Can Language Models Play the Wikipedia Game?

We evaluate six frontier language models on the two-agent $\log_2 N$-Questions game (Potash et al., 2019) to measure self-communication across an information asymmetry. A questioner with access to $N$ candidate Wikipedia lead paragraphs ($N = 4$ to $1024$) must identify a secret target using exactly $\log_2 N$ binary questions answered by an agent from the same provider that sees only the target. Across 408 games, win rate decays cleanly as a geometric power of horizon length, $p^{\log_2 N}$ ($p \approx 0.93$). Per-round failure rates are flat across the horizon, indicating that errors compound because more rounds must succeed rather than because individual rounds grow harder. Adjudication across three independent judges shows that losses divide between single-agent answer errors and discrimination failures, which become undetectable and unrecoverable under the two-agent structure rather than from channel breakdown. Claude Opus 5 lags behind due to systematic false-negative answers (82% answer errors), whereas the five leading models (GLM-5.3, GPT-5.6 Sol, Grok 4.6, Gemini 3.8 Flash, and Kimi K3) are closely clustered. Maximizing information gain requires structural partitioning (e.g., splitting on document titles), and neither reasoning-token expenditure nor API cost correlates with success ($r = -0.05$), highlighting communicative reliability as a distinct bottleneck from inference compute.

Wikidata is one of the largest open knowledge bases, yet answering a complex question over it still requires a SPARQL query that names the right entities and properties and chains their relations. Language models offer a natural-language alternative but answer largely from memory, which is least reliable for less prominent entities. We study agents that instead answer by exploring the graph, and argue that two obstacles limit them: the lack of training data recording how a solver explores, and interfaces that add large graph results directly to the model's context. We test three hypotheses: that the difficulty of graph search can be controlled through the structure of a question rather than only through obscure entities or wording; that much of the failure on long-horizon search comes from how retrieved evidence is managed rather than from the model itself; and that, in a suitable environment, open-weight models can match commercial closed ones. We construct multi-hop questions on a frozen Wikidata snapshot by replacing named entities with nested conditions, checking after each expansion that the target remains unique and that every new condition is necessary. We release 10,235 solving traces over single-entity and multi-hop questions, together with the recursive language model (RLM) harness that produced them, in which models batch graph calls, keep results in persistent Python state and interpret selected evidence through sub-calls. On 100 questions, the harness improves both models we ran under both interfaces compared with direct tool calling over the same functions: gpt-6-luna rises from 49 to 61 correct answers, doubling its multi-hop accuracy, and Qwen3.8-27B, an open-weight model served on a single GPU, from 60 to 74.

Large Language Models increasingly serve as interfaces for knowledge-intensive information seeking tasks across languages by synthesizing multilingual evidence. Prior work has shown that they often exhibit query-language preference -- the tendency to favor sources written in the language of the query -- but has largely examined this behavior in settings where equivalent knowledge is available across languages. However, this bias becomes consequential when sources in different languages provide incomplete or inconsistent accounts of the same fact, since the information users receive then depends on the sources a model selects to use. To characterize query-language preference under such cross-lingual knowledge disparities, we introduce Waldo, a multilingual Question-Answering (QA) benchmark constructed from Wikipedia. Waldo contains 12K QA pairs targeting knowledge gaps, where a fact is available in one language but absent in another, and knowledge conflicts, where language editions provide conflicting versions of the same fact. Evaluating eight models across five languages, we find that when one language edition merely lacks the relevant fact, models generally use evidence from the other language regardless of the query language. Under conflicting accounts, however, model responses strongly align with the document in the query language, causing semantically equivalent queries to elicit different accounts depending on the user's language. Finally, we explore two different approaches that could mitigate this preference under knowledge conflicts: a mechanistic intervention that ablates attention heads associated with query-language preference, and LoRA-based training, which reduces the preference gap by up to 61.5%.