Abstract
The 2 × 2 game is the simplest and most commonly employed representation of strategic conflict. The 78 strict ordinal 2 × 2 games have been used as conflict models extensively, and have been related in several different taxonomies. However, interest has recently focussed on the full set of 726 general ordinal games, in which one or both players may have equal preferences for two or more outcomes. This paper describes the development of a practical taxonomy of all 726 ordinal 2 × 2 games. The taxonomy provides for rapid identification of particular games, gives a convenient ordering, is as consistent as possible with previous work, and yet is not tied to any specific solution concepts. As well, definitions of several significant game properties are developed or extended to general ordinal games and applied in conjunction with the taxonomy.
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Bibliography
Axelrod, R.: 1984, The Evolution of Cooperation, Basic Books, New York.
Brams, S. J.: 1985, Superpower Games: Applying Game Theory to Superpower Conflicts, Yale University Press, New Haven CT.
Brams, S. J.: 1977, ‘Deception in 2 × 2 games’, Journal of Peace Science 2, 171–203.
Brams, S. J. and M. D. Davis: 1983, ‘The verification problem in arms control: A game theoretic analysis’, in Interaction and Communication in Global Politics, ed. C. Cioffi-Revilla, R. L. Merritt, and D. A. Zinnes, Sage Press, London, 133–154.
Brams, S. J. and D. M. Kilgour: 1986, ‘Notes on Arms Control Verification: A Game-Theoretic Analysis’, in Modeling and Analysis of Arms Control Problems, ed. R. Avenhaus, R. K. Huber and J. D. Kettelle, Berlin: Springer-Verlag, 409–420.
Fraser, N. M. and D. M. Kilgour: 1986a, ‘Nonstrict ordinal 2 × 2 games: A comprehensive computer-assisted analysis of the 726 possibilities’, Theory and Decision 20, 99–121.
Fraser, N. M. and D. M. Kilgour: 1986b, ‘General ordinal 2 × 2 games’, Technical Report # 172, Department of Management Sciences, University of Waterloo, Waterloo, Ontario, Canada.
Friedman, J.W.: 1984, ‘On characterizing equilibrium points in two person strictly competitive games’, International Journal of Game Theory 12, 245–247.
Guyer, M. and H. Hamburger: 1968, ‘A Note on a “Taxonomy of 2 × 2 games”’, General Systems 13, 205–208.
Kalevar, C. K.: 1975, ‘Metagame taxonomies of 2 × 2 games’, General Systems 20.
Rapoport, A.: 1967, ‘Exploiter, leader, hero, and martyr: The four archetypes of the 2 × 2 Game’, Behavioral Science 12, 81–84.
Rapoport, A. and A. M. Chammah: 1965, Prisoner's Dilemma, University of Michigan Press, Ann Arbor.
Rapoport, A. and A. M. Chammah: 1966, ‘The game of Chicken’, American Behavioral Scientist 10, 23–28.
Rapoport, A. and M. J. Guyer: 1966, ‘A taxonomy of 2 × 2 games’, General Systems 11, 203–214.
Rapoport, A., M. J. Guyer and D. G. Gordon: 1967, The 2 × 2 Game, University of Michigan Press, Ann Arbor, MI.
Snyder, G. H.: 1971, ‘Prisoner's dilemma and chicken models in international politics’, International Studies Quarterly 15, 97.
Snyder, G. H. and P. Diesing: 1977, Conflict Among Nations, Princeton University Press, Princeton, NJ.
Von Neumann, J. and O. Morgenstern: 1953, Theory of Games and Economic Behavior, 3rd edition. Princeton University Press, Princeton, NJ.
Zagare, F. C.: 1981, ‘Non-myopic equilibria and the Middle East Crisis of 1967’, Conflict Management and Peace Science 5, 139–162.
Zagare, F. C.: 1985, ‘The pathology of unilateral deterrence’, in Dynamic Models of International Conflict, M. D. Ward and U. Luterbacher, eds., Lynne Rienner, Boulder, CO.
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Kilgour, D.M., Fraser, N.M. A taxonomy of all ordinal 2 × 2 games. Theor Decis 24, 99–117 (1988). https://doi.org/10.1007/BF00132457
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DOI: https://doi.org/10.1007/BF00132457