A Geometric Classification System for 2 × 2 Interval-Symmetric Games

Assessment of comparability among experimental game studies is aided by a two-dimensional geometric classification system for all 2 × 2 games which “look the same,” up to a linear transformation, to the two players. Each game is represented as a point on a plane whose two coordinates, r3 and r4, are readily calculated from the entries of the game matrix. Spatial location of the various games on the (r3, r4) plane is shown to be related to (a) the ordinal relationships among the payoffs, (b) the availability of alternation strategies, (c) the ordinal relationships among the joint outcomes, (d) the probability of a cooperative choice in the Prisoner's Dilemma, and (e) the set of perceived games which might arise from a given set of experimenter-defined payoffs for subjects attempting to maximize different linear combinations of own and other's payoffs. The system is easily adapted to classification of games on the basis of any interval-scale property of interest.