Evolutionary governance of water infrastructure ppps under interval grey information: Robust dynamics of monitoring and opportunism

Water-infrastructure public–private partnerships combine long-duration public-service obligations with incomplete knowledge about governance costs, opportunistic gains, enforcement consequences, and the public-loss implications of hydrological-risk exposure. This study develops a two-population evolutionary game in which government decision makers choose routine governance or enhanced monitoring and private participants choose cooperative performance or opportunistic behavior. Interval grey numbers represent defensible epistemic bounds, while conventional worst-case inequalities establish robust stability over the resulting sets. The reformulated payoff mechanism embeds water risk through public loss, separates latent trust from observable choices, and evaluates all four boundary rest points. Under the maintained assumption that c>0, RC, RO, and MO have nonempty strict stability regions, whereas MC is unstable; the model also yields an interior center. A separable first integral proves that regular interior level sets are closed orbits; the center is not a convergent state. The computational analysis covers 16 effective-box vertices, 50,000 independent-box observations, five linked designs based on a shared 50,000-row whitening sample, and 336 sensitivity cells. In the independent coverage sample, 27,689 rows exhibit the interior center, whereas the midpoint classification disagrees with 22,311 rows (coverage share 0.44622). Positive affine linkage reduces disagreement and improves several worst-case margins, but every baseline robust margin remains negative, so no strict robust regime holds over the full admissible set. The contribution is a water-specific, analytically proved, and reproducibly computed framework that distinguishes grey epistemic representation from robust-set mathematics and supports conditional governance implications tied to named parameters and interval bounds.