ANC Analytical Payoff Functions for Networks with Endogenous Bilateral Long Cheap Talk
We derive an almost non cooperative (ANC) analytical payoff function for all three-agent Aumann-Myerson (1988) games, and tractable ones exist for all three-agent A-M-like network games with any fixed valuation, in contrast to restricted results in the literature, if at all. Unlike link proposal game A-M and Myerson (1986), ANC has dynamic bilateral cooperation as we assume bilateral long cheap talk among three agents (differing from A-Hart (2003)), i.e., (1) pairs "smooth" Nash bargain during link discussions over credible expected payoffs induced by equilibria of a Nash demand-like game-where a link forms if the two agents match (2) double proposals, i.e., payoffs that sum up to their Myerson values in the prospective graph, and future bilateral coordination schemes. Thus, payoffs in the final graph of ANC yield a "variable Myerson value pair" which accounts for future possibilities of link formation. Instead, A-M has (a) "fixed" Myerson values (1977). In ANC, key (b) multiple equilibria in A-M-with conflicting requests of two agents to an indifferent third one-are solved, as coordination on requests by earlier linked pairs prevails if credible. This follows from (3) almost assuming that schemes are reminded chronologically "behind closed doors" as there is almost a natural first-mover advantage. (c) Inefficiency is possible in A-M, but not in ANC. We state some of the complete analytics for A-M. Also, in strictly superadditive games, only two-link graphs form. If only a link-coalition of two-forms then they achieve the grand coalition's worth
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