DipLLM: Fine-Tuning LLM for Strategic Decision-making in Diplomacy

Dongbin Zhao; Jiajun Chai; Kaixuan Xu; Sicheng Li; Yuanheng Zhu; Yuqian Fu

REVIEW 4 major objections 8 minor 2 cited by

DipLLM: Fine-Tuning LLM for Strategic Decision-making in Diplomacy

T0 review · 4 major / 8 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that a fine-tuned LLM can learn near-equilibrium Diplomacy policies by decomposing joint moves into autoregressive unit-level decisions, beating Cicero with roughly 1.5% of its training data.

desk verdict Strong empirical result with an overstated theoretical wrapper; the equilibrium-policy claim is not supported by the actual loss used, but the agent clearly learns to play well. read the letter →

arxiv 2506.09655 v2 pith:DONUVYDD submitted 2025-06-11 cs.AI cs.LG

Kaixuan Xu , Jiajun Chai , Sicheng Li , Yuqian Fu , Yuanheng Zhu , Dongbin Zhao This is my paper · ORCID

classification cs.AIcs.LG

keywords Diplomacylargelanguagemodelsfine-tuningequilibriumpolicyautoregressivefactorizationno-pressmultiplayergames

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that a large language model can be fine-tuned to play the seven-player game Diplomacy at a level above the state-of-the-art Cicero model while using only about 1.5% of Cicero's training data. The key move is to treat the assignment of orders to all of a player's units not as one giant action choice but as a sequence of unit-level decisions, each conditioned on the earlier decisions. Within this autoregressive factorization, the paper defines a per-unit learning objective derived from the piKL-Hedge equilibrium-search policy, and fine-tunes Llama-3-8B to match it. In no-press Diplomacy games against a pool of opponents, DipLLM scores 23.0% on the sum-of-squares metric versus 20.8% for Cicero, and the improvement is attributed to combining factorization with equilibrium-targeted fine-tuning.

What carries the argument

The load-bearing object is the autoregressive factorization of the joint Diplomacy policy. Instead of sampling an action for all units at once, $\pi_i(a^{1:D}_i|s)$ is written as $\prod_{d=1}^D \pi^d_i(a^d_i|s,a^{1:d-1}_i)$, and each factor's target is the softmax of a conditional Q-value $Q^d_i$ defined by marginalizing (log-sum-exp) over later unit actions. The equivalence theorem means training each unit separately with this objective reproduces the full piKL-Hedge equilibrium policy. In practice the log-sum-exp is replaced by a lower bound computed from the single sampled ground-truth joint action, and the LLM is fine-tuned with the resulting $\exp(Q^d_i)$-weighted next-token loss, with LoRA on Llama-3-8B.

What would settle it

Take a fixed set of board states, compute unit-level targets both by the paper's lower bound and by exact log-sum-exp (or many Monte-Carlo samples) over later actions, fine-tune two otherwise identical DipLLM agents, and play them against the same baseline pool; if scores are statistically identical, the approximation is not load-bearing, and if the exact-Q agent wins, the claimed equivalence to the piKL-Hedge equilibrium is not what the approximation delivers.

Watch

Extended reading notes

Core claim

The central discovery is that an equilibrium policy for Diplomacy can be factorized exactly into conditional unit-level policies, so that an autoregressive language model can represent it. Defining $Q^d_i(s,a^{1:d-1}_i,a^d_i)$ as the log-sum-exp over all later unit actions of the joint reward-plus-anchor term yields $\prod_{d=1}^D \pi^{d,*}_i = \pi^*_i$ (Theorem 1), and in two-player zero-sum games the iterated factored update reaches an approximate Nash equilibrium (Theorem 2). The authors then train an LLM by maximizing $\log \pi_\phi(a^d_i \mid s,a^{1:d-1}_i) \cdot \exp(Q^d_i)$, with data produced by running piKL-Hedge against a human-like anchor policy. The resulting agent, DipLLM, is reported to surpass all compared baselines on no-press Diplomacy, including Cicero, even though it is evaluated without equilibrium search at inference.

Load-bearing premise

The load-bearing premise is that the lower-bound estimate of each unit-level Q-value, formed from a single sampled ground-truth joint action, is tight enough that fine-tuning against it still yields the piKL-Hedge equilibrium policy.

Editorial extensions

If this is right

Training an LLM for Diplomacy no longer requires millions of equilibrium-search rollouts; the paper's numbers suggest that a few hundred games of fine-tuning data can suffice to beat domain-specific models.
The factorization gives a natural interface between LLM policies and classical game-theoretic search, because each unit's conditional policy can be reweighted by search values; the paper's preliminary search experiments show additional gains.
The method is portable in principle to any multi-unit or multi-agent decision problem with a combinatorial joint action space, a point the authors gesture at in framing the work as a step toward broader strategic decision-making.
Evaluated without search, DipLLM's end-to-end policy already exceeds Cicero's policy, and against Cicero augmented with up to eight equilibrium-search iterations it retains a win rate above the even 14.3% baseline.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: The lower-bound Q-value approximation is the most fragile link in the pipeline; if the single-sample bound is loose, the learned policy may drift from the piKL-Hedge equilibrium, and a multi-sample Monte-Carlo version would directly test this.
Editorial inference: Because the training data still comes from DipNet rollouts plus piKL-Hedge, the method inherits the biases of that anchor policy; replacing it with self-play data would test whether the LLM can eventually generate its own training signal.
Editorial inference: The reported dominance over GPT-4o and o3-mini suggests that task-specific fine-tuning outweighs general reasoning scale in this setting, but that comparison relies on a single evaluation protocol and should be read cautiously.
Editorial inference: An ablation that randomizes or shuffles the Q-value labels would isolate whether the gains come from the equilibrium weighting or merely from supervised next-token training on unit-level data.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The thing to know: DipLLM is a fine-tuned 8B LLM that plays no-press Diplomacy at a level above Cicero in a 1v6 population, trained on a few hundred games of piKL-Hedge-labeled data. That empirical result is worth taking seriously, even though the theoretical framing around 'learning equilibrium policies' does not survive contact with the actual training loss.

What is genuinely new: applying autoregressive factorization of joint actions to LLM fine-tuning for Diplomacy, with a KL-weighted objective that uses equilibrium-search Q-values as soft labels. The factorization itself is not new (Q-transformer and others), but the combination with LLMs for Diplomacy and the demonstration of data efficiency is a real step. The paper is honest about relying on an external anchor policy (DipNet) and equilibrium search to generate data; the limitation section says as much.

The soft spot is the one the stress-test identifies. Theorem 1 is true by construction: Eq. (4) defines the factored policy so that the product telescopes to the piKL-Hedge target. But the training does not use Eq. (3)'s log-sum-exp Q^d; it replaces it with the lower bound Q_i(a*) + β log τ_i(a*) for a single sampled joint action. The claim in Appendix C that this bound is 'tight' is not right—log-sum-exp equals the max only when all other actions have zero mass, which is false for any softmax target. The gap is never quantified, so the loss in Eq. (6) is not an unbiased estimator of the KL objective in Eq. (5). It may instead concentrate probability on the stored argmax actions, which could still be a reasonable imitation objective but is not the claimed equilibrium matching. Figure 7, a single opening-state comparison, cannot establish distributional equivalence.

That said, the empirical core holds up conditionally. The 23.0 vs 20.8 SoS gap over Cicero is meaningful, and the ablations show both factorization and fine-tuning matter. The main evaluation is fair (no search for either side), and the additional comparison against Cicero with search rollouts is a nice robustness check. The biggest practical gaps: no code or data released, and the '1.5% of Cicero's data' figure is an estimate based on GPU usage, not a direct count.

Who is this for? Anyone working on LLM agents for games or offline RL with factored action spaces. It deserves a serious referee, but the theoretical claims need to be scaled back or the approximation needs a real analysis. I would ask for code/data and a revised narrative.

Referee Report

4 major / 8 minor

Summary. The paper proposes DipLLM, an LLM-based agent for no-press Diplomacy. The agent factorizes the joint action selection over a player's units into an autoregressive sequence of unit-level decisions, defines a conditional Q-function for each unit (Eq. (3)), and shows that the product of the resulting softmax policies (Eq. (4)) equals the piKL-Hedge equilibrium policy (Theorem 1). The LLM is then fine-tuned with a weighted log-likelihood loss (Eq. (6)) on data generated by running piKL-Hedge with DipNet as the anchor policy. The authors report that DipLLM achieves a 23.0% SoS score in a population of baselines, outperforming Cicero (20.8%) while reportedly using only 1.5% of Cicero's training data, and they include ablations, a data-efficiency study, and a case study.

Significance. If the empirical results are reproducible, the paper would be an interesting demonstration that a fine-tuned 8B LLM can compete with and exceed a specialized 2.7B model in no-press Diplomacy using relatively small amounts of equilibrium-search data. The autoregressive factorization is a sensible and potentially reusable design for LLM decision-making in combinatorial action spaces. The paper provides a detailed experimental setup, standard baselines, full prompts, and hyperparameter tables, which aid reproducibility. However, the central theoretical claim -- that the fine-tuning objective is equivalent to learning the factored equilibrium policy -- is not established, because the loss relies on an approximate lower bound for Q^d and the derivation of Eq. (6) contains a gap. The paper would be considerably strengthened by a corrected derivation, a quantitative analysis of the lower-bound approximation, and a more careful statement of the data-efficiency claim.

major comments (4)

[§4.3 and Appendix C (Eq. (3) and 'Lower Bound of Q-value')] The unit-level Q-values Q^d_i stored in the dataset are not the exact values defined in Eq. (3); they are replaced by the single-sample lower bound Q_i(s, a^{1:D}_i) + β log τ_i(a^{1:D}_i|s), with a^{1:D}_i ∼ π^*_i(·|s). The log-sum-exp inequality gives a lower bound, but equality holds only if the sampled joint action is a maximizer of Q_i + β log τ_i, which is not the case for a sample from the Gibbs distribution π^*. The gap log(1 + Σ_{a' ≠ a^*} exp(f(a') - f(a^*))) is never quantified, and because Eq. (6) weights log π_φ by exp(Q^d), the trained objective is not an unbiased estimator of the KL objective in Eq. (5) with respect to the true π^{d,*} of Eq. (4). The equilibrium-policy claim is therefore not supported unless the tightness of this approximation is demonstrated; Figure 7, a single opening state, cannot establish distributional equivalence.
[Appendix C.1 (derivation of Eq. (6))] The derivation that Eq. (6) is equivalent to Eq. (5) is not valid as written. The step replacing the sum over all unit actions a^d_i in the objective with an expectation over the dataset D requires D to be the full conditional distribution π^{d,*}, and it drops the state-dependent partition function Z(s, a^{1:d-1}_i) = Σ_{a^d_i} exp(Q^d_i(·)). Dropping Z changes the relative weighting of states in the expected loss, so maximizing Eq. (6) is not generally equivalent to minimizing Eq. (5) for a shared-parameter model. Please provide a corrected derivation or state explicitly the additional assumptions under which the equivalence holds.
[Appendix C, Theorem 2 proof] The proof of Theorem 2 is not rigorous as written. The theorem statement bounds exploitability by (max_{i=1,2} β_i δ_i), but the proof introduces an undefined λ_i and the subsequent inequalities mix λ_i with δ_i without a clear chain; in particular, the negative-entropy and KL terms are bounded in a way that does not transparently yield the stated constant. Since Theorem 2 is invoked to claim that the proposed objective is 'optimal' and that insights transfer to multiplayer games, the theoretical basis for that claim is currently incomplete. Please provide a corrected proof or an explicit citation to the exact result being extended.
[Abstract, Conclusion, and §5.2 (footnote 1)] The headline claim that DipLLM requires 'only 1.5% of the data required by Cicero' is based on estimated GPU usage (footnote 1), not on the number of training games or samples. This conflates compute with dataset size and is not a direct measure of data efficiency. The authors should either provide exact data counts for both methods or rephrase the claim. The direct data-efficiency comparison in Figure 6 against DipNet is a better-supported statement and should be the primary basis for the data-efficiency claim.

minor comments (8)

[Abstract] The phrase 'an challenging environment' should be 'a challenging environment'.
[Section 2] The sentence 'LLM-based agent have gained generalized reasoning abilities' should be 'LLM-based agents have gained ...'.
[Section 3.3] The notation vout_i = π_φ(vin) conflates a policy distribution with a sampled output; use vout_i ∼ π_φ(·|vin) or a similar convention.
[Section 4.2] The product notation 'QD d=1 πd,∗ i' is nonstandard; use an explicit product symbol with lower and upper limits.
[Section 5.1] The sentence 'When the game ends,' appears truncated; the description of the 'most SCs' outcome is cut off in the manuscript.
[Table 1 and Figure 4] The number of games used for each reported entry is not stated; please report game counts so that the standard errors can be interpreted.
[Appendix C] The typo 'corrsponding' should be 'corresponding'.
[Appendix C.1] The notation π∗_unit appears in the derivation without definition; please define it or use the previously defined π^{d,*}.

Circularity Check

1 steps flagged · score 4.0 of 10

The equilibrium-equivalence theorem is a definitional tautology, but the headline SoS result is externally benchmarked and not circular.

self definitional [Section 4.2, Eqs. (2)-(4) and Theorem 1]
"Q^d_i(s,a^{1:d-1}_i,a^d_i) ≜ log Σ_{a^{d+1:D}_i} exp{Q_i(s,a^{1:d}_i,a^{d+1:D}_i)+βlogτ_i(a^{1:d}_i,a^{d+1:D}_i|s)} ... π^{d,*}_i(a^d_i|s,a^{1:d-1}_i) ≜ exp{Q^d_i(...)} / Σ_{a^d_i} exp{Q^d_i(...)} ... Theorem 1: The joint policy derived using the learning objective in autoregressive factorization form, Π_{d=1}^D π^{d,*}_i(...), is equivalent to the original policy distribution π^*_i."

The unit-level Q^d in Eq. (3) is defined as the log-sum-exp of the same joint utility Qi+βlogτi that defines the piKL-Hedge target π* in Eq. (2), and the factored policy in Eq. (4) is the softmax of that Q^d. Telescoping the product of softmax factors cancels all intermediate partition functions, so Theorem 1 holds by construction. It is an algebraic reparameterization of the input piKL-Hedge objective, not an independent derivation; the paper nonetheless presents it as a theoretical justification for the claim that fine-tuning learns the equilibrium policy. The identity is exact, but as a 'prediction' or 'first-principles result' it adds no content beyond the definitions.

full rationale

The headline numerical claim (SoS 23.0 vs. Cicero 20.8 in Table 1) is obtained by playing the fine-tuned model against independent external baselines in 1v6 no-press Diplomacy games; that evaluation does not reduce to the training targets and is not circular. No load-bearing self-citation appears: the piKL-Hedge convergence result is attributed to Jacob et al. (2022), an external reference, and Theorem 2 builds on that external result. The Appendix C lower-bound approximation is a genuine correctness/approximation gap: the stored unit Q-values replace the exact log-sum-exp of Eq. (3) with a single-sample lower bound, and the assertion that the bound is 'achieved exactly' for the ground-truth joint action is not justified because equality in log-sum-exp would require all non-max suffix terms to vanish. Consequently Eq. (6) is not proven equivalent to Eq. (5), and Figure 7 is a reconstruction check against the same piKL-Hedge quantities used to generate labels rather than an independent test. These are validity threats to the 'learns equilibrium policies' claim, not input/output circularity. The one definitional circularity is Theorem 1, which is a tautological factorization identity; because the central empirical benchmark is external, the score is 4 rather than higher.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central result rests on a chain of assumptions: piKL-Hedge convergence, its extension to multiplayer games, the quality of DipNet as an anchor, and the tightness of the sampled lower-bound approximation to the factored Q-values. The free parameters are inherited from the piKL-Hedge data generation stage and influence the resulting Q-values and the fine-tuning target.

free parameters (4)

Beta (trade-off factor) = 0.1
Controls the balance between reward and anchor policy in the equilibrium objective (Eq. 2-4). Adopted from piKL-Hedge hyperparameters.
Search iterations = 256
Number of piKL-Hedge iterations used to generate Q-values and action data (Table 3).
Number of candidate actions = 50
Action candidate set size in piKL-Hedge (Table 3).
Nash explore epsilon = 0.1
Exploration parameter in piKL-Hedge (Table 3).

assumptions (4)

domain assumption piKL-Hedge converges to a Nash equilibrium in two-player zero-sum games
Theorem 2 relies on Corollary 1 from Jacob et al. (2022) for piKL-Hedge convergence, which is cited but not reproved.
domain assumption Theoretical insights from two-player zero-sum games generalize to multiplayer games
The paper assumes that convergence results for 2p0s extend to 7-player Diplomacy (Section 4.2, after Theorem 2).
domain assumption DipNet provides a suitable human-like anchor policy tau
DipNet is used both as the anchor in piKL-Hedge and as the data-generating opponent (Section 4.3).
ad hoc to paper The sampled lower bound for Qd is sufficiently tight to preserve the equilibrium objective
Appendix C uses the log-sum-exp inequality to bound Qd by a sampled max; this is not proven to be a good approximation in practice.

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Cite this review

Pith. "Pith review of DipLLM: Fine-Tuning LLM for Strategic Decision-making in Diplomacy." pith.science (2026). https://pith.science/paper/DONUVYDD

@misc{pith2026250609655,
  author       = {Pith},
  title        = {Pith review of: DipLLM: Fine-Tuning LLM for Strategic Decision-making in Diplomacy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DONUVYDD}},
  note         = {Machine review of arXiv:2506.09655}
}

read the original abstract

Diplomacy is a complex multiplayer game that requires both cooperation and competition, posing significant challenges for AI systems. Traditional methods rely on equilibrium search to generate extensive game data for training, which demands substantial computational resources. Large Language Models (LLMs) offer a promising alternative, leveraging pre-trained knowledge to achieve strong performance with relatively small-scale fine-tuning. However, applying LLMs to Diplomacy remains challenging due to the exponential growth of possible action combinations and the intricate strategic interactions among players. To address this challenge, we propose DipLLM, a fine-tuned LLM-based agent that learns equilibrium policies for Diplomacy. DipLLM employs an autoregressive factorization framework to simplify the complex task of multi-unit action assignment into a sequence of unit-level decisions. By defining an equilibrium policy within this framework as the learning objective, we fine-tune the model using only 1.5% of the data required by the state-of-the-art Cicero model, surpassing its performance. Our results demonstrate the potential of fine-tuned LLMs for tackling complex strategic decision-making in multiplayer games.

Figures

Figures reproduced from arXiv: 2506.09655 by the authors.

**Figure 1.** An overview of our agent, DipLLM and performance of various agents in a population. action space that can exceed 1064 possible choices per turn. This complexity stems from the game’s mechanics, where each player controls up to 34 units, each with around 26 possible actions. The exponential growth in possible action combinations, coupled with the intricate interactions among players, makes Diplomacy an challenging en… view at source ↗

**Figure 2.** The inference process of our LLM-based autoregressive factorization agent. DipLLM sequentially decides the action for each unit by prompting the Text State and unit Task, and finally sends the joint actions to the environment for execution. ri : S × A1 × · · · × An → R is the reward function for player i, p : S × A1 × · · · × An → S is the transition function. The objective of each player i is to select a policy πi(… view at source ↗

**Figure 3.** Pipeline for fine-tuning the LLM-based autoregressive factorization agent. Raw data is collected by interacting with the environment via DipNet. Q-values are generated through piKLHedge search, and the data is stored in prompt form. The LLM is then fine-tuned using a designed loss function. 4.3. Fine-tuning for Equilibrium Policy The fine-tuning process, as depicted in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 5.** Figure 5: Performance comparison of our agent playing against six Cicero agents, with each Cicero agent incorporating different numbers of equilibrium search iterations. The purple dashed line indicates equal performance, i.e., a win rate of 1/7 ≈ 14.3%. any power without SCs is…

**Figure 6.** Figure 6: Performance comparison of fine-tuned DipLLM and DipNet (Paquette et al., 2019a), both trained using different numbers of games. Each model is evaluated by playing against six original DipNet agents without fine-tuning. et al., 2024). • SFT: An LLM agent trained with S…

**Figure 8.** Figure 8: An example of DipLLM-controlled England strategically defeating Cicero-controlled France. AF Finetune SoS Score ↑ Win ↑ Survived ↑ Defeated ↓ ✗ ✗ 0.2% 0.0% 4.3% 95.7% ✗ ✓ 0.8% 0.0% 19.2% 80.8% ✓ ✗ 9.9% 6.7% 40.0% 53.3% ✓ ✓ 29.4% 25.2% 45.9% 29.0% [PITH_FULL_IMAGE:fig…

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