Deterrence theory was the cornerstone of U.S. foreign policy during the Cold War when it came to implementing the strategy of containment. In a nutshell, deterrence theory explores the conditions under which a state can deter another opponent from taking an action that is contrary to that state's interests. Most often, deterrence involves the threat to use force in response to such action, although many analysts also allow for a wide range of options, including positive inducements for keeping the status quo.
All this research is in the grand Clausewitzian tradition of what war is all about. That is, the theory attempts to find ways of using force in the pursuit of political objectives. Thomas Schelling pioneered the view that war is essentially a bargaining process where opponents influence each other's expectations by threats, promises, and (regrettably) actions. Viewing conflict as a non zero-sum game proved to be an especially fruitful way of thinking about international relations, and much of the discussion of deterrence owes a huge conceptual debt to Schelling.
What eventually emerged from the studies of deterrence is the central concept of credibility. To be effective in influencing the expectations of the opponent (and thereby help secure a good outcome), threats and promises, collectively called "commitments", have to be communicated properly and, crucially, have to be credible. If they are no believable, then the opponent will not revise its expectations. Schelling then proposed several ways of how credible commitments can be established. A very famous one is the strategy of constraining one's own options: by deliberately weakening oneself in this way, one can emerge in a stronger bargaining position because a commitment that one is unable to escape from has the ultimate credibility.
Another strategy that Schelling proposed involved the deliberate creation of risk of shared disaster. If the outcome one wants to threaten with is so bad even for the threatener, then the opponent will not believe it. Instead of threatening this outcome, one can instead create a risk of it occurring. The pressure of this risk can be the threat. Schelling called this the "strategy that leaves something to chance" and it essentially involves the deliberate manipulation of risk.
How does this relate to nuclear deterrence? After the Soviets acquired secure second-strike capability, the world entered the era of Mutually Assured Destruction (MAD). Regardless of who struck first, its opponent had enough nuclear weapons to launch a devastating retaliatory strike, obviating any possible gains from the use of the nuclears. In the world of MAD then, are nuclear weapons essentially irrelevant for the pursuit of political objectives through military threats? If the shared disaster is so painful, can a state rationally pursue a strategy that relied on such threats? Would they be credible?
This is where Professor Powell's book comes in. The basic question is addresses is exactly this: Is it possible to use nuclear threats for political purposes under MAD? Taking Schelling as a point of departure, Powell argues that there are really two options states can potentially pursue if they want to use such threats. First, they can use the strategy that leaves something to chance by deliberately creating a risk of an accidental nuclear war even though they would not rationally start one. Second, they can use the strategy of limited retaliation, which threatens with limited punishment increasing both the credibility of the threat and the incentives of the opponent to comply.
The author uses a series of formal game-theoretic models to probe the incentives for strategic behavior in stylized settings that are designed to capture what he believes are the essential features of each situation. He first analyzes the strategy with random component. Under complete information crises that involve nuclear threats are impossible because players can look down the game tree and see the point at which the one with lower risk tolerance will back down instead of escalating the crisis and risking war. If this is the Challenger, then no initial demand is ever made and the status quo prevails. If this is the Defender, then the Challenger's initial demand is accepted and, again, no crisis occurs.
Under incomplete information, in contrast, players do not know what their opponent's level of resolve is. (Resolve, by the way, is modeled as the highest risk a player is willing to run before backing down. As the crisis continues, the risk of accidental war increases, and so both state would eventually back down because neither would launch an attack deliberately. The question becomes who will do so first.) When states are uncertain about their opponent's resolve, they can end up in crises where they run the risk of war while simultaneously trying to determine the type of their opponent.
Because of the simple way Powell models incomplete information (only two types of players are allowed, and even these are restricted in a way that shortens the possible crisis to at most three periods), the equilibria he finds involve mixed strategies. He finds that beliefs interact with strategies in complicated ways that undermine the simple logic of the nonformal discussions. In particular, he finds that it is not always the case that the player with the highest resolve will win (in fact, the relative resolve of the players does not matter nearly as much as the beliefs they have about it). Players use the opponent's actions to infer something about the unknown level of resolve. This opens up opportunities for bluffing on both sides unless both are pretty sure that they are quite resolute.
To see how bluffing may work, suppose the defender is quite resolute and is, in fact, more resolute than the challenger. They both know each other's beliefs and suppose the challenger's belief that it is facing a strong defender is high. The resolute defender will escalate the crisis and, knowing this, the challenger would not even begin one, or so the standard logic would go. But the standard logic ignores the interaction of strategies and beliefs. If the defender is resolute and the challenger believes this with sufficiently high probability, this belief is common knowledge, the challenger may make a demand. The reasoning is that when the defender sees the demand, he infers that the challenger is actually resolute because only a resolute challenger would initiate a crisis. Given this updated belief, the defender may actually back down instead of escalating even though it is also resolute. But as the defender becomes more likely to back down, even less resolute challengers find it worthwhile to initiate a crisis and bluff. At some point, initiating the crisis can no longer serve as a signal of how resolute the challenger actually is because every type initiates it. But when this is the case, the resolute defender will choose to escalate instead because there is no longer new information transmitted from the act of initiating the crisis.
To make the long story short, Powell finds several crisis equilibria, all of which involve mixed strategies, where players are indifferent between escalating and backing down at various points in the crisis. While the insight about the crucial role of interaction of beliefs and strategies is important, a lot of the conclusions involve the knife-edge calculations that mixed strategies require. In the end, it is not clear what insights are substantively interesting and what results are simply artifacts of the model. In cases like these, mixed strategies are simply not convincing enough, especially to people unfamiliar with game theory.
The rest of the book then addresses various modeling issues by relaxing different assumptions of the original model. With the relaxation comes a price because the new models become more complicated to solve. Powell is forced to simplify other parts of the structure, sometimes in questionable ways. For example, in the reputational model in Chapter 4, he assumes that one of the possible player types is irrational in the sense that (a) it always plays a fixed strategy that does not take into account the actions of the opponent, and (b) it will escalate the crisis even when doing so means certain war. The other type of player then tries to create the impression that it is really the irrational type by escalating more than it otherwise would. That is, it is trying to build a reputation for toughness. This is a common way reputation is modeled in economics and I never quite liked it (but this is a separate discussion).
Finally, Powell addresses the alternative strategy of limited retaliation. His claim is that both it and the threat that leaves something to chance work in essentially the same way. They bridge the gap between doing too much (which is incredible because it is disastrous for both) and doing too little (giving in to the demands of the opponent with no resistance) by offering an array of options that enhance the credibility of the threats. This may be so, but it appears to me that the limited retaliation strategy involves much more explicit bargaining than the other, which makes it different.
In it, the essential feature is not the credibility of the ultimate sanction, but the costs the opponent is made to endure. By gradually turning on the screw, a player does not have to spend a whole lot of its own resources initially. More importantly, by not destroying everything of value to the opponent, he gives the opponent an incentive to strike a bargain and avoid future destruction. Limited retaliation involves persuading the opponent to quite while he has things to lose. The threat that leaves something to chance involves persuading him to quit because he becomes convinced that you will not. It is not clear to me how the limited option can be exercised with nuclear weapons either. I rather see it as a conventional engagement in the shadow of nukes. If the use of nuclear weapons becomes a possibility, then we are back to the MAD problem: if it is irrational to use them, why fear an escalation where one threatens to use them?
The problem with the limited option also involves that bargaining issue: The more you hurt the opponent today, the less you can hurt him in the future, which diminishes your bargaining power. Striking the balance between hurting him just enough not to kill him but also keep him sensitive to the pain seems quite difficult. This is in addition to the empirical difficulties with the other argument: there seems to be no evidence of policy makers actually deliberately pursuing risk strategies. If anything, they do whatever they can to minimize the risk of accidents. In the end, the decision to go to nuclear war must involve implementing the appropriate procedures through a deliberate choice. An accidental nuclear war (where "accidental" means because of some fluke) is extremely unlikely given all the checks in place to prevent it. If this is the case, we're back to trying to explain the final choice to push the button.
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