The Metaverse play-to-earn games have been gaining popularity as they enable players to earn in-game tokens which can be translated to real-world profits. With the advancements in augmented reality (AR) technologies, users can play AR games in the Metaverse. However, these high-resolution games are compute-intensive, and in-game graphical scenes need to be offloaded from mobile devices to an edge server for computation. In this work, we consider an optimization problem where the Metaverse Service Provider (MSP)'s objective is to reduce downlink transmission latency of in-game graphics, the latency of uplink data transmission, and the worst-case (greatest) battery charge expenditure of user equipments (UEs), while maximizing the worst-case (lowest) UE resolution-influenced in-game earning potential through optimizing the downlink UE-Metaverse Base Station (UE-MBS) assignment and the uplink transmission power selection. The downlink and uplink transmissions are then executed asynchronously. We propose a multi-agent, loss-sharing (MALS) reinforcement learning model to tackle the asynchronous and asymmetric problem. We then compare the MALS model with other baseline models and show its superiority over other methods. Finally, we conduct multi-variable optimization weighting analyses and show the viability of using our proposed MALS algorithm to tackle joint optimization problems.
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