Integrating Strategic Properties with Social Perspectives: A Bipartite Classification of Two-by-Two Games

Classifying games according to their strategic properties provides meaningful insights into the motivations driving the interacting parties, suggests possible future trajectories, and in some cases also points to potential interventions aiming to influence the interactions’ outcomes. Here, we present a new classification that merges two perspectives: (i) a revised version of Rapoport and Guyer’s taxonomy, which extends beyond the original 78 games they describe by classifying all two-by-two games according to fundamental strategic properties, and (ii) a novel classification grounded in the theory of subjective expected relative similarity, which addresses not only the games’ payoffs but also the players’ strategic perceptions of their opponents. While Rapoport and Guyer’s original taxonomy classifies only strictly-ordinal games, the revised classification addresses all two-by-two games. It comprises eleven categories that are further grouped into five super-categories that focus on the game’s expected outcome and its strategic stability. The second, similarity-based, classification comprises four main categories, specifying whether players’ perceptions of their opponents have the potential to influence strategic decision-making. The merged classification comprises 14 game types, offering a holistic account of the strategic interaction, the players’ underlying motivations, and the expected outcome. It combines the fixed strategic properties with the variable social aspects of the interaction. Moreover, the novel classification points to the potential of social interventions that may influence the game’s outcome by altering strategic similarity perceptions. Therefore, the present work is relevant for both theoretical and experimental research, providing insights into actual choices expected inside and outside of the laboratory.