The Topology of Conflict and Co-operation

The class of simultaneous 2x2 pure-strategy ordinal games (which include well-known games such as Prisoner’s Dilemma, Chicken and Stag Hunt) have received considerable attention, including complete classification schemes by amongst others Rapoport & Guyer (1978) and Robinson & Goforth (2005). This paper focuses on a particularly pertinent subset of these games, described as the ‘Co-operate-Defect’ (C-D) games, which are characterised by each player having a dominant preference for a particular strategy by the other player. These games are therefore relevant in a number of contexts, including arms race games and collective action problems. The C-D games may be efficiently classified by assigning each player one of six distinct types, a classification that cannot be naturally extended to the full class of 2x2 games. The six types and the resulting game forms are analysed, and the subclass of CD games are identified within a topological structure for the 2x2 games devised by Robinson & Goforth (2005).