The aim of the present study was to test the extent to which groups manage to attain synergy (both strong and weak) in the context of multiparty systems. We also aimed to test the effects of power (budget size), and goal difficulty, alongside their interaction effect. We have used a behavioral multiparty simulation in which Romanian participants first negotiated individually and then, in the second stage, they were organized into groups and asked to engage in intergroup negotiations. Results showed that, in general, best negotiators outperform groups, yet groups obtain higher negotiation payoffs than the average payoff obtained by their members in the first negotiation stage, but only for dyads. Moreover, powerful stakeholders and those that have high goals end up with the highest payoff. Last, our results show that power accentuates the positive relationship between goal difficulty and payoffs. The results have important implications for delegating representatives to multiparty negotiations and for the management of power asymmetry in multiparty systems.