns was how a country could engage in successful deterrence. If the behavioral assumptions that commonly underpin game theory are taken seriously and applied consistently, however, nuclear adversaries are almost certain to engage in devastating conflict, as John von Neumann forcefully asserted. The history of the last half century falsified von Neumann’s prediction, and the “event that didn’t occur” formed the subject of Schelling’s Nobel lecture. The answer to the question “why?” is the central concern of this paper. Keywords: game theory; deterrence; nuclear strategy; Schelling; von Neumann 1. Introduction Thomas Schelling is widely thought of, and was recognized by the Nobel Prize committee as a pioneer in the application of game theory and rational choice analysis to problems of politics and international relations. Much of the popularity of his work and other analysis in this vein stemmed from the perception that it contributed to the development and application of new “tools” for understanding and analyzing social phenomena. Following the prize award, the economics journalist David Warsh described him as “the pioneering strategist who made game theory serve everyday economics for thirty years” [1, p. 7]. Games 2014, 5 54 However, although Schelling makes frequent references in his writings to rational choice and game theory, his analysis of deterrence1 is based on assumptions about human behavior and logic which, although useful in thinking practically about strategic policy, are at variance with those commonly adduced by game theorists, at least those specializing in its non-cooperative variant. 2 In areas especially relevant for strategy and conflict, game theory leads to behavioral predictions which are simply not borne out in the laboratory or, as will be apparent, in the real world. In the Prisoner’s Dilemma played once, for example, the Nash prediction is unambiguous: no cooperation. Defection is the strictly dominant strategy. Experimental evidence, however, provides abundant evidence of positive rates of cooperation. Similar “anomalies” are found in voluntary contribution to public goods games (which are multi person Prisoner’s Dilemmas), where one sees positive contribution levels, in the trust game, where one sees positive transfers in both directions, and in many other instances.3 Game theory has faced similar predictive failures in its treatment of behavior in the real world. As John von Neumann argued (citations follow), its canonical behavioral assumptions predicted devastating conflict between nuclear adversaries.4 This has not happened, and the nonoccurrence of the “most spectacular event of the last half century” was the subject of Schelling’s Nobel lecture [2, p. 1]. Schelling could refer to this as an event—something which has taken place—even though it had not— because choice by self-regarding players predicted it so unambiguously. The reality, I will argue, is that because of the disjuncture between human behavior and the self-regarding assumptions often used in formal game theory, the latter offers little guidance, normatively or predictively, in thinking about behavior or strategy in a world of potential conflict.5 1 Deterrence most commonly brings to mind the prevention of attacks on one’s own territory or that of close allies. But it can, more aggressively, be used in furtherance of other foreign policy aims. Schelling was interested in both defensive deterrence and its more aggressive forms, and the role that nuclear arms might play in either. 2 Non-cooperative theory studies interactions in which players are not allowed to make binding commitments among themselves. Cooperative theory allows such agreements, without specifying or exploring the behavioral attributes that might make them possible. 3 See Kagel and Roth [3], Camerer [4] or Field, [5–8] for more discussion. In the trust game A can anonymously give B some or none of an initial stake, which is multiplied in value in the transfer. B then may, but is not obligated to return as much as she wants to A. If self-regarding players are rational, there are no transfers in either direction. 4 One can object that the unitary actor assumption is simply inappropriate when thinking about interactions among states, although one can also object that the approach is inappropriate when applied to individuals (see Thaler and Shefrin [9]). Two points are indisputable: first, von Neumann argued (and believed) that superpower confrontation was a PD, and second, if that was indeed the game, it did not end with the Nash equilibrium. Von Neumann was a pioneer in developing game theory as well as nuclear weapons, and this has resulted in a tension which can be resolved in one of two ways. The first is to argue that nuclear confrontation was not a PD, in other words, that von Neumann did not know what he was talking about. The second approach, adopted here, is to accept the PD metaphorically as representative of superpower confrontation, but to argue that the behavioral assumptions that drove von Neumann’s (and many other’s) thinking were flawed. The central premise of this paper is that the reason we did not and have not experienced nuclear annihilation is that evolutionary history has endowed most humans with predispositions against playing defect in a PD that might well end up being played only once (Field [5,8,10]). People (and states) do indeed sometimes defect. But even when the logic of a strictly dominant strategy is fully understood, individuals frequently choose not to play it. 5 Developers of formal theory have not been particularly concerned about this, placing more weight on logical consistency and theoretical novelty than on empirical validity. Games 2014, 5 55 Before considering in more detail Schelling’s evolving acknowledgements of the limitations of game theory in understanding deterrence, it is important to reflect on exactly why the theory is so barren in terms of its implications for policy or behavior. The main reason can be stated simply. So long as agents are self-regarding and there is some possibility of destroying an adversary’s offensive capability and/or its will to retaliate, von Neumann was right to characterize nuclear confrontation is a Prisoner’s Dilemma. 6 And, because of the almost unimaginable destructive power of nuclear weapons, particularly thermonuclear weapons, it is a PD that will be played only once if the Nash equilibrium is realized on the first iteration.7 In the Prisoner’s Dilemma played once, defect (which in this instance means preventive war, preemption, or first strike) is the strictly dominant strategy for both players. As von Neumann argued, it is the only strategy a rational self-regarding player, assuming he is playing against a similar adversary, can choose. 8 But it is evidently not the strategy chosen by either the United States or the 6 A long tradition in the deterrence literature objects, and instead treats nuclear interaction as a game of chicken (see Zagare and Kilgour [11, p. 18]). Chicken involves A threatening to harm B in a way that will also damage A unless B backs off. The best response for either party is to back off in the face of a threat, but if both choose to escalate, the worst (least preferred) outcome ensues for both. Von Neumann did not see nuclear interaction as a game of chicken. Words were cheap. He did not argue that we should try and intimidate the Soviets by threatening to attack. He argued for attacking, and for attacking now. Those who reason in this manner tend to downplay or dismiss fears of retaliation, since self- regarding agents would never retaliate ex post (as opposed to threatening to do so ex ante, which would not be credible). A large literature attempts to solve this problem essentially by assuming it away [11, ch. 2]. 7 Preempters like von Neumann saw the nuclear standoff as a Prisoner’s Dilemma in which the strategy space was limited to “attack immediately” or “wait.” No truly self-regarding player, reasoned von Neumann, would ever wait. Doing so exposed the actor to avoidable risk and granted a benefit to the adversary (the continued option of preemptive strike). Wait turned the PD into a game of trust: the question then became whether the restraint would be reciprocated. Actual political actors, who are human, often do wait, and establish expectations of reciprocity through diplomacy or other means that sometimes are realized. Von Neumann had little interest in wasting time on the dynamics of deterrence, or why people might make transfers in trust games. His counsel was to launch now, and his argument is unassailable if parties are indeed entirely self-regarding. If one finds this conclusion unpalatable something has to give. This paper argues (and Schelling suggests the same), that deterrence worked and von Neumann’s predictions failed because humans are not entirely self-regarding (a position anathema to those who consider themselves hard-headed realists). If that is so, behavioral science will be messier than economists and game theorists might prefer, because the ways in which human predispositions differ from the self-regarding baseline are not deducible from a simple set of first principles.