THE PRESENT ESSAY relates to the extensive discussion in the anthropological literature on the role of unilineal descent groups in politics, i.e. the theory of lineage systems (cf. Fortes I953). It is, however, concerned with the analysis of a divergent case: a political system in which ramifying patrilineal descent is of prominent importance in politics, yet where larger lineage groups do not emerge as corporate units.' The case analysed is the acephalous political system of the Yusufzai Pathans of the Northwest Frontier Province, Pakistan. To elucidate this case, it will be necessary to present considerable detail on their organization. This consists of field material, collected in the course of the year I954. Further material has been, and will be, published elsewhere (Barth I956; Mss). In the analysis of this data, I shall utilize some of the elementary concepts and procedures of the Theory of Games (cf. Neumann and Morgenstern I947; Stone I948), as well as the relevant anthropological theory relating to descent groups and corporate groups. The argument of the essay depends on a distinction between the purely structural arrangement of units defined by a unilineal descent charter, and the manner in which these units are made relevant in corporate action. In the description of lineage systems in the literature, this distinction is not often made. The analysis of the solidarity of unilineal descent groups usually relies on a Durkheimian conception of mechanical solidarity. In such a framework, solidarity derives from likeness. The descent charter defines a hierarchy of homologous groups, and thus directs the fusion of political interests within a merging series of such groups. This particular expression of the descent group charter has been incorporated into our whole conception of lineage organizations, as if it were a necessary derivative of the descent structure. The present case study describes a different political application of unilineal descent. Descent units are arranged in a recognizable manner by patrilineal genealogies, and hold joint rights to large territories. But close collaterals in the system do not join in corporate groups in opposition to more distant collaterals. The genealogical charter is none the less relevant to the structure of the corporate groups that do emerge; essentially, it defines rivals and allies in a system of two opposed political blocs. Closely related descent units are consistent rivals; each establishes a net of political alliances with the rivals of allies of their own rivals. In this fashion a pervasive factional split into two grand alliances of descent segments emerges, with close collateral segments consistently in opposite moieties. Clearly, though this is a unlineal descent system of a kind, the analysis of the internal solidarity of the political units which emerge can not be contained in a schema based on the concept of mechanical solidarity. Among the Yusufzai Pathans, the recruitment of corporate political units depends on the exercise of individual choices between alternative allegiances. Thus descent charters do not unequivocally define corporate units; these charters are made relevant to political action indirectly through their strategic implications for the choices of individuals. Therefore, the manner of recruitment of Pathan political groups can not be understood directly in terms of the descent system; it requires some analysis of the bases of individual choices and the sources of the internial solidarity of the groups which do emerge. The 'Theory of Games' is designed precisely for the analysis of such strategic choices, and will be utilized in the latter part of this essay. The essay thus falls roughly into three parts: I, a descriptive and comparative account of Yusufzai Pathan uniline al descent groups and political organization; II, an attempted analysis wof