An ANC Payoff Function for Networks with Sequentially Nash Coherent Plans

Abstract

I add endogenous bargaining possibilities do develop criteria to determine which statements are credible in a three-player model with complete information where pairs, in a sequential order, can formulate simultaneous negotiation statements. Joint plans are credible if they are the outcome of a plan Nash bargaining problem-the pair bargains cooperatively over the equilibrium payoffs induced by tenable and reliable plans-unless one or both bargainers are indifferent to bargaining. Then, a credible plan is up to the future-request by the oldest pair ("of friends") among the past pairs that successfully cooperated and included one of the indifferent players. I interpret this model as an almost non cooperative (ANC) modification of the three-player Aumann-Myerson (1988) sequential network formation game. Whenever discussing a link two players can bargain non cooperatively out of the sum of their Myerson values (1977) in the prospective network and enunciate simultaneous negotiation statements. The disagreement plan suggests link rejection. Sequentially Nash (1950) coherent plans can be defined and exist. Analytical payoffs are unique. In strictly superadditive cooperative games the complete graph never forms.