This study proposes a novel energy management strategy for residential neighborhoods that enables peer-to-peer energy transactions among households without the need for energy storage or distributed generation. The proposed strategy is based on a Mixed-Integer Linear Programming (MILP) optimization model that minimizes the overall cost per household, including energy consumption cost, flexibility procurement cost, flexibility selling gain, and penalty cost caused by exceeding the limits. The strategy aims to optimize the energy consumption and production patterns of households with just inverter-based air conditioner loads, while also ensuring that the overall load limit for the neighborhood is not exceeded during certain periods. The results of the MILP-based optimization model demonstrate that the proposed strategy can significantly reduce the overall cost per household, providing a more efficient and cost-effective energy system for residential neighborhoods. The strategy utilizes a flexible energy trading platform, with a pricing mechanism designed to incentivize households to optimize their energy consumption and production patterns and support the transition to a low-carbon energy future.