The game of Matching Embeddings is stated as an extension and a generalization of such well known games as Matching Pennies and Rock{Paper{Scissors. Various variants of the game of Matching Embeddings are considered both as multi-objective and in nite strategy games. Formally, the payo matrix of the game of Matching Embeddings is de ned similar with the de nition of the payo matrix in the games of Matching Pennies and Rock{Paper{Scissors. As the game of Matching Embeddings is appropriate geometricaly to problems of set nesting/embedding [2], it may be solved by similar special algorithms [3, 4] and approaches [1] when the objective functions are linear and strategy sets are convex polyhedral sets. As a consequence of mentioned anities, the properties of the game may be stated and proved, as well the approaches to nd strategic equilibria may be developed.