In multi-agent reinforcement learning, the behaviors that agents learn in a single Markov Game (MG) are typically confined to the given agent number. Every single MG induced by varying population sizes may possess distinct optimal joint strategies and game-specific knowledge, which are modeled independently in modern multi-agent algorithms. In this work, we focus on creating agents that generalize across population-varying MGs. Instead of learning a unimodal policy, each agent learns a policy set that is formed by effective strategies across a variety of games. We propose Meta Representations for Agents (MRA) that explicitly models the game-common and game-specific strategic knowledge. By representing the policy sets with multi-modal latent policies, the common strategic knowledge and diverse strategic modes are discovered with an iterative optimization procedure. We prove that as an approximation to a constrained mutual information maximization objective, the learned policies can reach Nash Equilibrium in every evaluation MG under the assumption of Lipschitz game on a sufficiently large latent space. When deploying it at practical latent models with limited size, fast adaptation can be achieved by leveraging the first-order gradient information. Extensive experiments show the effectiveness of MRA on both training performance and generalization ability in hard and unseen games.