An Analytical Solution for Networks of Oldest Friends

Sequentially Nash Credible Joint Plans (SN) as in Nieva (February 2006) are shown to exist also whenever actions sets are infinite in a modification of all three-player Aumann-Myerson (1988) (A-M) bilateral link formation games. In contrast to A-M, binding transfers can occur if pairs match pairs of non negative payoff proposals out of the sum of their Myerson values (1977) in the prospective network. Pairs can also enunciate simultaneous negotiation statements about payoff-relevant play and bargain cooperatively over payoffs induced by tenable and reliable joint plans where the disagreement one suggests link rejection. A SN is for the most the one that suggests credibly−so followed through−the Nash solution in the bargaining game. In contrast to the bargaining network literature and the transfer game in Bloch and Jackson (2005), the one here is bilateral, sequential and has unique payoff predictions. In strictly superadditive cooperative games the complete graph never forms. The simple majority game yields the nucleolus in coalition structure