Domains of social choice functions on which coalition strategy-proofness and Maskin monotonicity are equivalent

It is known that on some social choice and economic domains, a social choice function is coalition strategy-proof if and only if it is Maskin monotonic (e.g. Muller, E., and Satterthwaite, M., (1977). The equivalence of strong positive association and strategy-proofness. J. Econ. Theory, 14 pp412–18.). This paper studies the foundation of those results. I provide a set of conditions which is sufficient for the equivalence between coalition strategy-proofness and Maskin monotonicity. This generalizes some known results.