Coupling injunctive social norms with evolutionary games

Human behaviors are strongly influenced by social norms. This work couples injunctive social norms with evolutionary games. Injunctive norms refer to behaviors which individuals should conform to and thereby entail social pressure to adhere to a particular action. Here we investigate impact of such social norms on both pairwise and multi-player games. It is shown that injunctive norms can enforce the system to either extreme, meaning that they give rise to the possibility of bi-stability (two stable equilibrium states) in evolutionary games. We derive the condition for such bi-stability in the mean-field limit. While investigating pairwise games with social norms, we observe that —besides other possibilities—Prisoner's dilemma (PD), snow-drift (SD), and Trivial (TR) games may experience the bi-stability like the stag-hunt (SH) game. Interestingly, SD game with social norms exhibits four possible asymptotic outcomes: all-cooperation (AllC), all-defection (AllD), either AllC or AllD (bi-stable), and coexistence. However, its multi-player variant does not manifest a unique coexistence equilibrium. Moreover, it demonstrates another bi-stable equilibrium, comprising either coexistence or AllC, besides other outcomes observed in the two-player case. Conversely, PD and its multi-player variant, i.e., public goods game with injunctive norms show identical evolutionary outcomes (AllD or bi-stable).