Strategic Self Arbitration in LLM Agents: A Three Seat Architecture Grounded in Chess Theoretic Decision Making

Abstract

Language model agents that operate over long contexts face a recurring problem: how much weight to give what has already happened versus what might happen next when choosing a single action in the present. I introduce CHESS, a three seat meta cognitive architecture in which a present self arbitrates between a hindsight self, which summarizes relevant prior interaction, and a foresight self, which generates and evaluates candidate continuations. The arbitration is formulated as variational inference and evaluated in a reduced scope Phase 1 pilot across three open source language models. Three empirical hypotheses were tested. H1 examines positional retrieval of critical information in long contexts; H2 tests whether injecting compressed records of prior interaction improves task performance; and H3 compares variational arbitration with greedy and fixed weight policies. H2 showed consistent improvements, with mean uplifts of 0.56 to 0.62 on a zero to one scale and Wilcoxon p < .001 for all three models. H3 likewise favored variational arbitration, exceeding greedy arbitration by 48 to 80 percentage points and fixed weight arbitration by 10 to 50 percentage points. H1 produced mixed, model dependent evidence: two models reached ceiling level retrieval, while one showed irregular positional degradation. These results are reported as an interim pilot rather than a confirmatory study, with a larger pre registered factorial protocol identified as the next step.