In Formula 1, race strategies are adapted according to evolving race conditions and competitors' actions. This paper proposes a reinforcement learning approach for multi-agent race strategy optimization. Agents learn to balance energy management, tire degradation, aerodynamic interaction, and pit-stop decisions. Building on a pre-trained single-agent policy, we introduce an interaction module that accounts for the behavior of competitors. The combination of the interaction module and a self-play training scheme generates competitive policies, and agents are ranked based on their relative performance. Results show that the agents adapt pit timing, tire selection, and energy allocation in response to opponents, achieving robust and consistent race performance. Because the framework relies only on information available during real races, it can support race strategists' decisions before and during races.