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Themodelhastodetermine the label yk of the query input by applying the nearest neighbor algorithm in its forward pass (Figure 1c). This task subsumes various associative recall tasks considered in earlier works (cf.

Theyaredesigned tohaveagame-theoretic equilibrium where everyone reveals their private information truthfully.

Theyaredesigned tohaveagame-theoretic equilibrium where everyone reveals their private information truthfully.

Large Language Model (LLM) agents are increasingly studied in multi-turn, multi-agent scenarios, yet most existing setups emphasize open-ended role-play rather than controlled evaluation. We introduce AsymPuzl, a minimal but expressive two-agent puzzle environment designed to isolate communication under information asymmetry. Each agent observes complementary but incomplete views of a symbolic puzzle and must exchange messages to solve it cooperatively. Using a diverse set of current-generation and open-source LLMs, we show that (i) strong models such as GPT-5 and Claude-4.0 reliably converge across puzzle sizes on the solution by sharing complete information in two turns, (ii) weaker models often ignore partner messages or over-correct their hypotheses, and (iii) feedback design is non-trivial: simple self-feedback improves success rates, while detailed joint feedback can hurt performance. These findings show that even in simple cooperative tasks, LLM communication strategies diverge and depend on the granularity of feedback signals. AsymPuzl thus provides a testbed for probing the limits of multi-turn cooperation and opens avenues for studying coordination mechanisms.

We consider a setting in which a principal gets to choose which game from some given set is played by a group of agents. The principal would like to choose a game that favors one of the players, the social preferences of the players, or the principal's own preferences. Unfortunately, given the potential multiplicity of equilibria, it is conceptually unclear how to tell which of even any two games is better. Oesterheld et al. (2022) propose that we use assumptions about outcome correspondence -- i.e., about how the outcomes of different games relate -- to allow comparisons in some cases. For example, it seems reasonable to assume that isomorphic games are played isomorphically. From such assumptions we can sometimes deduce that the outcome of one game G' is guaranteed to be better than the outcome of another game G, even if we do not have beliefs about how each of G and G' will be played individually. Following Oesterheld et al., we then call G' a safe improvement on G. In this paper, we study how to derive safe improvement relations. We first show that if we are given a set of games and arbitrary assumptions about outcome correspondence between these games, deriving safe improvement relations is co-NP-complete. We then study the (in)completeness of a natural set of inference rules for outcome correspondence. We show that in general the inference rules are incomplete. However, we also show that under natural, generally applicable assumptions about outcome correspondence the rules are complete.

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Harsanyi's theorem shows that when the principals have a