Linearly-Additive Decomposed 2 × 2 Games: A Primer for Research

2 × 2 games (such as the Prisoner’s Dilemma) are economic games for studying cooperation and social decision-making. Linearly-additive decomposed games are variants of 2 × 2 games that can change the framing of the game and thereby provide researchers with additional flexibility for measuring preferences and social cognition that would not be possible with standard (matrix-form) 2 × 2 games. In this paper, we provide a systematic overview of linearly-additive decomposed 2 × 2 games. We show which 2 × 2 games can be decomposed in a linearly-additive way and how to calculate possible decompositions for a given game. We close by suggesting for which experiments decomposed games might be more conducive than matrix games.