Brams was a co-discoverer, with Alan Taylor, of the first envy-free cake-cutting solution for n people.[3]
Previous to the Brams-Taylor procedure, the cake-cutting problem had been one of the most important open problems in contemporary mathematics.[4] He is co-inventor with Taylor of the fair-division procedure, adjusted winner,[5] which was patented by New York University in 1999 (# 5,983,205).[6]
Brams has applied game theory to a wide variety of strategic situations, from the Bible[7][8] and theology [9] to international relations [10][11] to sports.[12][13]
Game Theory and Politics. New York: Free Press, 1975. Rev. ed., 2004 (Dover).
Paradoxes in Politics: An Introduction to the Nonobvious in Political Science. New York: Free Press, 1976.
The Presidential Election Game. New Haven, CT: Yale University Press, 1978. Rev. ed., 2008 (A K Peters).
Co-edited with A. Schotter and G. Schwödiauer, Applied Game Theory: Proceedings of a Conference, Vienna, 1978. Würzburg, Germany: Physica-Verlag, 1979.
Biblical Games: Game Theory and the Hebrew Bible. Cambridge, MA: MIT Press, 1980. Rev. ed., 2003 (MIT Press). Japanese and Russian translations, 2006.
Co-edited with William F. Lucas and Philip D. Straffin, Jr., Modules in Applied Mathematics: Political and Related Models, vol. 2. New York: Springer-Verlag, 1983.
Co-authored with Peter C. Fishburn, Approval Voting. Cambridge, MA: Birkhäuser Boston, 1983. Rev. ed., 2007 (Springer).
Superior Beings: If They Exist, How Would We Know? Game-Theoretic Implications of Omniscience, Omnipotence, Immortality, and Incomprehensibility. New York: Springer-Verlag, 1983. Rev. ed., 2007 (Springer).
Superpower Games: Applying Game Theory to Superpower Conflict. New Haven, CT: Yale University Press, 1985.
Rational Politics: Decisions, Games, and Strategy. Washington, DC: CQ Press, 1985. Reprinted by Academic Press, 1989.
Co-authored with D. Marc Kilgour, Game Theory and National Security. New York: Basil Blackwell, 1988. Spanish translation, 1989.
Negotiation Games: Applying Game Theory to Bargaining and Arbitration. New York: Routledge, 1990. Rev. ed., 2003.
Theory of Moves. Cambridge, UK: Cambridge University Press, 1994.
Co-authored with Alan D. Taylor, Fair Division: From Cake-Cutting to Dispute Resolution. Cambridge, UK: Cambridge University Press, 1996.
Co-authored with Alan D. Taylor, The Win-Win Solution: Guaranteeing Fair Shares to Everybody. New York: W. W. Norton, 1999. Japanese, Portuguese, and Spanish translations, 2000; Chinese, Korean, and Russian translations, 2002.
Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures. Princeton, NJ: Princeton University Press, 2008.
Co-edited with William V. Gehrlein and Fred S. Roberts. The Mathematics of Preference, Choice, and Order: Essays in Honor of Peter C. Fishburn. Berlin: Springer, 2009.
Game Theory and the Humanities: Bridging Two Worlds. Cambridge, MA: MIT Press, 2011.
Divine Games: Game Theory and the Undecidability of a Superior Being. Cambridge, MA: MIT Press, 2018
^Brams, Steven J.; Taylor, Alan D. (1995). "An Envy-Free Cake Division Protocol". The American Mathematical Monthly. 102 (1). Mathematical Association of America: 9–18. doi:10.2307/2974850. ISSN1930-0972. JSTOR2974850.
^Brams, Steven J.; Ismail, Mehmet S.; Kilgour, D. Marc; Stromquist, Walter (2018-10-21). "Catch-Up: A Rule That Makes Service Sports More Competitive". The American Mathematical Monthly. 125 (9). Informa UK Limited: 771–796. arXiv:1808.06922. doi:10.1080/00029890.2018.1502544. ISSN0002-9890. S2CID4691445.