Toward a Topological Treatment of the Non-strictly Ordered 2× 2 Games
David Rodney Robinson, David Goforth, Matt Cargill · 2007
AbstractThe 2×2 games, the the simplest of all games, serve as the workhorsesof applied game theory. Robinson and Goforth[10] introduced a systematic,topologically-based treatment of the relations among the 144 2x2 strictlyordinal games, but there is no systematic general treatment that includesgames with ties. This paper introduces a systematic topologically-basedapproach to the the entire set of 1413 ordinal games. The nonstrictlyordinal 2×2 games are located relative to the strict-ordinal games, someproperties of the topological space are described and a small sampling ofobservations based on the method is provided. 1 Introduction to the Nonstrict Games 2 ×2 games are characterized by 8 numbers, and the space of 2 ×2 games istherefore an infinite 8-space. The most familiar classificat ion divides the spaceby restricting attention to games which differ ordinally. Relations among the 144strictly ordinal 2×2 games have been presented systematically in Robinson andGoforth [10] using a preference-based topology.