INTRODUCTION
There is general consent that game theory provides by its very nature the appropriate tools for the analysis and eventual solution of conflicts of any kind, that is, also as considered here, international conflicts.
In fact, there are books dealing with this subject that express this already in their titles. The Strategy of Conflict, written by Schelling in 1960, was an early and highly influential book on the subject, Game Theory as a Theory of Conflict Resolution was edited in 1974 by Rapoport, another important researcher of those years. Resolving Conflicts with Mathemetica - Algorithmsfor Two-person Games, published by Canty in 2003, demonstrates the use of Mathematica software for analyzing those models which are too complicated for traditional pen and pencil methods.If one studies the published literature on game theoretic approaches to conflict resolution, there are a large number of contributions written by game theorists which deal with mathematical aspects but present only illustrative examples instead of real applications. One also finds many papers written by political or social scientists who analyze international conflicts with the help of very simple formal models, or by just the use of game theoretical terminology. There are, however, relatively few studies that use genuine and non-trivial formal methods in order to analyze concrete international conflicts. Some of them will be discussed subsequently.
Since game theory as of today is a very large field - the three volumes of the Handbook of Game Theory (1994-2002) comprise 2200 pages with thousands of references - we do not attempt here to systematically scan different areas and methods in order to find models of, in and for resolving international conflicts. Also, we do not try to classify international conflicts in order to see if there are analyses which use specific game theoretical methods.
(This has been done in some way in 1994 by O'Neill who listed more than 600 references on game theoretic models for peace and war.) Finally, we do not enter into a general discussion of the value of game theoretic models since this has been done extensively on several occasions - see, such as the Journal International Security (1999), or Snidal (2005). Nevertheless, there remains a challenge.Here, we choose the following approach: instead of any kind of systematic procedure, a few case studies are given which are selected in order to demonstrate at the same time the variety of problems as well as methods for their solution. In addition, the case studies are discussed and commented on, such that, with additional references, at least some kind of coverage of the area is given. Of course, there remain gaps both in theory and application, and even more so in the literature.
In this chapter, we do not attempt to present any kind of introduction into game theory itself, since there are so many excellent introductory textbooks, for example, by Myerson (1991), or by Fudenberg andTirole (1998).We try to answer the question: what is the purpose of game theoretical models of conflicts? In general, they enable the analyst to do the following:
Describe a conflict in terms of a general theory, namely, formulate strategies, payoffs, information, and the like, and interpret the resolution - if there is one - as an application of some general principles covering human action.
Gain insights into apparently strange - we avoid saying irrational - behavior of participants in a conflict and show how such behavior can be understood in terms of an appropriate general theory.
Advise those who are involved in a concrete conflict, if possible, or at least advise retrospectively if a conflict has already been solved, and assess the actual resolution of a conflict in terms of the preferences of the participants and their strategic possibilities.
With respect to the first two purposes, we consider game theory a descriptive theory; for the last, we consider it a normative theory. Our case studies of the past are of a descriptive nature, whereas some of the case studies which deal with not yet solved conflicts, at least to some degree, may be considered normative ones.