Robert Powell

Allocating Defensive Resources with Private Information about Vulnerability

In many resources-allocation problems, strategic adversaries move sequentially and are likely to have private information about the effectiveness of their spending. A defender, for example, often has to allocate its defensive resources before an attacker (e.g., a terrorist group) decides where to strike. Defenders are also likely to have private information about the vulnerability of the things they are trying to protect. Sequential decisions and private information about effectiveness creates a dilemma for a defender. Allocating more to a highly vulnerable site reduces the expected losses should that site be attacked but may also signal that that site is more vulnerable and thereby increase the probability of an attack. Modeling this tradeoff as a signaling game, the analysis shows that secrecy concerns generally swamp vulnerability concerns when more vulnerable sites are weakly harder to protect on the margin. The defender pools in equilibrium, that is, allocates its resources in the same way, regardless of the level of vulnerability. If more vulnerable sites are easier to protect on the margin, vulnerability concerns may swamp secrecy concerns.

Uncertainty, Shifting Power, and Appeasement

Great Britain faced an immensely complicated strategic problem in the 1930s, and important aspects of it can be stylized as a situation in which a state that is declining in power is unsure of the aims of a rising state. If those aims are limited, then the declining state prefers to appease the rising states demands rather than go to war to oppose them. If, however, the rising states demands are unlimited, then the declining state prefers fighting. And, given that the declining state is becoming weaker over time, it prefers fighting sooner rather than later if there is to be a war. This situation creates a trade-off: The earlier a state stands firm, the stronger it will be if war ensues, but the higher the chance of fighting an unnecessary war. In equilibrium, the declining state generally tries to appease the rising state by making a series of concessions.

Nuclear Deterrence and the Strategy of Limited Retaliation.

Recent formal work in nuclear deterrence theory has focused on brinkmanship crises in which states exert coercive pressure by manipulating the risk of an unlimited nuclear exchange. This essay extends the formal analysis of deterrence theory to the strategy of limited retaliation in which states exert coercive pressure by inflicting limited amounts of damage in order to make the threat of future punishment more credible. This strategy is modeled as a game of sequential bargaining with incomplete information. The equilibria suggest that states prefer relatively smaller, less-destructive limited options; that counterforce options are desirable even if they cannot limit the total amount of damage an adversary can inflict; that smaller, less-destructive limited nuclear options may make a nuclear exchange more likely; and that uncertainty and incomplete information may significantly enhance deterrence.

The Modeling Enterprise and Security Studies

The modeling enterprise is a way of trying to improve our understanding of empirical phenomena. Models serve in this enterprise as a tool for disciplining our thinking about the world, and formal models instill a particular type of discipline. Formalization provides a kind of “accounting standard” that can often help us think through some issues more carefully than ordinary-language arguments can. Just as good accounting standards make a arm’s anancial situation more transparent to those inside the arm and those outside it, formalization makes arguments more transparent to those making them and to those to whom they are made. When mathematical models are well constructed, they offer us a relatively “clear and precise language for communicating ideas and intuitions.” 1 The contribution that such a standard has to offer to security studies is likely to appear small to those who believe that nonformal or traditional work has already proved its power by amassing a large number of well-established empirical regularities and theoretical explanations of them. By contrast, the beneat of a more transparent standard will seem much higher to those who believe that security studies, like much of international relations theory, has established few robust empirical regularities; to those who have been frustrated to see that almost any outcome can be “explained” after the fact in a way that makes it consistent with existing theories; and to those who have repeatedly tried to formalize many widely held ordinary-language arguments in international relations theory (e.g., anarchy induces a concern for relative gains, anarchy leads to a tendency to balance, and a balance of power is more stable than a preponderance of power), only to and that these arguments are, at best, seriously incomplete and in need of signiacant qualiacation.

Crisis Stability in the Nuclear Age

In the logic of crisis stability, first-strike advantages may still be destabilizing, although even a successful first strike cannot protect a state from a terribly costly retaliatory second strike. If there is an advantage to striking first and if war seems sufficiently likely, launching a preemptive first strike may seem to be the least of evils. I reconsider the logic of crisis stability by studying games that are completely stable, although there are first-strike advantages. Four general conditions ensure stability. Identifying these conditions refines our understanding of crisis stability by also identifying the potential sources of instability, and this more refined understanding shows that the logic of crisis stability focuses attention too narrowly on first-strike advantages. Stability results from a more subtle interaction of several factors of which a first-strike advantage is only one.

Taking Sides in Wars of Attrition

Third parties often have a stake in the outcome of a conflict and can affect that outcome by taking sides. This article studies the factors that affect a third partys decision to take sides in a civil or interstate war by adding a third actor to a standard continuous-time war of attrition with two-sided asymmetric information. The third actor has preferences over which of the other two actors wins and for being on the winning side conditional on having taken sides. The third party also gets a flow payoff during the fighting which can be positive when fighting is profitable or negative when fighting is costly. The article makes four main contributions: First, it provides a formal framework for analyzing the effects of endogenous intervention on the duration and outcome of the conflict. Second, it identifies a “boomerang” effect that tends to make alignment decisions unpredictable and coalitions dynamically unstable. Third, it yields several clear comparative-static results. Finally, the formal analysis has implications for empirical efforts to estimate the effects of intervention, showing that there may be significant selection and identification issues.