Brams - Game theory and politics

Davis, Morton D. Game Theory: A Nontechnical Introduction. New York: Basic Books, 1970.

As its subtitle implies, this book uses almost no mathematics. Yet it offers a rather sophisticated treatment of the subject matter of game theory and also contains many provocative (though mostly hypothetical) examples.

McDonald, John. Strategy in Poker, Business and War. New York: W. W. Norton & Co., 1950.

The first popular treatment of game theory, which also includes a discussion of games of chance, viz., poker; contains some delightful illustrations.

Rapoport, Anatol. Fights, Games, and Debates. Ann Arbor, Mich.: University of Michigan Press, 1960.

About one-third of this book is devoted to a discussion, with examples, of elementary game theory. The contrast between games, on the one hand, and fights and debates on the other, provides a useful perspective on different approaches that have been used to study cooperation and conflict in social situations.

Shubik, Martin (ed.). Game Theory and Related Approaches to Social Behavior. New York: John Wiley & Sons, 1964.

A rather diffuse collection of articles containing a useful expository essay by the editor.

Singleton, Robert R., and William F. Tyndall. Games and Programs: Mathematics for Modeling. San Francisco: W. H. Freeman, 1974.

Includes a description of the relationship between game theory and linear programming.

Farquharson, Robin. Theory of Voting. New Haven, Conn.: Yale University Press, 1969.

An elegant treatment of strategic voting that is marred by numerous errors. Many details are omitted from the analysis, making its appearance deceptively simple.

Luce, R. Duncan, and Howard Raiffa. Games and Decisions: Introduction and Critical Survey. New York: John Wiley & Sons, 1957.

A superb treatment of applied game theory and related topics, though now somewhat dated.

Rapoport, Anatol (ed.). Game Theory as a Theory of Conflict Resolution.

Dordrecht-Holland: D. Reidel Publishing Co., 1974.

Although this volume contains some purely mathematical contributions, theyalong with the more empirically oriented articlesraise questions of an applied nature relevant to the study of real-life conflicts and their resolution.

Rapoport, Anatol. N-Person Game Theory: Concepts and Applications.

Ann Arbor, Mich.: University of Michigan Press, 1970.

Rapoport, Anatol. Two-Person Game Theory: The Essential Ideas. Ann Arbor, Mich.: University of Michigan Press, 1966.

Both books are characterized by a strenuous effort on the part of the author to explain verbally the intuitive meaning of mathematical concepts.

Rapoport, Anatol, and Albert M. Chammah. Prisoners Dilemma: A Study in Conflict and Cooperation. Ann. Arbor. Mich.: University of Michigan Press, 1965.

A review of mathematical and empirical research up to 1965 on game theorys most famous game.

Riker, William H. The Theory of Political Coalitions. New Haven, Conn.: Yale University Press, 1962.

The first major application of n -person game theory in political science and now a modern classic that has stimulated numerous subsequent studies.

Schelling, Thomas C. The Strategy of Conflict. Cambridge, Mass.: Harvard University Press, 1960.

A critique of classical game theory with suggestions for its reorientation, especially as applied to the analysis of bargaining in international relations.

Burger, Ewald. Introduction to the Theory of Games, translated by John E. Freund. Englewood Cliffs, N.J.: Prentice-Hall, 1963.

Good coverage of most major topics.

Dresher, Melvin. Games of Strategy: Theory and Applications. Englewood Cliffs, N.J.: Prentice-Hall, 1961.

Contains several well-developed examples relevant to the study of defense and military strategy.

Howard, Nigel. Paradoxes of Rationality: Theory of Metagames and Political Behavior. Cambridge, Mass.: MIT Press, 1971.

A major extension of classical game theory with applications to the study of international conflict.

Owen, Guillermo. Game Theory. Philadelphia: W. B. Saunders Co., 1968.

A widely used mathematics textbook.

Parthasarathy, T., and T. E. S. Raghavan. Some Topics in Two-Person Games. New York: American Elsevier Publishing Co., 1971.

The best modern treatment of two-person game theory.

von Neumann, John, and Oskar Morgenstern. Theory of Games and Economic Behavior. Princeton, N.J.: Princeton University Press, 1944, 1947, 1953.

The classic study, for which perseverance pays; remarkable in its breadth and depth of coverage, especially as the original work in the field.

Most discussions of game theory in the international relations literature hardly go beyond a presentation of a few hypothetical examples used in general expository treatments of the subject. Although some vague analogies are usually drawn to situations of conflict and cooperation in international relations, there seems to be little in the substance of international relations that has inspired rigorous applications of the mathematics of game theory. An exception is the considerable work (some classified) that has been done on specific problems related to the use and control of weapons systems (e.g., targeting of nuclear weapons, violation of arms inspection agreements, search strategies in submarine warfare), but these are not problems of general strategic interest.

Given this dichotomy between general but vague and rigorous but specialized studies in international relations, we shall try to tread a middle ground in our discussion of applications. At a mostly informal level, we shall indicate with several real-life examples the relevance of game-theoretic reasoning to the analysis of different conflict situations in the international arena. At a more formal level, we shall develop some of the mathematics and prove one theorem in two-person game theory that seem particularly pertinent to the identification of optimal strategies and equilibrium outcomes in international relations games.