Evolutionary Thresholds in Kantian Optimization: A Sign Correction to Chapter 8 of How We Cooperate

Chapter 8 of Roemer’s How We Cooperate claims that a stable interior population composition of Kantian and Nash types can emerge when coordination and prisoner’sdilemma games occur with positive probabilities. This comment identifies a sign reversal in the stability calculation. Under Roemer’s stated parameter restrictions, his payoff equations imply that the Kantian fitness advantage is strictly increasing in the Kantian population share, whereas equation (8.15) uses the corresponding negative derivative. The purported attracting interior state is repelling under Roemer’s adjustment rule itself and under any positive, locally regular rescaling of that rule. Under the standard two-type replicator equation, the corrected fixed-action model has either global attraction to the all-Nash boundary or bistability separated by an unstable critical mass. The pure-coordination threshold is the endpoint of these dynamics and coincides with the mixed-equilibrium threshold of the underlying coordination game.