In this paper, we address the case where two microgrids are isolated from the main power grid but can exchange energy with each other in a peer-to-peer (P2P) manner. The goal is to minimize the total cost resulting from energy generation and transportation, while each microgrid satisfies its local power demand. We first propose a centralized solution. In this approach, a central controller must have access to all the information. For those situations where privacy must be protected, we propose a distributed approach, in which each microgrid solves a local optimization problem in an iterative fashion by exchanging some information with the other one.