Strategic Reasoning Under LCIA Confidentiality: Rule-Constrained Bayesian Game-POMDPs for International Arbitration

Confidential arbitration is a poor fit for ordinary supervised legal prediction. Under the London Court of International Arbitration (LCIA) Rules, party materials, awards, and arbitration-created documents are confidential by default, and award publication depends on consent. The resulting public record is not merely sparse; it is a strategically selected observation channel. A model trained on public or disclosed awards therefore estimates a public-slice distribution rather than the latent distribution of LCIA proceedings. This paper proposes a rule-constrained Bayesian Game-POMDP for strategic reasoning under LCIA confidentiality. A rule compiler maps LCIA Rules 9B, 14, 21, 22, 22A, 28, 30, 30A, and the Annex on representative conduct into state variables, valid-action masks, observation functions, payoff deformations, and audit obligations. Approximate policies are computed with CFR/Deep-CFR style self-play over LCIA-valid actions and evaluated by exploitability, hard-rule compliance, belief calibration, and weak-spot robustness rather than award-prediction accuracy alone. Three synthetic experiments test the core claims: (i) a missing-not-at-random public-slice ablation, (ii) rule-constrained equilibrium learning for complex LCIA proceedings, and (iii) adversarial weak-spot hardening. The contribution is not an award predictor or legal-advice engine. It is a benchmarkable framework for legal Al systems that must reason strategically while respecting institutional confidentiality and procedural legality.