Pith. sign in

REVIEW 3 major objections 5 minor 17 references

An Improved Multi-Agent Algorithm for Cooperative and Competitive Environments by Identifying and Encouraging Cooperation among Agents

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Amplifying rewards when several teammates score positive at once improves both team and individual returns over the standard MADDPG baseline.

desk verdict A simple reward-scaling heuristic on top of MADDPG, but the paper is missing the equation that defines the scale factor, so the method cannot be reproduced and the single unseeded experiment cannot carry the claim. read the letter →

arxiv 2508.14131 v1 pith:BSEOM2MN submitted 2025-08-19 cs.MA cs.AI

Junjie Qi , Siqi Mao , Tianyi Tan This is my paper · ORCID
classification cs.MAcs.AI
keywords multi-agentreinforcementlearningcooperationMADDPGrewardweightingcritictargetmodificationteammixedcooperative-competitiveenvironmentsmulti-particle
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 tries to show that a small change to MADDPG—a standard multi-agent actor-critic algorithm—makes agents cooperate better in a mixed cooperative–competitive game. In the critic target $y = \varphi_i r_i + \gamma Q'_i$, the paper replaces the recorded reward $r_i$ with an amplified version whenever enough agents on agent $i$'s team receive positive rewards at the same time; in the experiments the multiplier is set to $\varphi_i = 2$ when at least $L=1$ teammate reward is positive. The authors' rationale is that positive rewards on most cooperating agents are the signature of cooperative behavior, so boosting those transitions reinforces cooperation. On a two-team multi-particle environment with four chasers, two evaders, and three obstacles, the modified algorithm reports higher team reward for the chasing team and higher individual rewards for each chaser than the unmodified baseline, with the evaders' reward nearly unchanged.

What carries the argument

The central mechanism is the cooperation-reward multiplier $\varphi_i$ inserted into the TD target of the MADDPG critic. It is a step function: $\varphi_i = \phi$ (with $\phi = 2$) when the count $k$ of positive rewards among the $m$ agents on agent $i$'s team exceeds $L$ (with $L=1$), and $\varphi_i = 1$ otherwise. This single parameter does the work of the whole proposal—identifying cooperative transitions by reward coincidence and strengthening their learning signal by reward amplification—while leaving MADDPG's actor-critic structure, experience replay, target networks, and decentralized execution untouched.

What would settle it

Run the same algorithm on a two-agent cooperative task where one agent must sacrifice its own reward to give its teammate a positive reward. Under the paper's rule with $L=1$, the sacrificing agent's transition has $k=1$ (only the teammate's reward is positive), so the boosting applies to the teammate but not to the sacrificer; if the modified algorithm still beats MADDPG, the positive-reward count is not the active mechanism, and if it fails, the reward-coincidence mechanism is confirmed as essential.

Watch

Extended reading notes

Core claim

The central claim is that cooperative behavior in multi-agent reinforcement learning can be detected by counting positive rewards within a team and encouraged by scaling the reward that enters the TD target. For agent $i$, the loss is $L(\theta_i) = \mathbb{E}_{x,a,r,x'}\left[(Q^{\mu}_i(x,a_1,\ldots,a_N)-y)^2\right]$ with $y = \varphi_i r_i + \gamma Q^{\mu'}_i(x',a'_1,\ldots,a'_N)$. The multiplier $\varphi_i$ is determined by the number $k$ of positive rewards among the $m$ agents on $i$'s team: when $k$ exceeds the threshold $L$, $\varphi_i$ becomes the hyperparameter $\phi$ (chosen as 2), and otherwise it stays 1. The authors state this motivation explicitly: they assume that when agents e

Load-bearing premise

The load-bearing premise is that cooperative behavior reliably shows up as simultaneous positive rewards for most agents on a team, so counting positive rewards is a dependable way to identify the transitions worth amplifying; if a helpful action usually rewards only one teammate or rewards arrive late, the multiplier will fire on the wrong transitions and the reported gain would not generalize.

Editorial extensions

If this is right

  • For the chasing team, the modified algorithm reaches a higher total reward than MADDPG over 25,000 episodes, while the evading team's total reward is essentially the same.
  • Each red agent's individual reward is higher under the modified algorithm, and the per-agent reward curves become similar late in training, pointing to a shared cooperative policy.
  • The change is a one-line modification to the critic target, so the same default MADDPG settings and hyperparameters can be kept except for the new pair $(L, \phi)$.
  • Higher individual reward accompanies higher team reward in this environment, so the encouragement does not appear to force agents to sacrifice personal return.
  • The result supports the paper's claim that amplifying rewards in episodes identified as cooperative improves both team-level and individual-level outcomes.

Reading between the lines

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

  • A natural extension is to replace the binary threshold $k>L$ with a graded multiplier such as scaling with the fraction of positive teammate rewards, which would test whether the discontinuity is necessary for the reported gain or merely an artifact of the chosen hyperparameters.
  • The same positive-reward-count rule could be layered onto other centralized-critic MARL algorithms, not only MADDPG, whenever the critic target exposes the per-agent reward; that generalization is not tested in the paper.
  • The paper's own motivation implies a boundary condition: if cooperation often gives the acting agent zero or delayed reward while rewarding only the teammate, the count $k$ will not fire on the right transitions, so the method should be stress-tested in such asymmetric-payoff tasks.
  • The observed convergence of per-agent reward curves suggests behavioral convergence, and measuring policy entropy or action agreement across agents would tell whether the agents truly specialize or become interchangeable—something the paper does not examine.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes an extension of MADDPG for cooperative/competitive multi-agent environments. The algorithm introduces a per-agent multiplier phi_i in the critic's TD target: y = phi_i r_i + gamma Q'_i, where phi_i is meant to amplify the reward when a sufficient number of teammates simultaneously receive positive rewards. The authors claim that this reward shaping encourages cooperation and yields higher team and individual rewards than MADDPG in a PettingZoo Multi-Particle Environment with two teams. The manuscript includes one experiment comparing the proposed method to MADDPG over 25,000 episodes and reports qualitatively that the proposed algorithm achieves higher red-team and individual rewards.

Significance. If the method were fully specified and the empirical claims were rigorously supported, the contribution would be a simple, potentially useful heuristic for reward shaping in cooperative MARL. The paper does not provide a theoretical derivation, machine-checked proofs, or reproducible code; its value would rest entirely on empirical demonstration. As submitted, however, the core algorithm is underspecified and the experimental evidence is anecdotal, so the significance cannot be assessed.

major comments (3)
  1. [Section 3, Eq. (3)] The defining formula for phi_i is missing. The text states 'Then, we can calculate φi as follows:' followed by an empty display '((3)'. Algorithm 1 line 12 also instructs the reader to 'Calculate ϕ_i according to the formula (3)', but no such formula appears anywhere. This is a load-bearing omission: the method is undefined without knowing the default value of phi_i when the cooperation condition fails, whether the trigger is k > L or k >= L, and how 'positive rewards' are determined. The reported improvement cannot be reproduced or even formally interpreted.
  2. [Section 4, Experiments] The empirical comparison is statistically unsupported. The paper does not report the number of random seeds, error bars, confidence intervals, or any statistical significance test. Only one environment is used, and its exact PettingZoo scenario is not identified. Figures 2-4 appear to be placeholders or are not legible in the submission, and no numerical reward values are given. Consequently, the central claim that the algorithm yields higher team and individual rewards is not established.
  3. [Section 4, hyperparameters L and phi] No ablation or sensitivity analysis is provided for the two introduced hyperparameters L and phi. The paper fixes L=1 and phi=2 without justification. Since the entire method reduces to the rule 'if at least L teammates have positive rewards, multiply the reward by phi,' the behavior of the algorithm under other settings is unknown. This is particularly important because the paper's motivation—that positive teammate rewards identify cooperative episodes—is asserted rather than demonstrated.
minor comments (5)
  1. [Abstract and throughout] The manuscript contains numerous typos and grammatical errors, e.g., 'higer' instead of 'higher', 'an cooperative behavior' instead of 'a cooperative behavior', and 'teach agent' instead of 'each agent'. These should be corrected.
  2. [Section 2, notation] Several equations are missing or garbled. For example, the Markov Game tuple is incomplete, and the Q-function definition is not fully written out. The notation phi_i versus φ_i is inconsistent.
  3. [Section 4, figure references] The text says 'We also compare each team's reward in Fig 1,' but Figure 1 shows the MPE environment; the comparison plots appear to be Figures 2 and 3. The figure numbering should be corrected.
  4. [References] The citation to MADDPG is inconsistent: the background cites [5] for MADDPG, but [5] is a paper on peer-to-peer energy trading, while [7] is the original Lowe et al. paper. Several references are also incomplete or incorrectly formatted.
  5. [Introduction] The introduction mentions that PPO is employed, but PPO is never used in the methodology or experiments. This is misleading and should be removed or clarified.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the reward-scaling parameter φ_i is a hand-set hyperparameter and the reported comparison is against environment reward, so the central claim is not forced by the algorithm's definitions.

full rationale

The paper proposes a modification to MADDPG by altering the TD target to y = φ_i r_i + γ Q_i' (Eq. 2), where φ_i is a predetermined multiplier intended to be defined by a missing Eq. (3). The accompanying text states: 'Therefore, formulation (2) means when k exceeds L, agent i will get a higher reward φri instead of ri.' This is a hand-specified reward-shaping rule, not a quantity derived from the output metric. The paper's central claim—that the algorithm yields 'higher team reward and individual reward'—is evaluated using the environment reward in PettingZoo/Multi-Particle Environments, which is independent of the modified training target. Thus the conclusion is an empirical finding, not an identity forced by construction. There are no self-citations, no imported uniqueness theorems, and no ansatz smuggled in via citation. The most significant issue is not circularity but completeness: Eq. (3) is absent from the manuscript, Algorithm 1 line 12 instructs 'Calculate ϕ_i according to the formula (3)' without providing that formula, and the experiment appears to rely on a single unseeded run without error bars. These are reproducibility and correctness concerns, not circularity. Hence score 0.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central contribution rests on two hand-set hyperparameters (L and phi) and on the unvalidated assumption that simultaneous positive rewards are a reliable signal of cooperation. No new entities are introduced.

free parameters (2)
  • L = 1
    Minimum number of agents with positive rewards required to trigger the reward multiplier. Chosen by hand without sensitivity analysis; directly controls when cooperation is 'identified'.
  • phi = 2
    Multiplicative reward boost applied to each team member's reward when k >= L. Chosen by hand; the reported improvement likely depends on this value, but no ablation is given.
assumptions (3)
  • domain assumption The environment can be modeled as a Markov game with two teams and a centralized training critic.
    Assumed in Section 2 and 3, following MADDPG. If the true dynamics are not Markov or the centralized critic cannot access needed information, the approach may fail.
  • domain assumption Cooperative behavior is characterized by simultaneous positive rewards among teammates.
    Stated as 'A primary motivation behind our algorithm is that we think the individual rewards of most of the cooperating agents are positive when agents exhibit cooperative behavior' (Section 3). This is the key assumption that links the reward count to cooperation.
  • standard math Standard Bellman equation and policy gradient updates are valid for the modified reward target.
    The critic update in Equation (2) uses the Bellman equation with phi-scaled rewards; the paper does not address whether this modified fixed point corresponds to any well-defined optimality criterion.

how reviews work

0 comments
Cite this review

Pith. "Pith review of An Improved Multi-Agent Algorithm for Cooperative and Competitive Environments by Identifying and Encouraging Cooperation among Agents." pith.science (2026). https://pith.science/paper/BSEOM2MN

@misc{pith2026250814131,
  author       = {Pith},
  title        = {Pith review of: An Improved Multi-Agent Algorithm for Cooperative and Competitive Environments by Identifying and Encouraging Cooperation among Agents},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BSEOM2MN}},
  note         = {Machine review of arXiv:2508.14131}
}
read the original abstract

We propose an improved algorithm by identifying and encouraging cooperative behavior in multi-agent environments. First, we analyze the shortcomings of existing algorithms in addressing multi-agent reinforcement learning problems. Then, based on the existing algorithm MADDPG, we introduce a new parameter to increase the reward that an agent can obtain when cooperative behavior among agents is identified. Finally, we compare our improved algorithm with MADDPG in environments from PettingZoo. The results show that the new algorithm helps agents achieve both higher team rewards and individual rewards.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

17 extracted references · 14 canonical work pages

  1. [1]

    cooperative agents

    Tan, M.: Multi-agent reinforcement learning: independent vs. cooperative agents. In: Proceedings of the Tenth International Conference on Machine Learning, pp. 330–337. Morgan Kaufmann (1993)

    work page 1993

  2. [2]

    Canese, L., et al.: Multi-agent reinforcement learning: a review of challenges and applications. Appl. Sci. 11(11) (2021). 10 (a) Agent1 (b) Agent2 (c) Agent3 (d) Agent4 Figure 4: Comparison of MADDPG and our algorithm on each agent’s reward

    work page 2021

  3. [3]

    CoRR abs/1906.04737 (2019)

    Papoudakis, G., Christianos, F., Rahman, A., Albrecht, S.V.: Dealing with non- stationarity in multi-agent deep reinforcement learning. CoRR abs/1906.04737 (2019)

    arXiv 1906

  4. [4]

    Daskalakis, C., Foster, D.J., Golowich, N.: Independent policy gradient methods for competitive reinforcement learning. Adv. Neural Inf. Process. Syst. 33, 5527–5540 (2020)

    work page 2020

  5. [5]

    Samende, C., Cao, J., Fan, Z. (2022). Multi-agent deep deterministic policy gradient algorithm for peer-to-peer energy trading considering distribution network constraints. 11 Applied Energy, 317, 119123. https://doi.org/10.1016/j.apenergy.2022.119123

    work page arXiv 2022

  6. [6]

    Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O. (2017). Proximal Policy Optimization Algorithms. arXiv preprint arXiv:1707.06347. Retrieved from

    arXiv 2017

  7. [7]

    Multi-agent actor-critic for mixed cooperative- competitive environments[J]

    Lowe R, Wu Y I, Tamar A, et al. Multi-agent actor-critic for mixed cooperative- competitive environments[J]. Advances in neural information processing systems, 2017, 30

    work page 2017

  8. [8]

    A Concise Introduction to Decentralized POMDPs[M]

    Oliehoek F A, Amato C. A Concise Introduction to Decentralized POMDPs[M]. Springer, 2016

    work page 2016

Show all 17 references
  1. [9]

    Cooperative multi-agent control using deep reinforcement learning[C]//International Conference on Autonomous Agents and Multiagent Systems

    Gupta J K, Egorov M, Kochenderfer M. Cooperative multi-agent control using deep reinforcement learning[C]//International Conference on Autonomous Agents and Multiagent Systems. 2017: 66-83

    2017

  2. [10]

    Learning to communicate with deep multi -agent reinforcement learning[C]//Advances in Neural Information Processing Systems

    Foerster J, Assael Y M, de Freitas N, et al. Learning to communicate with deep multi -agent reinforcement learning[C]//Advances in Neural Information Processing Systems. 2016, 29

    2016

  3. [11]

    Partially Observable Mean Field Multi-Agent Reinforcement Learning Based on Graph-Attention[J]

    Yang M, Liu G, Zhou Z. Partially Observable Mean Field Multi-Agent Reinforcement Learning Based on Graph-Attention[J]. arXiv preprint arXiv:2304.12653, 2023

    2023 arXiv

  4. [12]

    Multi-agent reinforcement learning: A review of challenges and applications[J]

    Duan X, Zhang Y, Wang H, et al. Multi-agent reinforcement learning: A review of challenges and applications[J]. IEEE Access, 2019, 7: 101996-102016

    2019

  5. [13]

    Coordinating multi-agent reinforcement learning with limited communication[C]//Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems

    Zhang C, Lesser V. Coordinating multi-agent reinforcement learning with limited communication[C]//Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems. 2013: 1101-1108

    2013

  6. [14]

    QMIX: Monotonic value function factorisation for deep multi-agent reinforcement learning[C]//International Conference on Machine Learning

    Rashid T, Samvelyan M, de Witt C S, et al. QMIX: Monotonic value function factorisation for deep multi-agent reinforcement learning[C]//International Conference on Machine Learning. PMLR, 2018: 4295-4304

    2018

  7. [15]

    Tesseract: Tensorised Actors for Multi- Agent Reinforcement Learning[C]//International Conference on Machine Learning

    Mahajan A, Samvelyan M, Mao L, et al. Tesseract: Tensorised Actors for Multi- Agent Reinforcement Learning[C]//International Conference on Machine Learning. PMLR, 2021: 7313-7324. 11

    2021

  8. [16]

    Asynchronous Multi-Agent Reinforcement Learning for Efficient Real-Time Multi-Robot Cooperative Exploration[J]

    Yu C, Yang X, Gao J, et al. Asynchronous Multi-Agent Reinforcement Learning for Efficient Real-Time Multi-Robot Cooperative Exploration[J]. arXiv preprint arXiv:2301.03398, 2023

    2023 arXiv

  9. [17]

    Imitation Learning with Concurrent Actions in 3D Games[J]

    Harmer J, Gisslén L, del Val J, et al. Imitation Learning with Concurrent Actions in 3D Games[J]. arXiv preprint arXiv:1803.05402, 2018. Acknowledgement Junjie Qi, Siqi MAO, and Tianyi TAN contributed equally to this work and should be considered co-first authors

    2018 arXiv

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.