We propose a decentralized resource allocation scheme in the two-user multiple-input single-output interference channel. The mechanism is motivated by economic models which define equilibria in competitive settings. We model the situation between the links as a competitive market where the links are consumers, the transmission strategies are goods. In Walrasian equilibrium, the demand of each good equals the supply which constitutes an efficient operating point. For the two-user case, the Walrasian equilibrium and the corresponding prices can be computed in closed form. An arbitrator with perfect channel knowledge computes and distributes the Walrasian prices to the consumers (transmitters) which calculate in a decentralized manner their optimal demand (beamforming) of each good subject to their budget constraint (initial maximum ratio transmission solution). The Walrasian equilibrium is Pareto optimal and dominates the Nash equilibrium. Moreover, utilizing the conflict representation of the consumers in the Edgeworth box, we provide the closed-form solution to all Pareto optimal points for the two-user case.