The article is devoted to the actualization of research on the family functions and forms in the context of the strategic interaction analysis in the marriage market under the conditions of the family institution transformation. Recent studies in this area show the transformation of the family internal organization and structure, the spread of marriage-like unions and so on. In this regard, it is necessary to actualize the basic family functions as a household in relation to: the multidirectional influence on the economic behavior of marital-specific capital; fulfilling the function of reducing uncertainty regarding the future family structure and organization through temporary partnership agreements; consideration of the spouses rational choice within the identification space framework of family relations they are included. A common formalized model of building a family is the stable marriage problem, but in the context of the noted family institution transformation, as well as the latest developments in the field of institutional grammar and design of mechanisms, it also should be rethought. This task has strict assumptions and describes the interaction in a single identification field and the algorithm acting on it. There is a possibility of to find a partner on various interaction «fields» were built on the basis of various institutional mechanisms, which is becoming more relevant nowadays because of decreasing transaction cost for «inclusion» and monitoring of alternatives. Accepting this assumption, a single agent in the marriage market may be included in several stable matches that correspond to different interaction «fields». Thus, the individual has a choice – which of the available matches to participate in (which field to play). In other words, the agent chooses a marriage partner while chooses an interaction field.