Equitable and efficient allocation is one of the basic principles in all energy management systems. Classic allocation methods tend to maximize the customers' total surplus to achieve the maximum possible efficiency. From the perspective of equity, there are some elements of ambiguity in this approach, In this paper, a new approach is proposed to allocate consumed energy to the customers aimed at holding equity, while achieving maximum possible efficiency is taken into account. For this purpose, the energy consumption allocation is studied for a cluster of interconnected price-responsive demands (i.e., a group of loads, such as an industrial compound, which are interconnected to each other in a geographical area and also to the main network via a local electrical network). A centralized energy management for a cluster of members is a cooperative game. In this paper, the equilibria of the cooperative game are determined by solving a multi-objective optimization problem, constrained to the constraints of the local electrical network operation and also the demands constraints. The solution of this optimization problem results in a Pareto front of which each point represents an equilibrium of the cooperative game. Then, an equilibrium is selected based on the proposed equitable allocation. The nature of the proposed model is a bi-level optimization problem. In the first level, the optimization problem of selecting an equilibrium is formulated. In the second level, a multi-objective optimization problem is modeled to calculate all equilibria of the cooperative game. Accordingly, the energy consumed by demands is allocated through the proposed centralized energy management system which is established based on equity and efficiency. The results obtained from a test system show the advantages of the model in performing energy management for a cluster of price-responsive demands.