FURTHER APPROACHES AND CHALLENGES

There are further game theoretic concepts which provide valuable insight into interna­tional conflicts and their resolution; some of them could eventually be used for normative purposes.

In all game theoretic concepts discussed so far, the payoffs to the players were scalar utilities, that is, they were characterized by one single quantity for each possible outcome. Since this is in most cases a gross simpli­fication, games with vector-valued payoffs have been developed. Usually these games have many equilibria and therefore they are less suited for practical use, even though just because of that fact they may describe the conflict more realistically. There are not many applications. Wierzbicki (1990) has studied fishery conflicts this way. Avenhaus and Krieger (2007) analyzed the Rambouillet negotiations of the Kosovo conflict (2007), and Avenhaus and Huber (2007) recently studied the conflict about Iran's nuclear program with the help of vector-valued payoffs.

Sequential bargaining models like those by Stahl (1972) and Rubinstein (1981) look very attractive for the study of international conflicts since they take into account the dynamics of the problem (even though the solution does not). There are, however, to our best knowledge so far no applications in the area considered here.

Fair division procedures are another wide field of game theoretic research, and by definition they serve normative purposes (although in serious conflicts they will at best provide some guidelines for political action). Raiffa (1982) discusses in detail the application of such a procedure to the Panama conflict in 1974, and Massoud (2000) has applied the so-called Adjusted Winner procedure to the conflict between Israelis and Palestinians.

Finally, there is the very large area of cooperative game theory dealing with coalitions which, however, is mathemati­cally demanding.

In the future, what are the challenges of the game theoretical approach to international conflict resolution that need to be met? Some of them, which are of a more technical nature, have already been mentioned above. Quite generally, as also demonstrated by our case studies, only relatively simple models have been used or developed in the field considered here. In other areas, like economics or, very specially, the verification of treaties and agreements, the art of using sophisticated game theoretic models is more advanced, and one might learn from this experience.

The simple models generally used in polit­ical science, together with the dearth of intro­ductory textbooks on game theory dealing seriously with real-world applications, have led to a considerable degree of misperception (see, for example, International Security, 1999). This misperception is perhaps best characterized by the question: “what can all of these graphs and equations tell us that can't be expressed just as well in simple language?” We hope that the case studies presented here help to answer this question and make it clear that it is simply not possible to understand or appreciate such a paradoxical situation as the prisoners' dilemma without resorting to the formalism of noncooperative game theory. Nor can one understand the consequences of incomplete or imperfect information in conflict situations without this formalism. It will certainly remain a challenge to convey this message to the political science community as a whole.

More importantly, however, is another challenge which Raiffa formulated in 1991 for the Processes of International Nego­tiations (PIN) Program of the Interna­tional Institute for Applied Systems Analysis (IIASA).

Regrettably, a lot of profound theorizing by economists, mathematicians, philosophers, and game theorists on topics related to negotiation analysis has had little or no impact on practice. An important question for the PIN Project to answer will be why this is so. An important reason is clearly the lack of effective communication and dissemination of theoretical research results. Such communication could be improved if there were more intermediaries who are comfortable in both worlds and who could act as inventive go- betweens to facilitate the transfer of information that shows how theory can influence practice and how practice can influence the research agendas of theorists. The information must flow in both directions; many practitioners have developed valid, extremely useful, and often profound insights and analyses, which should help to guide the agendas of researchers in this field.

We think that Raiffa's 1991 diagnosis and proposed therapy, applied to the more general field of resolving international conflicts, holds true today.