Team-Fictitious Play for Reaching Team-Nash Equilibrium in Multi-team Games

Summary

This paper introduces a new variant of fictitious play where agents respond to the last actions of team members. The authors need to improve their academic writing skills largely. The expression between paragraphs and sentences lacks logic and consistency. Moreover, the paper does not list the challenges and gaps in current research and why this research can solve the recent issue. Furthermore, from my point of view, I did not see particular novelty or practical value in this research.

Strengths

This paper introduces a new variant of fictitious play where agents respond to the last actions of team members.

Weaknesses

The authors need to improve their academic writing skills largely. The expression between paragraphs and sentences lacks logic and consistency. Moreover, the paper does not list the challenges and gaps in current research and why this research can solve the recent issue. Furthermore, from my point of view, I did not see particular novelty or practical value in this research.

Questions

I suggest the author reorganize the paper and improve the academic writing skills.

Rating

3

Confidence

4

Soundness

1

Presentation

1

Contribution

1

Limitations

I suggest the author reorganize the paper and improve the academic writing skills.

Summary

This paper addresses the complex problem of multi-team games by introducing a new variant of fictitious play called Team-FP. The method aims to enable teams of self-interested agents to reach Team-Nash Equilibrium (TNE) in multi-team games, with a particular focus on zero-sum potential team games (ZSPTGs). The authors present a rigorous convergence analysis and extend the Team-FP dynamics to multi-team Markov games. Extensive simulations are provided, comparing Team-FP with other algorithms to demonstrate its effectiveness and practical applicability.

Strengths

The paper introduces Team-FP, a novel variant of fictitious play specifically designed for multi-team games. The approach incorporates inertia in action updates and agents’ responses to the last actions of team members, which enhances team coordination. This creative extension of classical fictitious play is valuable in advancing the understanding of team dynamics in multi-agent settings. The paper is well-structured and organized, making it easy to follow the progression from the introduction of the problem to the presentation of the proposed methods.

Weaknesses

Despite the novelty of the Team-FP approach, the modifications to classical fictitious play are not significantly groundbreaking. The methods, while creative, represent incremental improvements rather than major innovations in the field. I am not familiar with the convergence proof; thus, I cannot and do not have the time to verify the proof. The authors put a lot of effort into the theoretical part. The experiment setting and results are simple. For a theoretical paper, it is better to prove the convergence through experimental results. Thus, I think the paper is below the acceptance bar of NeurIPS.

Questions

1. How can we get the Eq.4? 2. Can you provide experimental evidence to support your convergence proof?

Rating

5

Confidence

3

Soundness

3

Presentation

2

Contribution

3

Limitations

n/a

Summary

This paper introduces Team-Fictitious Play (Team-FP) dynamics as a novel approach for teams of self-interested agents to converge to Team-Nash equilibrium in multi-team games. The study focuses on games where multiple teams interact strategically, aiming to maximize their collective utilities. For this purpose, this paper (1) introduces Team-FP as a method for teams to converge to Team-Nash equilibrium in multi-team games; (2) extends the convergence analysis of Team-FP dynamics to multi-team Markov games; (3) demonstrates the effectiveness of Team-FP dynamics through theoretical analysis and empirical evaluations in various multi-team game scenarios.

Strengths

1. The introduction of Team-FP represents a novel approach to address the challenge of teams reaching equilibrium in multi-team games. 2. The detailed numerical analysis and simulations conducted to evaluate the behavior of Team-FP dynamics in various multi-team game settings reflect the thoroughness and quality of the method.

Weaknesses

1. The notations are confusing and it's hard to keep up. For example, 'agent index' and 'team index' both use lowercase letters. 2. Limited discussion on computational complexity. The paper could provide more insights into the computational complexity of implementing Team-FP dynamics in large-scale multi-team games. Discussing the scalability of the approach, potential bottlenecks, and computational efficiency considerations would be beneficial for understanding the practical feasibility of deploying Team-FP in complex settings.

Questions

The authors provide some experiments, but it would be helpful to see more extensive experiments, including a larger-scale multi-team game to demonstrate the effectiveness of the algorithm in a more complex setting.

Rating

6

Confidence

2

Soundness

3

Presentation

2

Contribution

3

Limitations

The authors have adequately addressed the limitations

Summary

In this work, the authors introduce a novel variant of virtual play, referred to as **Team-Fictitious Play (Team-FP)**, aimed at assisting self-interested agents within teams to reach **Team Nash Equilibrium (TNE)** in multi-team games. The paper focuses on zero-sum potential team games (ZSPTGs), where teams interact pairwise, but the payoffs to team members are not necessarily identical. The main contributions include the introduction of inertia in action updates and responses to the last actions of team members, which are crucial for team coordination. The authors provide theoretical convergence guarantees and validate the efficacy of the approach through extensive simulations.

Strengths

1. The introduction of Team-FP fills a gap in the multi-team game theory literature, particularly in the context of zero-sum potential team games. 2. The paper offers rigorous theoretical analysis and practical insights, including convergence proofs and error bounds. 3. Extensive simulations compare Team-FP with other algorithms, demonstrating its effectiveness and exploring the impact of various parameters on convergence speed. 4. The grammar and expression are accurate and professional.

Weaknesses

- Adding more background or appendix sections on Nash equilibrium and related solution algorithms would greatly help the reader's understanding. - The theoretical analysis section is quite technical; including more intuitive explanations and illustrations could be beneficial. For instance, adding a diagram in Section 3 to visually depict the workflow of Team-FP might help. - A more detailed analysis of the parameters used in Team-FP and their sensitivity to performance could provide deeper insights. - While the paper focuses on zero-sum potential team games, discussing how Team-FP could be adapted or extended to other types of multi-team games would be valuable. - The numerical experiments section could benefit from more qualitative analysis. - The discussion on practical applications is not sufficiently thorough; adding more experiments and analysis in specific application scenarios would be beneficial. - Section 5 could include experimental comparisons with other multi-team learning algorithms.

Questions

All my questions are written inside the weakness part.

Rating

6

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

The paper explicitly discusses its limitations.

thanks and raise score

Thank you for your response to my comments. I have read your rebuttal and am happy to raise the score.