Online multiplayer games are population-dependent systems whose playability depends on the continued presence of an active player base. We propose a formal framework for reasoning about viability collapse in such systems under explicit scope conditions. The framework introduces a conditional Critical Mass Threshold $Φ$, below which queue times, match quality, or role balance render a game operationally non-viable under a fixed operational profile; an uninhabited runtime taxonomy spanning pre-launch and post-decline states; and a Nostalgia Inversion Point $ψ$, at which cultural memory exceeds active participation. We model post-peak decline using a threshold-sensitive hazard model and show how games in the modeled class can cross below viability under finite official-service horizons or bounded novelty under continuing exposure. Case studies based on public concurrent-player data are used illustratively rather than as formal validation. The contribution of the paper is not a universal law, but a formal vocabulary, a collapse model, and an empirical agenda for studying online game decline, preservation risk, and uninhabited virtual worlds.

翻译：在线多人游戏是依赖玩家群体的系统，其可玩性取决于活跃玩家群体的持续存在。我们提出了一个形式化框架，用于在显式范围条件下推理此类系统中的生存性崩溃问题。该框架引入了一个条件性临界质量阈值$Φ$，当队列等待时间、匹配质量或角色平衡在固定运行剖面下低于该阈值时，游戏将失去运营生存性；一个覆盖发布前和衰退后状态的无玩家运行时分类法；以及一个怀旧反转点$ψ$，在此点文化记忆超过活跃参与度。我们使用阈值敏感性风险模型对峰值后衰退进行建模，并展示在所建模类别中，游戏如何在有限官方服务期限或持续接触下的有限新颖性条件下跌破生存性阈值。基于公开并发玩家数据的案例研究仅用于说明性目的而非形式化验证。本文的贡献不在于普适定律，而在于一套形式化词汇、一个崩溃模型以及一个用于研究在线游戏衰退、保存风险及无玩家虚拟世界的实证研究框架。