Data-informed modeling of the formation, persistence, and evolution of social norms and conventions

The paper defines the neighbor-averaged payoffs for a general 2×2 game A=[[a,b],[c,d]] (its Eq. (6)) and the coordination-game special case A=diag(1,1+α) (its Eq. (7)), then derives best-response updates xi(t+1)=1 iff the neighbor share exceeds a threshold 1/(2+α) (its Eq. (10)) and, in general, (a−c)/(a−c+d−b) (its Eq. (13)), concluding that any game with a>c and d>b is best-response equivalent to a coordination game with α=(d−b)/(a−c)−1. The candidate’s derivation reproduces exactly these steps and formulas and even notes tie-breaking and sign edge cases; the paper itself already addresses tie-breaking under best response and restricts to a>c and d>b, which ensures positivity and avoids degeneracy. Hence, both are correct and essentially the same proof, with consistent assumptions and thresholds (see the paper’s Eq. (5)–(13) discussion ).