Playing log(N)-Questions over Wikipedia Abstracts: Communication Efficiency Between Paired Frontier Models

arXiv:2609.19113v1 Announce Type: new Abstract: We evaluate six frontier language models on the two-agent log(N)-Questions game. A questioner sees N Wikipedia lead paragraphs and must identify a secretly chosen target using exactly log_2 N yes/no questions. An answerer sees only the target and the question, and replies with one word. Both roles run on the same provider, so the game measures how well a model communicates with itself across an information asymmetry. We run 408 games over document sets of 4 to 1024 paragraphs at a total API cost of 363. One model finishes well behind the others: Claude Opus 5 wins 28 of 68 games, against 45 to 56 for GLM-5.3, GPT-5.6 Sol, Grok 4.6, Gemini 3.8 Flash and Kimi K3. The leading five are only marginally separable. Pooling those five, win rate declines with set size at r=-0.973 and is fit by a single per-round reliability parameter. The form is ext{win}=p^{log_2 N} with p=0.928. Losses divide into answer errors and discrimination failures in roughly equal measure, and models almost never name a document their own evidence excludes. Every unanimous answer error from the weakest model was inspected: 32 of 34 are No'' answers, on properties stated in the document's first sentence, under an instruction that explicitly warns against defaulting to No''. Information per question, estimated from answer balance, correlates with win rate at r=+0.88. The only two models to extract a full bit per question are the only two that partition on document titles, a strategy absent below N{=}32 and used in a quarter of questions above it. Reasoning-token expenditure varies 4.5imes$ across models with little relation to success, and the trace grows as the candidate set shrinks without a matching gain in reliability.

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Source: arXiv cs.CL | 2026-09-17