Background

Europe, in geographic terms, comprises 47 independent countries that jointly can be considered the largest economy on earth. The European Union (EU), as an economically and politically integrated group of member states, includes 28 countries, with 18 of these sharing the euro as their common currency. The EU member states have a total gross domestic product (GDP) of more than US$16 trillion, with a per capita GDP of roughly US$34,000. In terms of medical devices, the EU is often referred to as the “European market” because of its common device regulation under the CE mark. However, innovators should appreciate that the European market extends beyond the EU and includes such non-member states as Switzerland and Norway. Russia, which geographically belongs to both Europe and Asia, is also commonly considered part of the larger European medical device market, as most of its economy and population is located in the western portion of the country.

Europe has a population of nearly 740 million people, approximately 7 percent of the global population (with the current 28 EU member states accounting for 69 percent of the total). Compared to other parts of the world, population growth in Europe is rather slow and the median age comparatively high. Nine of the top 10 countries with the highest median age, worldwide, are European countries, with only Japan having an older population.

Spending on healthcare as a percentage of GDP ranges widely across European countries. France, Germany, the Netherlands, and Denmark commit more than 11 percent of GDP to health, while Romania and Cyprus spend less than 6 percent. In 2010, health expenditures as a percentage of GDP dropped in the EU for the first time since 1975. From an annual average growth rate of 4.6 percent between 2000 and 2009, growth in health spending per capita fell to –0.6 percent in 2010 and has been stagnant in many countries ever since. Among EU member states, those with higher average income levels per person generally spend more on health-related products and services. When considering absolute amounts of healthcare spending per capita, the variation in health-care spending is even more evident, ranging from about US$5,000 in France to merely US$500 in Romania.

Communication is an important aspect of international relations. While diplomacy goes back to antiquity, the institution of diplomacy as we know it was developed during the Italian Renaissance to facilitate communication between states (Nicolson 1954). We have already seen how private information can lead to conflict, and we, therefore, have a convincing rationale for how communication could prevent conflict. This chapter will introduce the topic of communication in international relations. First, I will discuss a class of models in which the communication is costless, so it is designed to represent ordinary verbal communication such as diplomacy in which the parties may lie if it suits their interests with no direct penalty, other than what the strategic situation they are in provides. These models are denoted “cheap talk” models in economics. We will see that there are limits to the effectiveness of cheap talk in dealing with situations in which the players have conflicting interests. In some cases, therefore, states resort to “costly signals”, in which the means of communication have direct costs attached. Examples include threats that invoke a state or leader's reputation or domestic job security and mobilization of military power and engaging in actions that generate a risk of war.

Communication in international relations

The study of communication and signaling in international relations has a long history. An eighteenth-century French diplomat, François de Callières, wrote a treatise on diplomacy that continues to be read today (de Callières 1994). International relations as a discipline grew out of the study of diplomatic history and international law (Nicolson, 1939). Influential works in the field focused heavily on diplomatic maneuverings and included case studies of important diplomatic conferences such as the Congress of Vienna that followed the Napoleonic wars (Taylor 1954, Kissinger 1954).

Schelling pioneered the analysis of communication in the context of international bargaining with a particular focus on how to make threats and commitments credible to adversaries when they might have reason to doubt that a state would fulfill them (Schelling 1960, 1966).

Bargaining is ancient and pervasive in international relations. Thucydides describes several instances of international bargaining in the Peloponnesian War. In one of the most famous incidents described, the Athenians attempted to persuade the Melians to surrender their city and ally with Athens (Thucydides 1954, 400). The Athenians threatened that if the Melians did not accept their offer, they would attack. The Melians, hoping for aid from Sparta, refused, so the Athenians besieged the city and eventually prevailed at great cost to the inhabitants. The ancient Greek city states signed peace treaties, trade agreements, and alliances with each other, as did Rome, Carthage, and other important states of the ancient world. The first treatise on diplomacy in the modern period was entitled, “The Art of Negotiating with Sovereign Princes” (de Callières 1994). Today, states bargain over territory, trade barriers, arms control, pollution, and many other issues. This chapter will examine a simple extensive form model of bargaining and some of its implications for international relations.

There are two basic questions we can ask about bargaining. First, when does bargaining succeed and when does it fail? Bargaining that succeeds usually results in an agreement of some kind, sometimes a written treaty in the international context, but sometimes a more informal understanding. When bargaining fails to generate an agreement, the parties may simply continue with the status quo or they may engage in more active forms of conflict such as war, as the Athenians and Melians did. States are usually motivated to negotiate with each other because the status quo is unsatisfactory, at least to one side, or because they wish to avoid the costs of conflict. If there are joint gains to be had by reaching an agreement, it seems wasteful for bargaining to break down. More pointedly, it seems to require some explanation: why would states fail to come to an agreement that would make them both better off than the alternative, be it war or the status quo?

Domestic politics has an extremely important impact on international relations. To begin to address this impact, it is possible to use unitary actor models that differentiate the actors according to variables that represent features of their domestic political makeup, for instance, their costs for fighting or their level of transparency. However, for some aspects of domestic politics, it is necessary to go beyond this and leave behind the unitary state assumption that I have maintained so far. Following the overall rationalist approach and commitment to parsimony, however, I will depart from it as little as possible. The usual method is to recast the state as an individual executive or leader, and add an additional (unitary) actor to the model, representing a domestic institution such as a legislature. If the other state is left unitary, this procedure results in a three actor model that is often quite useful without being overly complex.

The impact of domestic politics

The role of domestic politics in international relations, and vice versa, has been debated for centuries. Some nineteenth-century historians, such as Leopold von Ranke, argued for the “primat der aussenpolitik” or primacy of foreign policy, holding that international relations has a profound impact on domestic politics. Otto von Hintze (1975) famously argued that Prussia was autocratic because its exposed position on the European plain necessitated a strong state, while England had the freedom to develop democracy because it was protected from foreign threat by the English Channel. Marx, of course, focused on the class structure within states as the most important variable in explaining their behavior, and his disciple Lenin (1996 (1916)) blamed the origins of the First World War on capitalist imperialism. Subsequent historians attempting to come to grips with Germany's record of aggression in the twentieth century placed the blame squarely on domestic factors, arguing for the “primat der innenpolitik,” or primacy of domestic politics.

This chapter addresses the question of how exogenous changes in relative power affect bargaining between states. Exogenous power changes may happen for a variety of reasons – for instance, states differ in their economic growth rates. States that are undergoing industrialization usually experience a period of rapid economic growth before settling down to a more normal rate. As one state grows richer because of industrialization, it will be able to devote more resources to military power. This will shift the balance of power with other states who are not industrializing, or not as quickly. This process may lead to war if the parties are not willing to come to new agreements reflecting the new balance of power.

Thucydides argued that the Peloponnesian war began because of “the growth of Athenian power and the fear which this caused in Sparta” (Thucydides 1954, 49). Since that time, the idea that war could be caused by changes in relative power has become a mainstay of international relations theory (Levy 1988). The related literature on power transitions argues that war is especially likely when rising states overtake declining states (Gilpin 1981, Organski and Kugler 1980, Kugler and Lemke 1996, DiCicco and Levy 1999, Tammen et al. 2000). Fearon (1995) considered power change to be one of two main plausible rationalist explanations for war and Powell (1996, 2006) further investigated the conditions under which it operates. Fearon (2004) argues that this kind of commitment problem helps explain why some civil wars last so long, and Powell (2004) finds a similar mechanism at work in a variety of contexts where there is shifting power.

Another manifestation of this problem is the window of opportunity. A window of opportunity can arise if a state is temporarily weakened but will regain its strength over time (Van Evera 1999, Chapter 4).

States spend a great deal of money on their armed forces, and on other things designed to increase their power and military capabilities. Models of arms competition seek to explain this level of spending. Theories of international relations also link military spending to conflict and war in a variety of ways. Arms competition, therefore, can be considered as both a dependent and an independent variable.

Arms competition was first studied using formal theory by Lewis Fry Richardson in the wake of the First World War (Richardson 1960). He used a pair of linked differential equations to model the arms spending of two competing powers, in which each side's spending was a function of the other side's, as well as its own existing stock of weapons. Richardson's models did not assume that states are rational, but the principal results of his models can be replicated in the currently more conventional rational choice framework (Lichbach 1989, 1990). In particular, arms choices can look like a Prisoner's Dilemma, as discussed in Chapter 3. Downs and Rocke applied a continuous strategy space version of the repeated Prisoner's Dilemma model to the arms race context, to analyze when arms control agreements can be sustained (Downs et al. 1985, Downs and Rocke 1990).

The link between arms races and war has also been widely analyzed. (Kennedy 1984, Intrilligator and Brito 1984, Brito and Intrilligator 1985, Siverson and Diehl 1989, Downs 1991). There are three principal explanations of war that have to do with arms competition. First, is the simple idea that arms are expensive, and, more generally, deterrence is expensive. The tradeoff between “guns and butter” is well known, and is the foundation of all arms race analyses (Powell 1999a, Chapter 2). In judging war to be inefficient, as we did in Chapter 4, we compared it to an idealized version of peace in which there are no costs associated with deterring predation or revisionist demands from other states.

So far, we have considered interactions between pairs of states, using two player games. This is perfectly acceptable for a wide range of contexts. The Cold War was the heyday of bipolarity, in which the main security interactions were between the United States and the Soviet Union. Most wars (Levy 1983) and over 80% of militarized international disputes (Ghosn et al. 2004) are bilateral. The vast majority of international treaties are bilateral (Koremenos 2013). However, many international interactions involve more than two states. The major wars of the past 200 years, the Napoleonic Wars and the First and Second World Wars, each involved many states. The World Trade Organization has over 150 members, the International Monetary Fund over 180, and over 160 states have signed the United Nations Convention on the Law of the Sea. Thus, how states interact in groups of more than two is an important subject of study.

While multilateral bargaining has received some attention in international relations (Sebenius 1984, Gilligan 2004), most of the interest has been in the subject of multilateral cooperation. The main theoretical lens through which this problem has been examined is the theory of public goods (Samuelson 1954). The foundational work on this question in political science is Olson (1965). Olson was the first to ask how groups form to pursue their collective interests, given that individuals have an incentive to “free ride” off the efforts of others, what he dubbed the collective action problem. His main theoretical claim is that cooperation is harder to achieve the more actors are involved. Small groups find it easier to organize and overcome the collective action problem, and so can often prevail politically against larger but less well-organized groups. Applied to states, many have argued that small numbers of states find it easier to cooperate than large numbers (Oye 1986). Taken to its logical extreme, this argument has been used to support the claim that a hegemon or predominant state is needed to provide international public goods.

When states interact with each other in the international arena, they do so in a variety of strategic settings. In the context of an arms competition, states feel an imperative to keep up with their adversary, and surpass them, if possible. In international trade, states often have an incentive to protect domestic industries but a conflicting interest to widen markets for their exports. States attempting to coordinate on an international standard wish to harmonize their policies, but preferably on their own terms.

Each setting will present states with a different set of incentives and strategic opportunities. The primary question of interest in each case is how states will respond to these incentives and opportunities, or how they will behave. Some outcomes, called equilibria, will be stable or self reinforcing, in that if the players think they will occur, they have an incentive to fulfill that expectation and make them occur. Not all outcomes in a strategic setting have this property. Non-equilibrium outcomes are thought to be less likely to occur than equilibria, so by locating equilibria we can begin to make predictions about behavior.

More specifically, we can ask whether states will cooperate. Keohane (1984, 51) defined cooperation as a process by which policies that were not in harmony to start with are brought into conformity through a process of policy coordination. More formally, we can identify cooperation with the achievement of Pareto efficient outcomes by the players in a setting in which inefficient outcomes exist. That is, if a setting is positive sum, so that there is a possibility for joint gains, then it can serve as a model of a cooperation problem. If a Pareto optimal outcome is also an equilibrium, then cooperation is more likely in that setting than if the Pareto optimal outcomes are not equilibria.

These different strategic settings can be represented by simple two player, two strategy normal form games.

What causes war? Why do states sometimes trade freely and other times protect their domestic industries? Why are some environmental treaties successful and others fail? Wars, international trade, and environmental treaties shape the lives of people around the world. Whether people live or die, are prosperous or poor, have a clean environment or a polluted one, all are affected by international relations. Mistaken beliefs about how the world works can lead to flawed policies, which can cause unnecessary harm to millions.

This book presents an approach to international relations that yields at least some tentative answers to questions such as these. The approach analyzes international relations through the lens of game theory, the mathematical study of strategic interaction. In this introduction, I discuss international relations theory, why game theory is useful for studying it, how the approach fits into the overall international relations theory landscape, and why an acquaintance with the approach may be of use even to those who do not pursue it in depth.

International relations theory

Why would we want a theoretical approach to international relations when an empirical one would seem more practical and useful? Theory helps guide our thoughts when we approach the world for empirical answers. If our theoretical ideas are confused or inconsistent, we are unlikely to find solid answers to questions we might pose about world events (Mearsheimer and Walt 2013). Theory helps us formulate models or mechanisms of international processes that we can then compare with reality to see if they seem to capture what is going on.

Uncertainty has long been viewed as a central cause of conflict. Geoffrey Blainey famously argued that “wars usually end when the fighting nations agree on their relative strength, and wars usually begin when fighting nations disagree on their relative strength” (Blainey 1988, 122). Early crisis bargaining models pointed out that there would be no war with complete information but war was possible with incomplete information (Morrow 1989, Powell 1990). Fearon (1995) made it one of the three rationalist causes of war, and indeed the subsequent literature for a decade focused largely on this cause. This chapter will introduce the topic of how uncertainty can cause war.

Uncertainty is usually thought of as affecting one of three factors: the utility functions over the issue in dispute, the parties' relative power, and their costs of conflict. Some models, such as those by Fearon (1997) and Sartori (2002) (as well as the Bargaining model in Chapter 9), feature uncertainty about the states' valuations for the objects in contention. States value the (indivisible) good along a continuum, some not very much and some more so. States with a low valuation for the good are less likely to threaten or fight for it than states with a high valuation for it. Models of mistrust also usually focus on the states' utility functions, differentiating between status quo states and revisionists, where status quo states are satisfied with what they have and prefer to live in peace, while revisionists want more and may start a war to get it (Kydd 2005). Fear that the other state is a revisionist may lead even status quo states to engage in conflictual behavior and even fight a war.

Other models restrict the uncertainty to the war payoff (Powell 1999a) and focus on the likelihood of winning and the cost of conflict (Fey and Ramsay 2011).

In strategic settings where all out war is too costly or ineffective to be a live option, states face the prospect that they must live together for the indefinite future. Taking war off the table certainly makes life more civilized, but peace can be made better or worse, depending on the strategies states pursue and the level of cooperation they attain. The literature on international cooperation has developed to analyze such situations.

Cooperation theory arose in the 1980s and marked the first time game theory made a major impact on central debates in international relations theory. Prior to that point, the 2 × 2 normal form games of Chapter 3 had been widely applied to various strategic issues, such as nuclear deterrence and the security dilemma, and had served to clarify the logic involved. However, they had not posed a serious challenge to any extant international relations theory. In 1979, Waltz's Theory of International Politics reformulated and reinvigorated realism as a paradigmatic approach, and its pessimistic view of conflict as an inevitable consequence of anarchy was bolstered by the return to confrontation between the United States and the Soviet Union in that period. Scholars who viewed realism as unduly pessimistic, and the trend of world affairs with alarm, sought for ways to undermine or at least qualify the realist logic Waltz had laid out.

Fortuitously, applied game theorists had recently begun studying the Repeated Prisoner's Dilemma (RPD) game, which offers an explanation of how cooperation can be sustained without centralized enforcement. In the early 1980s, Robert Axelrod conducted a series of computer experiments to determine what strategy would fare best in an evolutionary setting based on the RPD and published a widely read book on the results (Axelrod 1984). This framework was seized upon by critics of Waltzian realism, who applied it to a variety of settings in both security and economic affairs (Oye 1986).