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]
^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.