Nash bargaining and risk aversion

It is widely accepted among axiomatic bargaining theorists that if one bargainer is more risk averse than a second, the second will be a tougher bargaining opponent than the first against all opponents. We argue that this relationship between risk aversion and bargaining toughness is both highly fragile, and more nuanced than previously articulated. In the Nash and Kalai-Smorodinsky bargaining frameworks, we establish that when a bargainer is compared with a second who is "almost globally" more risk averse than the first, the supposedly immutable relationship between bargaining effectiveness and risk aversion evaporates. Specifically, we identify an upper-hemicontinuity failure of a correspondence which maps the power set of all lotteries to those utility pairs that satisfy our "almost global" comparative risk aversion relation on these subsets. We trace the consensus view that tougher bargainers are less risk-averse to an exclusive focus on precisely the point at which this correspondence implodes