Hi everyone, this is a link to a new paper with Rajiv Vohra on "Nash bargaining with coalitional threats." Comments very welcome:
Abstract We axiomatically characterize bargaining outcomes in the presence of coalitional
threats. As in Nash’s solution, these involve the product of payoffs net of disagreement
points, but coalitional threats appear as conventional constraints, and are not netted out
from payoffs as disagreement points are. This asymmetry is implied by a new “expansion
axiom” (along with standard axioms), one that is automatically satisfied in the standard
bargaining problem. We then endogenize coalitional threats using internal consistency, requiring coalitions to be constrained by their subcoalitions just as the grand coalition is. For
games with convex payoff sets, this consistent solution coincides with one in which the
only threat from each coalition is their “standard” Nash solution, unconstrained by subcoalitions. For transferable-utility games, this observation uncovers a connection between
the coalitional solution and the egalitarian solution of Dutta and Ray (1989, 1991).