研究平衡状态下的因果推断，揭示哪些结论可从观测数据得出，哪些需实验干预。
Equilibrium Causal Games: Separation, Identification, and the Identifiability of Cyclic Latent States
- 构建均衡因果博弈模型，融合循环因果结构与传感器映射机制。
- 在非高斯条件下可识别交互矩阵，但高斯对称系统中仅能确定旋转模糊性。
- 适用于电力网络、市场等复杂系统的因果分析，适合从事因果推理的研究者。
电力系统、市场及相互作用的人群会进入由反馈驱动的平衡状态，其状态通过未知传感器观测。本文提出的均衡因果博弈（ECG）将博弈论与循环因果模型结合，包含隐变量、传感器映射、干预规则和均衡选择机制；干预修改声明对象后重新计算均衡。在给定条件下，ECG-分离性是可靠的但不完备。后门/半轨迹路径可识别可观测查询。对于未受扰动的旋转对称高斯块，二阶矩仅能确定源坐标系的旋转，在该旋转下不同变量效应通常改变。未知传感引入额外歧义。在无自效应的稳定线性模型中，若未知连接且传感满秩，则当维度d≥2时，交互矩阵B完全无法识别。在LiNG（线性非高斯）条件下，非高斯性消除源旋转；机制干预可分离传感与交互。在未知支持集下，若传感不变、响应对齐且干预设计良好，可识别(H,B)至声明等价类。在d个目标中，若唯一未靶向节点直接指向其余所有节点，则只需d−1个目标即可精确识别；否则需d个。排除采集探针；已知连接时无法给出通用数量。在非线性传感下，各向同性高斯源块在标记环境中允许隐藏扭曲，仍保持所需径向规律。反之，在正性、信息性单块变化、秩与不可约性条件下，最细粒度独立源块表示可在指定替代类中被识别，至块内置换与块内坐标变换，但不能确定下游机制或传感器/交互划分。这些结果共同表明，哪些因果结论可由均衡数据支持，哪些必须依赖有针对性的实验。
原文摘要 · Abstract (English)
Power grids, markets, and interacting populations, settle into feedback driven equilibria observed through unknown sensors. Our Equilibrium Causal Game (ECG) joins a game to its cyclic causal model, hidden inputs, sensor map, and rules for interventions and equilibrium selection; interventions edit declared objects and recompute equilibrium. Under stated conditions, ECG-separation is sound but incomplete in our examples. Back-door/half-trek routes identify observed queries. Yet for an untouched rotationally symmetric Gaussian block, second moments determine only a source-frame rotation, across which distinct-variable effects generically change. Unknown sensing creates a separate ambiguity. In passive stable linear models without self-effects, unknown wiring and full-rank unknown sensing leave $B$ completely unidentified for $d\ge2$. Under LiNG, non-Gaussianity removes the source rotation; mechanism interventions separate sensing from interactions. With unknown support, invariant sensing, aligned responses, and well-posed single-target interventions identify $(H,B)$ up to declared equivalence. Of $d$ targets, $d-1$ suffice exactly when the sole untargeted node directly parents all others; otherwise $d$ are needed. Acquisition probes are excluded; known wiring gives no universal count. With nonlinear sensing, isotropic Gaussian source blocks admit hidden twists within and across blocks in labelled environments preserving required radial laws. Conversely, under stated positivity, informative one-block changes, rank, and irreducibility conditions, the finest independent source-block representation is identified within the stated alternative class up to block permutation and blockwise coordinate changes, but not downstream mechanisms or the sensor/interaction split. Together, these results show which causal conclusions equilibrium data support and which require targeted experiments.
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