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We investigate monogamy relations and upper bounds for generalized $W$-classstates related to the R\'{e}nyi-$\alpha$ entropy. First, we present ananalytical formula on R\'{e}nyi-$\alpha$ entanglement (R$\alpha$E) andR\'{e}nyi-$\alpha$ entanglement of assistance (REoA) of a reduced densitymatrix for a generalized $W$-class states. According to the analytical formula,we show monogamy and polygamy relations for generalized $W$-class states interms of R$\alpha$E and REoA. Then we give the upper bounds for generalized$W$-class states in terms of R$\alpha$E. Next, we provide tighter monogamyrelations for generalized $W$-class states in terms of concurrence andconvex-roof extended negativity and obtain the monogamy relations forR$\alpha$E by the analytical expression between R$\alpha$E and concurrence.Finally, we apply our results into quantum games and present a new bound of thenonclassicality of quantum games restricting to generalized $W$-class states.

Monogamy relations and upper bounds for the generalized $W$-class states using R\'{e}nyi-$\alpha$ entropy