Beyond Self-Interest: How Group Strategies Reshape Content Creation in Recommendation Platforms?

For the Bandit C3 game, to get $PNE(G, s)$ you initialize all creators in the group $c$ with $s_c$, wlog say these are 1 to $n_c$; now from $n_c$ to $n$ you follow Algorithm 1?

We initialize the group of creators with $s_c = (s_1, s_2, \dots, s_{n_c})$, which are not necessarily identical across all members. As you mentioned, once the group strategy $s_c$ is selected, Algorithm 1 is applied to the remaining $n - n_c$ creators, who then sequentially choose their strategies to complete the profile.

In the Type 1 and Type 2 equilibria, and more generally for the theorems in Sections 4.1 to 4.4, each individual in the group c plays the same strategy $s_c$, right?

Note that $s_c = (s_1, s_2, \dots, s_{n_c})$. Creators within the group are allowed to adopt different strategies (actions), and these strategies are not necessarily identical. In both the Type 1 and Type 2 equilibria, the strategies of group members can differ—the equilibrium does not assume a single shared strategy across all group members. And in Figure 2 of the appendix, the group creators (represented by red triangles) indeed employ different strategies.

Can you specify how gradient descent is used to approximate the optimal group strategy at each round?

Thank you for pointing this out. The group aims to select $s_c = (s_1, s_2, \cdots, s_{n_c})$ in order to maximize its group utility, defined as $Q_c(s_c, s_{-c}) = \sum_{i \in \mathcal{C}} u_i(s)$. To approximate the optimal group strategy at each round, the group can perform multiple steps of gradient descent on the objective $Q_c(s_c, s_{-c})$ with respect to the group strategy $s_c$, assuming that the group has full knowledge of the game environment. In more realistic scenarios, the group can instead adopt trial-and-error approaches to iteratively improve its group utility over time. Alternatively, heuristic methods may be employed—for example, assigning certain creators to dominate the exposure of the largest user while others are allocated to target remaining users. This structured, adaptive strategy allows the group to improve utility even with limited information. We will include this clarification in our revised version.

I believe there’s a typo on line 175, column2: “… shapes the same”, I think you mean equal up to permutation of strategies?

Yes, we mean they are equal up to permutation of strategies.

Can you provide more insights on the importance reweighting method mentioned on line 356?

Thank you for pointing this out. The importance reweighting method, as proposed in (Yao et al., 2024b), enables the platform to steer creator incentives toward under-served users by modifying the reward structure. Specifically, the platform defines the creator's utility as

where $w(x)$ represents the importance weight of user $x$. When the platform detects that a user is being under-served under the current content distribution, it increases $w(x)$ for that user. This effectively amplifies the reward for creators who target such users, encouraging them to shift their content in that direction. Over time, this reshapes the content distribution and improves overall user welfare. As a concrete example, consider the game instance in Appendix B.3. In that case, we can set the reward as

$u_i(s) = w(x_1) \pi(x_1, s) P_i(s, x_1) + w(x_2) \pi(x_2, s) P_i(s, x_2),$ and choose $w(x_1)$ to be large and $w(x_2)$ small. This encourages all creators to shift from $s_i = e_2$ to $s_i = e_1$, leading to a new PNE where user welfare is optimal. Once this equilibrium is reached, the platform can reset the weights to $w(x_1) = w(x_2) = 1$, and creators will no longer deviate. We will include a detailed explanation and discussion of this method in revision.

One major issue is the definition of group deviations.

As we discussed in the paper (Lines 270-274), suppose that all creators have reached an equilibrium, and then some creators decide to form a group. Joining such a group becomes a dominant strategy because the group utility is at least as high as the individual case—at the very least, it remains unchanged if the creators continue their previous actions. If the group generates additional rewards, the bonus can be allocated among the group members, ensuring that each creator receives a reward greater than or equal to their original reward. Given this allocation rule, the formation of such groups is reasonable. Even if a creator deviates from the group strategy, they have an incentive to re-join the group. Furthermore, in the real world, groups of creators often exist and are typically united by a media company, such as an MCN (Lines 28–33).

When the users are not orthogonal or the creator strategy set is more general, it is unclear how the results would extend.

We use this simplified game to better unveil the theoretical insights. In Section 5, we address the general case, where the user population vectors are not orthogonal, and no assumptions are made regarding the parameter $p$. Theorem 5.3 demonstrates that the PoA under exposure reward can be arbitrarily bad, which aligns with the results in Theorem 4.7. Additionally, we provide bounds on the PoA under engagement rewards in the general case. Furthermore, our empirical results in Section 6 and Appendix C further support the theoretical claims in the general cases, where the user population vectors are not orthogonal and the creator strategy set is continuous.

In Theorems 4.7 and 4.9, the findings seem highly dependent on the choice of $p$. It would be helpful to understand how the results hold for different choices of these parameters.

Thank you for your valuable suggestions.

1. To emphasize the potential negative impact of group strategic behavior on user welfare, we consider the TvN game as an example for worst-case analysis (Yao et al., 2024a). The TvN game, although stylized, reflects user distributions in real-world online content platforms, which are often highly skewed and unbalanced.
2. Our choice of this representative $p$ is also primarily for clarity and simplification of presentation. Analogous to the proof of Theorems 4.7 and 4.9, we can extend our results to a more general unbalanced case, where the largest user proportion in the TvN game can vary, and this will provide a more smooth transit from the extreme case to the even case. We will incorporate these results into the revision. And we will expand the discussion to explicitly cover how the results extend to general $p$. In particular:
   • Under unbalanced $p$, similar welfare loss results hold, and group strategic behavior remains impactful.
   • Under more evenly distributed $p$, the impact of group behavior diminishes, as also implied by Theorem 4.6 and Theorem 4.12. For example, when $p$ is uniform, in Theorem 4.7, the welfare under both the individual case and the $n_c = n$ case equals 1, and the $K$ will no longer affects the user welfare in Theorem 4.9.

I would expect the authors to conduct experiments under varying choice of the vector $p$.

Thanks for your thoughtful suggestion. We will further strengthen our results by using a more general $p$ based on a Zipf-like or power-law distribution, where $p_j \propto \frac{1}{j^\alpha}$ with $\alpha > 1$. Such distributions have been widely observed in user preferences across online platforms[1][2][3]. Our current $p$ already follows a similarly skewed pattern, and we will clarify this in our revision. The additional experiment results under this new $p$ yield similar results and insights, further supporting the robustness of our conclusions. Please refer to the empirical results provided in our response to reviewer dTVP.

[1] Chowdhury et al. Popularity growth patterns of youtube videos-a category-based study.

[2] Cameron, S. Zipf’s Law across social media.

[3] Mosaic Ventures. The creator economy: a power law.

What is the optimistic tie-breaking rule in Line 203, ...?

Thank you for pointing this out. It refers to selecting $s_{-c}$ in a way that is most favorable to the group. This rule is specific to the equilibrium introduced in Line 203 and is unrelated to the tie-breaking rule mentioned in Theorem 4.6. In Theorem 4.6, the tie-breaking rule applies to individual creators when their utilities are equal for selecting different strategies. In such cases, a more general and consistent rule is to assume that creators will choose the user with the smaller index, which is generally used in game theory literature. This deterministic rule avoids ambiguity and is suitable for all cases discussed in the paper. In our revision, we will remove the optimistic tie-breaking rule and adopt this general tie-breaking assumption for clarity and consistency.

The paper focuses a bit too much on settings that are not algined with real-world applications. For instance, I think content creators are rewarded for engagement, but the paper focuses a lot on the setting where creators are rewarded for exposure.

As mentioned in the paper (Lines 144-148), the exposure reward mechanism is widely used in both theoretical and empirical settings (Ben-Porat et al., 2019; Hron et al., 2022; Jagadeesan et al., 2023; Meta, 2022; Savy, 2019), making it an important aspect to study in the context of recommendation systems. Furthermore, both exposure and engagement metrics are used in practice: user engagement tends to be used more often as a reward metric for established creators, while exposure is typically used for new creators (Yao et al., 2023). Thus, our focus on exposure rewards reflects a commonly encountered scenario in many platforms.

Another example is that users do have limited attention, but the paper focuses a lot on the case where users have infinite attention.

Thank you for your valuable comment. We would like to clarify that our analysis does not assume infinite user attention.

1. The constant attention model we use does not imply infinite attention. This attention truncated by the parameter $K$ and it assumes users allocate a fixed amount of attention uniformly across the top-$K$ items they are shown—e.g., $r_1 = r_2 = \dots = r_K = 1$. This setting is relevant in practice, particularly in user interfaces where content is displayed in fixed-sized, unordered blocks (e.g., a “For You” page with $K$ equally weighted items). Thus, the model captures a common real-world recommendation scenario without assuming that users consider all available content.

2. Our paper also considers another setting with diminishing attention, modeled as $r_1 = \dots = r_\tau = 1$, $r_{\tau+1} = \dots = r_n = 0$, which captures the case where users only pay attention to the top $\tau$ items. These two types—constant and diminishing—represent common user behaviors corresponding to slow-decay and rapid drop-off attention curves, respectively.

3. The theoretical results in Section 4 can be extended to more general attention profiles $\{r_i\}_{i=1}^n$. In particular:

   • Slow decay attention will lead to results akin to those in Theorem 4.7, implying that large group strategic behavior negatively impacts user welfare.
   • Under rapid drop-off attention, Theorem 4.9 and Corollary 4.10 hold similar results demonstrating that tuning $K$ and $\beta$ can help mitigate user welfare loss.

4. In our simulations, we also test log cutoff attention scores as an intermediate setting. These results are consistent with our theoretical findings, reinforcing the robustness of the insights under various attention models.

We chose to present constant and diminishing attention as representative cases to improve the readability and clarity of the exposition. We will clarify this modeling choice and its implications in our revision.

The paper primarily uses synthetic data for simulations. Including empirical validation with real-world data from online platforms would further strengthen the claims and demonstrate the practical relevance of the findings.

Thank you for the thoughtful suggestion. We will further strengthen the practical relevance and credibility of our results by using a more general $p$ based on a Zipf-like or power-law distribution, where $p_j \propto \frac{1}{j^\alpha}$ with $\alpha > 1$. Such distributions are well-documented in real-world platforms and capture the skewed nature of user preferences [1][2][3]. Our current setup already follows a similarly skewed pattern, and we will clarify this in the revision. The additional results under this new $p$ yield similar results and insights, further supporting our conclusions. We present results for two different $\alpha$ values below.

[1] Chowdhury et al. Popularity growth patterns of youtube videos-a category-based study.

[2] Cameron, S. Zipf’s Law across social media.

[3] Mosaic Ventures. The creator economy: a power law. https://www.mosaicventures.com/patterns/the-creator-economy-a-power-law.

$\alpha=1.1$

$\alpha=1.8$

The model relies on certain simplifications and assumptions (e.g., relevance function, user attention scores, specific game setups). The paper could discuss the limitations of these assumptions and their potential impact on the results.

We appreciate your valuable suggestion. Our model does make several stylized assumptions as many works in this line also do (Jagadeesan et al., 2023, Hu et al., 2023, Yao et al. 2024a;b). However, we do not see it as a major weakness but rather a necessary simplification to better unveil the theoretical insights. Below, we clarify the rationale and limitations associated with our assumptions:

1. Relevance function: The results in Section 4 are based on the dot product relevance score, which is for the simplification of presentation, and our results also hold for other reasonable relevance functions (e.g., $\sigma$ depending on $||s - x||$). And our general results—Theorems 5.3, 5.4, and 5.5—do not rely on specific assumptions about the form of the relevance function.
2. User attention scores: These two types—constant and diminishing—represent common user behaviors corresponding to slow-decay and rapid drop-off attention, respectively, providing results and insights under these two kinds of user attention.
3. Specific game setups: The bandits $C^3$ game simulates the fundamental scenario where every creator must select a topic to create content. And, the TvN game, where the user distribution is unbalanced, is recognized as a good example for worst-case analysis (Yao et al., 2024a). While generalizing Section 4's results to broader environments is a meaningful and challenging direction for future work, we highlight that Section 5 already addresses the general case: it makes no orthogonality assumptions about user population vectors and does not constrain the parameter $p$.

We will include a dedicated discussion about the limitations and potential impact of these assumptions in our revision.

In the simulations, were the differences in user welfare between exposure and engagement rewards statistically significant?

Yes, as shown in Figure 1, engagement reward consistently maintain higher user welfare, while exposure rewards lead to a notable decline. Each experiment is run 5 trials to avoid the randomness. We also emphasize that our simulations do not consider the worst-case group behavior under exposure reward. Under such behavior the user welfare could be even lower than reported. Under an alternative initialization where all creators are intialized around users 2–10, the resulting user welfare under exposure reward is worse. We present the empirical results here:

Furthermore, it is important to note that even small improvements in user welfare can have meaningful consequences in practice. For example, platforms like TikTok serve billions of content impressions daily. Thus, marginal gains in user welfare—achieved through better reward design—can translate into substantial improvements in user satisfaction, engagement, and platform revenue.