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In this paper the weighted potential incomplete-profile games are studied. First a potential equation with algebraic form is established to check whether an incomplete-profile normal form game (IPNFG) is a weighted potential game with weight w > or not, based on which, the potential function can be constructed. Then the weighted potential subspace and the non-strategic subspace and some properties of weighted potential incomplete-profile games are obtained. Finally, an example is given to illustrate our theoretical results.