arxiv: 2604.25088 · v1 · submitted 2026-04-28 · 💻 cs.AI · cs.CL

Recognition: unknown

Cooperate to Compete: Strategic Coordination in Multi-Agent Conquest

Abigail O'Neill, Alan Zhu, Joseph E. Gonzalez, Mihran Miroyan, Narges Norouzi

Authors on Pith no claims yet

Pith reviewed 2026-05-07 16:34 UTC · model grok-4.3

classification 💻 cs.AI cs.CL

keywords multi-agent negotiationlanguage model agentsmixed-motive gamesstrategic coordinationprompt engineeringhuman-AI comparisoncooperation and competition

0 comments

The pith

Adjusting language model agents to match human negotiation patterns raises their win rate from 22 percent to 33 percent in a new competitive game.

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

The paper introduces Cooperate to Compete, a multi-agent game in which players pursue secret asymmetric goals through private, non-binding negotiations while racing to win. It compares how humans and language-model agents behave in these mixed-motive settings and finds that humans favor simpler deals, prove less reliable as partners, and negotiate more aggressively. Prompt changes that steer the agents toward the observed human style produce a clear lift in performance against human opponents. A reader would care because many real deployments of AI agents will require exactly this blend of short-term cooperation and long-term competition.

Core claim

In the Cooperate to Compete environment, language-model agents produce more complex and more reliable negotiation behavior than humans, who accept deals without counter-offers only 56 percent of the time and favor lower-complexity agreements. Targeted prompting that aligns agent behavior with these human patterns improves the agents' win rate against human opponents from 22.2 percent to 32.7 percent across more than 1,100 games.

What carries the argument

The Cooperate to Compete (C2C) environment, in which players hold asymmetric secret objectives and conduct private non-binding negotiations that can form and dissolve as short-term interests align or diverge.

If this is right

Language-model agents can be steered toward more effective mixed-motive behavior without retraining, simply by changing their negotiation prompts.
C2C provides a scalable testbed for studying coordination failures and successes that occur when short-term alliances must serve long-term competitive goals.
The collected dataset of 16,000 private conversations supplies a concrete resource for measuring and improving agent reliability in negotiation.
Human-AI performance gaps in this setting are large enough that modest behavioral alignment yields double-digit win-rate gains.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same prompting approach could be tested in other non-binding negotiation domains such as automated bargaining or multi-party policy simulation.
If human unreliability is the dominant factor, future agents might benefit from explicit modeling of partner reliability rather than pure imitation of human style.
The 10-point win-rate improvement suggests that real-world deployments involving repeated human-AI interactions could see compounding advantages from similar alignment techniques.

Load-bearing premise

The differences between human and language-model negotiation styles observed in the user study will remain stable enough to guide prompt changes that continue to work against new opponents and in new game variants.

What would settle it

Re-running the same prompting modifications against a fresh pool of human players or with a different base language model and measuring whether the win-rate gain disappears.

Figures

Figures reproduced from arXiv: 2604.25088 by Abigail O'Neill, Alan Zhu, Joseph E. Gonzalez, Mihran Miroyan, Narges Norouzi.

**Figure 1.** Figure 1: Overview of C2C. (a) A sample game state from Red’s perspective. The board shows each territory’s owner (indicated by color) and troop count (indicated by number); territories marked with “?” are obscured and not visible to Red. (b) Available actions and a negotiation channel between Red and Blue. (c) Player strength comparison of various LM-based agents and humans based on the Plackett-Luce model. Human p… view at source ↗

**Figure 2.** Figure 2: A qualitative example of an evolving relationship. Early in the game view at source ↗

**Figure 3.** Figure 3: Win Rate, Negotiation, and Deal-making metrics. 95% confidence intervals shown. view at source ↗

**Figure 4.** Figure 4: Reliability and Relationships metrics. Note that human deception is omitted as it view at source ↗

**Figure 5.** Figure 5: Win rates across all interventions. Restricting negotiations and partnerships harms performance, while principled strategies improve performance. 95% confidence intervals shown. Unique Negotiation Targets Follow-Through Rate 0.0 0.5 1.0 1.5 Number Players 1.51 1.20 Reference Agents Single Partner 0 20 40 60 80 100 Percent (%) 70.6 77.0 view at source ↗

**Figure 7.** Figure 7: Relevant metrics for Aggressive Negotiation, Support Seeking, and Deceiving interventions. 95% confidence intervals shown. 8 view at source ↗

**Figure 8.** Figure 8: Overview of the human-AI game interface. view at source ↗

read the original abstract

Language Model (LM)-based agents remain largely untested in mixed-motive settings where agents must leverage short-term cooperation for long-term competitive goals (e.g., multi-party politics). We introduce Cooperate to Compete (C2C), a multi-agent environment where players can engage in private negotiations while competing to be the first to achieve their secret objective. Players have asymmetric objectives and negotiations are non-binding, allowing alliances to form and break as players' short-term interests align and diverge. We run AI only games and conduct a user study pitting human players against AI opponents. We identify significant differences between human and AI negotiation behaviors, finding that humans favor lower-complexity deals and are significantly less reliable partners compared to LM-based agents. We also find that humans are more aggressive negotiators, accepting deals without a counteroffer only 56.3% of the time compared to 67.6% for LM-based agents. Through targeted prompting inspired by these findings, we modify agents' negotiation behavior and improve win rates from 22.2% to 32.7%. We run over 1,100 games with over 16,000 private conversations totaling 15.2 million tokens and over 150,000 player actions. Our results establish C2C as a testbed for studying and building LM-based agents that can navigate the sophisticated coordination required for real-world deployments. The game, code, and dataset may be found at https://negotiationgame.io/c2c.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper delivers a new mixed-motive negotiation benchmark with direct human-AI comparisons and a prompting tweak that lifts reported win rates, but the lift lacks the basic statistical details needed to trust it.

read the letter

The main things to know are that they built C2C, a game where agents have secret asymmetric goals and can make private non-binding deals, and that they ran a large set of AI-only games plus a human user study to spot behavioral differences, then used those differences to prompt agents and report a win-rate increase from 22.2% to 32.7% across more than 1,100 games and 16,000 conversations. They also release the game, code, and dataset publicly. That combination of scale and artifacts is the concrete contribution here. The environment itself is straightforward to describe but fills a gap for studying short-term cooperation that serves long-term competition, and the human-AI comparison gives a baseline that most prior LM multi-agent work skips. The prompting intervention is a direct, if narrow, application of the observed differences in deal complexity and reliability. Those pieces are new relative to the cited literature and the public release makes the work usable right away. The soft spot is the central performance claim. The abstract and stress-test note give the two percentages and the total game count but no per-condition sample sizes, no variance measures, and no significance test. Without those, the 10.5-point shift could easily be noise or tied to the specific opponent pool rather than a stable effect of the prompting. The assumption that the human-AI differences will hold up and that the prompting will transfer is also stated without much further testing. This paper is for researchers who build or evaluate LM agents in strategic or social settings and want a reusable testbed with human data. A reader focused on multi-agent coordination or negotiation benchmarks will get immediate value from the environment and the released conversations. It deserves a serious referee because the scale of the experiments and the public artifacts are substantive even if the win-rate result needs tightening. I would send it out for review and expect the main questions to land on the missing statistics and the generalizability of the prompting change.

Referee Report

2 major / 2 minor

Summary. The paper introduces the Cooperate to Compete (C2C) multi-agent environment in which LM-based agents engage in non-binding private negotiations while pursuing asymmetric secret objectives. Through AI-only games and a human-AI user study, it identifies behavioral differences (humans favor lower-complexity deals, are less reliable partners, and accept deals without counteroffer only 56.3% of the time versus 67.6% for LM agents). Targeted prompting inspired by these differences is then shown to raise LM agent win rates from 22.2% to 32.7% across >1,100 games, >16,000 conversations, and >150,000 actions. The work positions C2C as a testbed and releases the game, code, and dataset.

Significance. If the central performance claim is statistically supported, the paper supplies a scalable, mixed-motive testbed and concrete evidence that human-AI behavioral differences can be leveraged to improve LM negotiation strategies. The large experimental scale and public artifacts are clear strengths that would enable follow-on work on coordination in politics-like settings.

major comments (2)

[Abstract and Results] Abstract and Results: the headline claim that targeted prompting improves win rates from 22.2% to 32.7% is reported without per-condition sample sizes, standard errors, bootstrap intervals, or any hypothesis test. With only the aggregate >1,100 games stated, it is impossible to determine whether the 10.5-point lift exceeds sampling variability or is attributable to the prompting rather than other factors.
[User-study and prompting sections] User-study and prompting sections: the manuscript states that prompting is 'inspired by' the observed human-AI differences (e.g., acceptance rates, reliability) but provides no explicit mapping from those statistics to the prompt modifications, nor any ablation showing that the specific changes (rather than generic prompting) drive the gain.

minor comments (2)

[Abstract] Abstract should include brief baseline details, opponent pool description, and mention of statistical testing to allow readers to evaluate the 10.5-point claim at a glance.
[Methods] Notation for negotiation complexity and reliability metrics should be defined consistently when first introduced and carried through tables or figures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We agree that the statistical details and the explicit link between user-study observations and prompting require strengthening. We address each point below and will revise the manuscript accordingly.

read point-by-point responses

Referee: [Abstract and Results] Abstract and Results: the headline claim that targeted prompting improves win rates from 22.2% to 32.7% is reported without per-condition sample sizes, standard errors, bootstrap intervals, or any hypothesis test. With only the aggregate >1,100 games stated, it is impossible to determine whether the 10.5-point lift exceeds sampling variability or is attributable to the prompting rather than other factors.

Authors: We agree that the current reporting is insufficient to evaluate the reliability of the improvement. In the revision we will report the exact number of games per condition, standard errors, bootstrap confidence intervals, and the result of an appropriate hypothesis test (two-proportion z-test) for the difference between 22.2% and 32.7%. The total exceeds 1,100 games with balanced allocation across conditions, which supplies adequate power for these analyses. revision: yes
Referee: [User-study and prompting sections] User-study and prompting sections: the manuscript states that prompting is 'inspired by' the observed human-AI differences (e.g., acceptance rates, reliability) but provides no explicit mapping from those statistics to the prompt modifications, nor any ablation showing that the specific changes (rather than generic prompting) drive the gain.

Authors: We acknowledge that the manuscript lacks an explicit mapping and an ablation. In the revision we will add a subsection that directly links each reported human-AI difference (e.g., 56.3% vs. 67.6% acceptance without counter-offer, lower human reliability) to the corresponding prompt modifications. We will also include an ablation comparing the targeted prompts against a generic negotiation-prompt baseline to demonstrate that the specific changes, rather than prompting in general, account for the observed gain. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical results are independent of inputs

full rationale

The paper reports results from separate runs of AI-only games (>1,100 total) and a distinct human-vs-AI user study. The win-rate improvement (22.2% to 32.7%) is obtained by applying prompting changes in new game instances, not by any re-use of the same data, fitted parameters, or self-referential definitions. No equations, uniqueness theorems, or ansatzes appear in the provided text, and no self-citations are invoked as load-bearing justification for the behavioral differences or performance gains. The derivation chain consists of observation followed by independent validation runs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard LLM prompting assumptions and the premise that observed behavioral differences can be translated into effective prompt modifications; no free parameters or invented entities are introduced.

axioms (1)

domain assumption Targeted prompting can reliably alter LM negotiation behavior in the direction suggested by human-AI comparisons
Invoked when the authors apply findings from the user study to modify agents and report the win-rate increase.

pith-pipeline@v0.9.0 · 5578 in / 1187 out tokens · 62542 ms · 2026-05-07T16:34:10.453099+00:00 · methodology

discussion (0)

Reference graph

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