A taxonomy of all ordinal 2 × 2 games

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.