Conditional investment strategy in evolutionary trust games with repeated group interactions

The paper numerically analyzes the full mutation–selection Markov chain via an MDP approach and consistently finds that an intermediate threshold M yields high T and CI with U suppressed, while extremal thresholds M=0 or M=N tilt outcomes toward U; these findings are documented in the text around Figs. 2–4 and the robustness sweeps (µ, β, RU, N) . The candidate solution gives a complementary small-mutation, strong-selection analytical justification using a three-state embedded chain on {T, CI, U} that reproduces the same qualitative orderings under open parameter sets. The approaches differ (full MDP vs. rare-mutation reduction), but their conclusions agree with the paper’s claims and figures.