TL;DR: In this article, it was shown that the bargaining power depends on the intensity of the agent's certainty effect (measured by the derivative at the point one of his probability perception function).
Abstract: The Axiomatic bargaining theory (Nash [1950]) has been developed in the Expected Utility (EU) Paradigm. Nevertheless in this latter, two bargainers with the same marginal utility must have the same risk aversion and therefore the same bargaining power. We show that, when the Risk Preferences are non-EU, the bargaining power depends on the intensity of the agent's certainty effect (measured by the derivative at the point one of his probability perception function).