Cautious Farsighted Stability in Network Formation Games with Streams of Payoffs

We propose a new notion of farsighted pairwise stability for dynamic network formation which includes two notable features: consideration of intermediate payoffs and cautiousness. This differs from existing concepts which typically consider either only immediate or final payoffs, and which often require a certain amount of optimism on the part of the players in any environment without full communication and commitment. We show that for an arbitrary definition of preferences over the process of network formation, a non-empty cautious path stable set of networks always exists, and provide a characterisation of this set. Strongly efficient networks do not always belong to a cautious path stable set for a common range of preference specifications. But if there exists a Pareto dominant network and players value payoffs in a final network most, then this Pareto dominant network is the unique prediction of the cautious path stable set. Finally, in the special case where players derive utility only from a final network, we establish some relationships between cautious path stability and a number of other farsighted concepts, including the pairwise farsightedly stable set, von Neumann-Morgenstern pairwise farsightedly stable set and largest pairwise consistent set.