Abstract: Competing firms and network users often negotiate in order to reach a satisfactory compromise. Such situations are mathematically modeled as conflicts where the disagreement vector is considered as the penalty of not reaching an agreement. If this penalty tends to infinity, then the one-step solutions (Szidarovszky, 2001) are convergent. This limit can be obtained by solving a monotonic equation of a single variable. The result shows that the relative power index of any player and his/her relative share form the penalty are interchangeable at the limit.