Overlapping coalitions, bargaining and networks

We model the formation of coalitions that are not necessarily disjoint. We propose a new bargaining game that yields an overlapping coalition structure as an outcome. Equilibrium does not always exist in pure strategies for such a game, but we show that it always exists with a mild degree of mixed strategies. We derive conditions for a complete duality between networks and overlapping coalitions, and we provide a new rationale for the sequential formation of networks.