Game dynamics have been widely used as learning and computational tool to find evolutionarily stable strategies. Nevertheless, most of the existing evolutionary game dynamics, i.e., the replicator. Smith. projection, Brown-Von Neumann-Nash, Logit and best response dynamics have been analyzed only in the unconstrained case. In this work, we introduce novel evolutionary game dynamics inspired from a combination of imitation dynamics. The proposed approach is able to satisfy both upper- and lower-bound constraints. Moreover, dynamics have asymptotic convergence guarantees to a generalized-evolutionarily stable strategy. We show important features of the proposed game dynamics such as the positive correlation and invariance of the feasible region. Several illustrative examples handling population state constraints are provided. (C) 2018 Elsevier Ltd. All rights reserved.