A taxonomy of all ordinal 2 � 2 games

Abstract

The 2 • 2 game is the simplest and most commonly employed representation of strategic conflict. The 78 strict ordinal 2 x 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 x 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.

Fuzzy Preferences in the Graph Model for Conflict Resolution

“…The Sustainable Development conflict (Hipel, 2002) is a 2 × 2 game having two DMs or players each of whom has two options or strategies (Kilgour and Fraser, 1988;Fraser and Kilgour, 1986;Rapoport et al, 1976). One DM represents the environmental agencies (ENV) and the other potential developers (DEV).…”

Resistance to Change in Recent Italy: Some Elements for a Theoretical Framework

“…We hereby focus on parallel games only, as in our opinion, they are particularly effective in revealing how and why the relationship among certain subjects is implemented only in case of multiple strategic situations. The 2 x 2 simultaneous ordinal games based on pure strategy are 726 (Kilgour and Fraser, 1988). Only 78 of them are ordinally different, meaning that all payoffs vary (Rapoport and Guyer, 1967;Robinson and Goforth, 2005).…”

Names for Games: Locating 2 × 2 Games

“…Several researchers have noted the payoff structure of the interesting Low Dilemma game that lies between Chicken and Prisoner's Dilemma [9,24], however it does not seem to have an established name. This game illustrates the limitations of dominant strategies as a solution concept, since they would lead to the unsatisfactory result of both getting the worst outcome.…”

“…However, the complete set of 38 symmetric ordinal games does not appear to have been previously published in normal form matrices, as shown in the lower section of Figure 1, including the 26 strategically distinct 2 × 2 symmetric ordinal games with ties. Games with ties can be categorized according to the number and type of ties [9,10]. In addition to the strict games with no ties, games may have two ties for the lowest, middle, or highest payoffs; two pairs of ties; three ties for highest or lowest payoffs; or all ties.…”

“…Kilgour and Fraser noted that little attention had been paid to games with ties (non-strict), in part due to the large number of such games. In addition to strict games without ties, there are seven possible types of ties, creating eight preference orderings [8][9][10]. Fraser and Kilgour used a computer program to enumerate the complete set of 2 × 2 ordinal games and analyze their properties.…”