At the 2014 Wales Summit, NATO members reaffirmed their commitment to work toward an expansion of their military spending to 2% of their gross domestic product (GDP); in the negotiations for the 2007–2013 financial framework for the EU, six member states demanded that contributions to the EU budget should be capped at 1% of a member’s gross national income (GNI)¹; and in the 1985 Helsinki Protocol on the Reduction of Sulphur Emissions (the major cause of acid rain), a significant number of European countries agreed to reduce their SO₂ emissions by 30%.

If you are like most people, you will not find the percentages of 1, 2 and 30 surprising. In fact, you probably would have been much more surprised if the percentages had been 1.0036723%, 1.97421% and 28.765213%, or another such number. Somehow, the roundness of 1%, 2% and 30% seem to make the figures more plausible and attractive—one could even claim more normal—than these (and other) random numbers in their vicinity. What reason could someone have to propose aiming for an increase in military spending to 1.97421% of GDP, and why would other parties to the negotiation agree to such an unusual number? Clearly, 2% is a more ‘natural’ number. Even so, the question arises why 2% is a better choice than 1.97421%. It seems highly unlikely that there was an underlying calculation that established that the optimal defense spending target required for NATO to achieve its goals was exactly 2%. Certain considerations surely substantiated that the military spending target should be in the area of 2% (1% would probably be insufficient and 3% would impose too much of an economic burden on the member states), but it seems quite likely that 1.97421% or 2.022178%, or any number close to 2% would have been suitable as well. There is no particular reason why 2% military spending is optimal or “better” in terms of balancing the various interests of adequate funding for defense and reasonable economic burden than any of the numbers close to it. If you are asked to provide reasons why 2% as a number was agreed upon, you will find the question very difficult to answer.

And yet, this attraction to round numbers is extremely widespread. As the chapters in this volume testify, both in the outcome of the negotiations (the treaties and agreements that were ultimately signed) and in the proposals made during the negotiation process, simple or round numbers featured prominently, even though there does not seem to be anything about such numbers that makes them inherently superior, other than that they are conspicuous. The same holds for non-numerical things that stand out. Peace or armistice agreements often end up drawing borders along rivers or mountain ranges, for instance.² Indeed, the case can be made that such solutions which, as regards actual use in negotiations, seem natural or palpable (albeit for inexplicable reasons) are far more effectual than many of the sophisticated mathematical solutions predicted, for instance, by disciplines of rational choice, decision and/or game theory.

This volume is about the role of these ‘obvious’ or ‘natural’ solutions to practical problems, solutions that seem to have little else in their favor other than that they happen to stand out, or that they are focal points as they are officially called. Thomas Schelling (1960) introduced the term ‘focal points’ to refer to particularly conspicuous objects, numbers or propositions, whose conspicuity is expected to be recognized by all parties involved. Simple round numbers, natural borders (rivers, seas or mountain ranges), straight lines (e.g. lines of latitude, such as the current border between North and South Korea), and geometrical symmetries commonly play a significant role in negotiations and treaties. According to Schelling, they do so too often to disregard this tendency.

This leads to a number of pressing questions. First of all, this phenomenon raises scientific and philosophical questions. How can we account for the fact that people use focal points so often?³ Is it a coincidence that we do so, is it a matter of evolutionary psychology or sociology, or can it be explained as deliberate, rational behavior?⁴ The significance of focal points is not a purely theoretical matter. As already mentioned, it is an empirical fact that focal points are frequently used in negotiations and other contexts. Therefore, they are phenomena that give rise to practical concerns as well. For instance, can a negotiator, who has a thorough understanding of focal points, use this knowledge to gain a strategic advantage and skew the results of the negotiations in her favor? Can a mediator, whose primary concern is for the negotiations to succeed, apply insights from focal point theory to bring deadlocked negotiations back on track? Or can focal points perhaps even be used to facilitate outcomes that are fairer or more even-handed to some degree, thus securing honest compromises? Such questions warrant investigation, especially as they have long been neglected by scholars who study the art and science of negotiation. Even though the phenomenon was described over half a century ago, focal points and their use still remain enigmatic in many respects.

Since the 1960s, when the systematic investigation of strategic coordination commenced, the use of focal points has primarily been studied from the perspective of game theory.⁵ Game theory examines the strategic behavior of economically rational agents in idealized model worlds, often relying heavily on sophisticated mathematical tools. The large body of game-theoretical research on focal points offers both opportunities and challenges for our inquiry into the use and usefulness of focal points in negotiations. Opportunities result from the fact that the game-theoretical literature on focal points offers an elaborate conceptual framework that we can glean from. Challenges arise from the (often considerable) abstractions game theorists’ neat idealized models rely on to derive their results, and the subsequent chasm that opens up between these models and the untidy complexities of real-world negotiations.

This problem even affects the notion or definition of ‘focal point’ itself. As the authors of one of the chapters in this volume note, in the field of real-world negotiations ‘there seems much consistency in the spirit and little in the letter of a definition of focal […] points’ (Chapter 4 by Brown and Zartman). Beyond the distinct attribute of ‘standing out’ and consequently, the ability to attract the attention of the parties involved, there is no consensus on what precisely constitutes a focal point in the practice of negotiations and, in fact, in politics. By contrast, in the model world of game theory, focal points are specifically tuned toward playing a clear-cut role in the solution of their idealized settings. That is, focal points in game theory are defined as the features of a game that are not only uniquely conspicuous, but that are also commonly known to be just that. Common knowledge in this case refers to knowledge that is shared by all; moreover, all involved are well aware that this knowledge is shared by all.⁶ In strategic practice, by contrast, a given situation frequently entails more than one single conspicuous feature, and ‘knowledge’ is much too strong of a concept to adequately capture agents’ often uncertain, and sometimes inaccurate, assumptions about their opponents’ beliefs.

Because one of the key defining features of focal points (as defined in game theory) clearly does not hold in the practical context of negotiations, it is necessary to determine how differences arise and how these differences are relevant. To this end, it should be mentioned that focal points in game theory are usually analyzed in the context of a very specific type of game: coordination games. In coordination games, two or more agents share an interest in coordinating their actions, but must do so without communicating. In fact, it is the absence of the possibility to communicate that makes coordination games interesting objects of study: if communication were possible, the agents could simply exchange messages and agree on a plan of action. Because coordination games are defined in such a way that the parties’ interests fully coincide, the ability to communicate would make the entire problem of coordination obsolete.

Since communication is assumed to be impossible, each party (A) in a coordination game finds itself in the same bind, namely trying to predict what the other party or parties (B, C, …) will do based on the fact that they, too, are trying to correctly predict what that party itself (A) will do, and thus to match each party’s action. Under such premises, a uniquely conspicuous choice—of which all involved know that all others involved are aware of its conspicuity (focal point)—may steer the agents toward a solution to their coordination problem. As in a cabinet of mirrors without loss of optical resolution, there is an infinite alternation of mutual perspicuity. In such a situation, all players will be aware that one point, item or feature of the situation that stands out from the others for one reason or other will be recognized as such by all players. Unless there are two points that equally stand out, all involved will know that the most conspicuous one is recognized by all as the one that stands out the most. Since this point or item is the one recognized by all as standing out, it draws everyone’s attention.⁷ It can thus almost literally be described as a focal point: everyone’s attention is ‘focused’ on it—just as in optics where a focal point is defined as the point where all rays meet. This also means that focal points are by definition unique. Coordination is only deemed successful when all parties involved are drawn to the same solution.⁸

In the real world, the convenient game theoretic assumptions of complete and common knowledge usually do not hold, of course; the context of negotiation is a very clear example of this. In negotiations, parties typically only have limited knowledge about the other party’s inherent interests and what it might be willing to accept, and their knowledge of the specifics of the situation they are in may sometimes be less than perfect. Moreover, although there is a cooperative aspect to negotiations in that when carried out in good faith, both parties seek to arrive at a solution that is acceptable to both, they often have contrary interests, too. Each party seeks to secure the best deal it can get for itself. Not only do parties to negotiations not have perfect knowledge about the other party’s inherent interests, one party may actively try to keep the other in the dark on certain issues (e.g. one party might not want the other to know exactly how much it would be willing to compromise in order to secure a deal).

Another difference to standard coordination theory is that negotiators typically communicate with each other. Though not everything that is being said during negotiations will be believed (and in some cases, very little may actually be believed), negotiators can talk to one another, make overtures and offer reasons for the fairness or unfairness of the various proposals being made. Consequently, parties are not fully at the mercy of their estimation about which solution(s) might stand out to their counterparts as is the case in standard coordination settings: they can relatively candidly point out to the other parties that certain solutions are more worthy of consideration than others by deliberately drawing attention to them. Hence, the setting of negotiations differs in various crucial aspects from that of standard coordination, i.e. focal points do not function in precisely the same way in negotiation contexts as they do in coordination games. Indeed, at first glance, it would seem that the communicative nature of negotiations would make focal points obsolete. That, however, is not the case. As their widespread and visible use shows, conspicuous proposals and solutions play an important strategic role in negotiations.

This raises the question why this is the case. What role do focal points actually play in negotiations, if their purpose is not to serve as a substitute for communication as is the case in coordination contexts? One of the possible answers is that communication itself may be used to produce conspicuity in a field of competing proposals or solutions (cf. Chapter 3 by Schuessler). In cases in which multiple solutions that present themselves as attractive in various ways are possible, the fact that one agent highlights a particular solution may render it not only uniquely conspicuous for all other agents, but they ...