In this paper, we focus on the cost of data centers in transmission and computation. Unlike previous research, we study it in a distributed, non-cooperative environment. An M/M/1 queueing model is established to characterize the task transmission. Because of the multi-core processors, we set an M/M/C queueing model to characterize the task computation. We consider the problem from the perspective of game theory and formulate it into a non-cooperative game among multi-agents in which each agent is informed with incomplete information (allocation strategy) of other agents. For each agent, we define a function of the expected cost of tasks as disutility function, and minimize the value subject to the QoS constraints. We analyze the existence of Nash equilibrium and develop a Greedy Energy-aware Algorithm (GEA) to choose active servers using the Limit Searching Algorithm (LSA) to find the ceiling utilization. Then we propose a Best Response Algorithm (BRA) to optimize the utility function. The convergence of the BRA algorithm has been discussed. Finally, the results demonstrate that the BRA algorithm can get a solution close to Nash equilibrium and reach it quickly.

Many real-world applications can be described as large-scale games of imperfect information, which require extensive prior domain knowledge, especially in competitive or human–AI cooperation settings. Population-based training methods have become a popular solution to learn robust policies without any prior knowledge, which can generalize to policies of other players or humans. In this survey, we shed light on population-based deep reinforcement learning (PB-DRL) algorithms, their applications, and general frameworks. We introduce several independent subject areas, including naive self-play, fictitious self-play, population-play, evolution-based training methods, and the policy-space response oracle family. These methods provide a variety of approaches to solving multi-agent problems and are useful in designing robust multi-agent reinforcement learning algorithms that can handle complex real-life situations. Finally, we discuss challenges and hot topics in PB-DRL algorithms. We hope that this brief survey can provide guidance and insights for researchers interested in PB-DRL algorithms.

Zero-shot coordination problem in multi-agent reinforcement learning (MARL), which requires agents to adapt to unseen agents, has attracted increasing attention. Traditional approaches often rely on the Self-Play (SP) framework to generate a diverse set of policies in a policy pool, which serves to improve the generalization capability of the final agent. However, these frameworks may struggle to capture the full spectrum of potential strategies, especially in real-world scenarios that demand agents balance cooperation with competition. In such settings, agents need strategies that can adapt to varying and often conflicting goals. Drawing inspiration from Social Value Orientation (SVO)-where individuals maintain stable value orientations during interactions with others-we propose a novel framework called \emph{Role Play} (RP). RP employs role embeddings to transform the challenge of policy diversity into a more manageable diversity of roles. It trains a common policy with role embedding observations and employs a role predictor to estimate the joint role embeddings of other agents, helping the learning agent adapt to its assigned role. We theoretically prove that an approximate optimal policy can be achieved by optimizing the expected cumulative reward relative to an approximate role-based policy. Experimental results in both cooperative (Overcooked) and mixed-motive games (Harvest, CleanUp) reveal that RP consistently outperforms strong baselines when interacting with unseen agents, highlighting its robustness and adaptability in complex environments.