Utilizing the real-valued parametrization of each transmitter’s efficient beamforming vectors, we propose a decentralized resource allocation scheme in the multiple-input single-output interference channel. The scheme is motivated by bargaining concepts in game theory. The aim of these concepts is to improve the joint payoff of the users from the Nash equilibrium outcome. In each bargaining-step, each user proposes a strategy. A user accepts any proposal if it increases his payoff. Otherwise, new proposals are made. When all proposals are accepted, a new bargaining-stage begins. We prove the scheme’s convergence and demonstrate its performance by simulations. In comparison to previous approaches, our bargaining outcome is arbitrarily close to the Pareto boundary of the achievable single-user rate region. We further discuss the control overhead and complexity of this scheme.