The 2-player, 2-strategy, strictly ordinal, normal form games were originally studied by Anotol Rapoport and Melvyn Guyer in a paper entitled A Taxonomy of 2x2 Games. Their paper appeared in 1966 and included an exact count, an enumeration (that is, a complete listing), and a taxonomy of such games. Since then it has been known that there are 78 such games. If we allow each player access to one additional strategy, however, the number of games explodes to nearly two billion. In this paper we compute the exact number of 2-player, 3-strategy, strictly ordinal, normal form games.

Author Bio

Austin Williams is a student of mathematics at Portland State University. This paper is the result of his undergraduate honors thesis project which he finished during the Spring 2011 academic term. He is now a graduate student working towards an MS in Mathematics. His academic interests include graph theory, algebra, number theory, combinatorics, game theory, complexity theory, and financial mathematics. When he's not doing math he enjoys day hikes with his wife, Niki.