Risk aversion can actually increase a bargainer's payoff in the Rubinstein bargaining game, contrary to previous beliefs. The study found that having a preference for avoiding risk can lead to higher payoffs for both players, even when they have different levels of risk aversion. This result challenges the idea that being more risk-neutral would result in smaller payoffs in this game. The findings were based on mathematical models that consider how players value future rewards and make decisions during the bargaining process.