The Selfishness Level of Social Dilemmas

A key contributor to the success of modern societies is humanity's innate ability to meaningfully cooperate. Game-theoretic reasoning shows however, that an individual's amenity to cooperation is directly linked with the mechanics of the scenario at hand. Social dilemmas constitute a subset of such scenarios where players are caught in a dichotomy between the decision to cooperate, prioritising collective welfare, or defect, prioritising their own welfare. In this work, we study such games through the lens of 'the selfishness level', a standard game-theoretic metric which quantifies the extent to which a game's payoffs incentivize self-directed behaviours. Using this framework, we derive the conditions under which SDs can be resolved and, additionally, produce a first-step towards extending this metric to Markov games. Finally, we present an empirical analysis indicating the positive effects of selfishness-level-directed mechanisms in such environments.