Is Knowledge Power? On the (Im)possibility of Learning from Strategic Interactions

Summary

This paper addresses the theoretical question of whether, through repeated interactions, strategic agents can overcome the uncertainty about the exact payoff structure of the game being played to achieve outcomes they could have achieved in the absence of uncertainty. The authors specifically consider a Stackelberg Game setting, where there are two players, each aiming to maximize their total payoff in the repeated games, with one being more informed about the game structure than the other. The degree of informedness is modeled as a real number $p \in [0,1]$, representing the precision of the signal. It denotes the player's probability of knowing the exact game structure being played each round in addition to a prior distribution. In this setting, the authors study the pure Nash equilibria (PNE) of a meta-game where players choose their decision-making algorithms as their actions. The results demonstrate that when player $P_1$ knows the game perfectly while player $P_2$ does not, there is a clear separation: $P_1$ can always achieve her Stackelberg value, while $P_2$ sometimes cannot. Conversely, if both players are not perfectly certain about the game being played, such separation is provably gone. Overall, this paper advances the theoretical understanding of learning in strategic environments by showing that repeated strategic interactions alone are not enough for an uninformed player to effectively play a Stackelberg Game.

Strengths

1. The topic being studied in this paper is fundamental and relevant to the NeurIPS community. 2. The theoretical findings are clean and fundamental. While non-trivial to prove, the statements of results are concise, and they reveal novel theoretical understandings of learning in strategic environments. 3. The paper is quite well-written, with good typesetting, clear notations, formal statements and proofs, understandable interpretation of results, and proper attribution of them in the introduction.

Weaknesses

I have no major concerns about this work as a theoretical paper in NeurIPS. If I had to mention a weakness, it would be that the theoretical findings of this work are currently somewhat detached from reality, limiting their direct impact on the real world. That being said, I think this is perfectly fine for a theoretical paper.

Questions

1. Am I correct that each game $G$ in the support of $\mathcal{D}$ must have the same action spaces for both players? Otherwise, it seems that if a player is not perfectly informed about $G$, it is possible for her to make an invalid action. 2. If applicable, can you explain the connection of this work with the real world? Feel free to skip this question if you prefer.

Rating

8

Confidence

4

Soundness

4

Presentation

4

Contribution

4

Limitations

I think the authors adequately mentioned the limitations.

Summary

In this paper, the authors study whether players can achieve the Stackelberg value when they have uncertainty about the game. Specifically, the authors consider a two-player setting where players can repeatedly interact with the environment. They consider the pure Nash equilibrium in the meta game where the strategies are long-term algorithms. They demonstrate that (1) when one player is perfectly informed, there exists a PNE where the player can achieve his Stackelberg value, (2) when one player is perfectly informed, there is a game where no PNE allows the other player to achieve his Stackelberg value, and (3) when both players are not perfectly informed, both players may not achieve their Stackelberg value in any PNE.

Strengths

1. Studying the results for games with uncertainty is an important and interesting research direction. 2. The theoretical results are generally sound. 3. The paper is well-written and easy to follow.

Weaknesses

I do not have major issues with this paper, but some results need further clarification. 1. In Section 3.2, the authors explain that learning and acting on this learned knowledge are intertwined. I would expect the authors to provide more details. Intuitively, in my opinion, if the less-informed player could estimate the game correctly, he can then behave as the perfectly informed player. Since the authors study the case when $T \rightarrow \infty$, it is possible for the less-informed player to study the game for the first $o(T)$ rounds and then use the same strategy as the perfectly informed player. I expect the authors to explain why this would not work. 2. Proposition 4.2 demonstrates that when both $p_1$ and $p_2$ are smaller than 1, both players cannot achieve the Stackelberg value in any PNE of the game. However, the result is different as long as one of $p_1$ or $p_2$ is 1. The change in the results when $p_1 = 1$ and $p_1 < 1$ is "non-smooth," and I expect the authors to provide further insight about this. 3. I found a typo. There are two words "about" in Line 162.

Questions

See the weakness part.

Rating

6

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

See the weakness part.

Summary

The paper studies two-player repeated games where both players use (no-regret) learning algorithms to choose strategies simultaneously in each stage, which are called meta-games. The authors define the pure Nash equilibria of the meta-games and explored the players' equilibrium utilities based on their initial information about the game. Specifically, they find that if one player is fully informed of the game while the other is partially informed, the fully informed player can always guarantee its Stackelberg utility at some equilibrium, while the partially informed one cannot. When both players are partially informed, then there are cases that either can fail to obtain her Stackelberg value.

Strengths

The meta-games where players use learning algorithms to play against each other is natural and important, due to the widespread use of machine learning techniques. The results into how initial information asymmetries influence the utilities players can achieve in equilibrium is interesting.

Weaknesses

1. The paper can be presented more clearly and rigorously in at least the following ways: 1. Beginning with the discussion of Stackelberg games in the introduction is confusing as the paper considers repeated simultaneously games. 2. The reason why take Stackelberg value as a benchmark is lacking. 3.The statements of the theorems do not mention which learning classes are used (no-regret or no-swap regrets, or hold for both), and whether two players have the same sets of learning algorithms. 4. The paper does not mention whether any meta-game holds a pure NE. 2. The paper lacks a clear explanation of its technical novelty compared to previous work on strategizing no-regret learners?

Questions

1. See weaknesses 2. 2. Do the agents's set of strategies need to be the same to obtain all the results? 3. Does the meta-game always admit a pure NE?

Rating

6

Confidence

3

Soundness

3

Presentation

2

Contribution

3

Limitations

1. The related work with on "Information asymmetry in repeated games" is missing references. I suggest the authors refer to the "related work" section in the paper they cite, "learning to manipulate a commitment optimizer", to include all references. Two references that I know are missing are: " - Thanh H. Nguyen and Haifeng Xu. Imitative attacker deception in Stackelberg security games. IJCAI'19 - Yurong Chen, Xiaotie Deng, and Yuhao Li. Optimal private payoff manipulation against commitment in extensive-form games. WINE'22 " 2. typos: 1. line 338: "that that" -> "that"

Summary

The paper explores the impact of information asymmetry on the ability of agents to achieve their Stackelberg optimal strategy in repeated games. It investigates whether agents can overcome initial uncertainty through strategic interactions alone. The authors propose a meta-game model where players' actions are algorithms that determine their strategies based on observed histories and knowledge of the game. The paper's main findings suggest that while an informed player can always achieve her Stackelberg value, an uninformed player cannot necessarily do so, even with repeated interactions.

Strengths

1 The paper presents a clear and novel perspective on information asymmetry in strategic interactions. 2 The theoretical model and meta-game framework are well-defined and contribute to the understanding of learning in games. 3 The analysis of pure Nash equilibria provides valuable insights into the limitations of learning through repeated interactions.

Weaknesses

While the paper discusses the inability of uninformed players to achieve their Stackelberg values, it could provide more insight into the learning dynamics and the rate at which players converge (or fail to converge) to these values. The findings of the paper, while theoretically sound, may not offer surprising or counterintuitive insights that significantly advance the field. The authors does not clearly articulate how its findings contribute to the existing body of work in the field of game theory and strategic interactions. The paper would benefit from a clearer exposition of how its findings contribute to the existing body of work.

Questions

Could the authors highlight their contributions and discuss the significance of the results?

Rating

6

Confidence

4

Soundness

4

Presentation

3

Contribution

3

Limitations

I did not find any limitations of the paper.