Competition Over Timeline: The Game Theory of Social Media Visibility

TL;DR

Social media is a battle for the "Top $K$" slots of a user's feed. This paper treats the user's timeline as a finite queue and uses non-cooperative game theory to find the "Nash Equilibrium" of posting frequency. It reveals that creators aren't always more aggressive when competition increases; there is a critical tipping point where the effort of staying visible outweighs the rewards.

Problem & Motivation: The "Page Fold" Constraint

Despite the infinite scroll of modern apps, user attention is a finite resource. Static studies show that 80% of user time is spent above the page fold. On platforms like Twitter or Facebook's "News Feed," this creates a high-stakes environment where a brand's content is only valuable as long as it isn't pushed down by newer posts.

The authors identify a gap: while we understand how news spreads, we don't fully understand the incentives that drive creators to "spam" or "re-share" content. They ask: What is the optimal rate for a creator to post content given the competition from others?

Methodology: The Timeline as a Markov Chain

The authors define a consumer's timeline as a vector of $K$ locations.

1. Stochastic Arrivals: Content from various sources arrives as a Poisson process.
2. The Shifting Mechanism: Every new arrival pushes existing content down one slot. After $K$ shifts, the content vanishes.
3. The Utility Function: Each creator $j$ chooses a posting rate ${\lambda }_j$ to maximize their occupancy probability while minimizing "effort cost" $\gamma$.

Figure 1: The Bipartite graph representing creators (J) and consumers (I), showing how multiple creators converge on a single user's timeline buffer.

The "ij-busy period"

A key contribution is the derivation of the ij-busy period, denoted as $T_{ij}(K)$. It represents the duration during which at least one post from creator $j$ is visible to user $i$. Using recursion, they find: $E[T_{ij}(K)]=\frac{1}{{\Lambda }_{[-j]}}\left(\frac{1-{\alpha }^{-K}}{1-{\alpha }^{-1}}\right)$ where $\alpha$ represents the ratio of competitor traffic to total traffic.

Experiments: The Tipping Point of Aggression

The paper explores a Symmetric Nash Equilibrium where all players face similar costs.

1. The Competition Paradox (Effect of $N$)

Surprisingly, as the number of competitors ($N$) increases, creators don't stay aggressive forever.

• Small $N$: Creators increase their rate $\lambda$ as more competition enters to defend their "shelf space."
• Large $N$: Once the timeline becomes too crowded, the probability of staying visible (payoff) drops so low that creators lose the incentive to post frequently, reducing $\lambda$.

Figure 2: Equilibrium rate $\lambda$ against number of competitors. Notice the bell-shaped curve indicating the "Threshhold of Futility."

2. Timeline Size ($K$) Effect

Similarly, increasing the timeline size $K$ (e.g., showing 50 posts instead of 10) initially encourages more posting because the "survival time" of a post increases. However, if $K$ becomes too large, the urgency drops, and the equilibrium rate stabilizes or decreases.

Figure 3: Equilibrium rate $\lambda$ against timeline size $K$. Smaller $N$ (fewer players) reach peak aggression faster.

Critical Analysis & Conclusion

Takeaways

• Strategic Posting: Brands should recognize that their optimal posting frequency is a function of the "noise" created by others they share followers with.
• Platform Control: Social media providers can manipulate creator activity levels simply by changing the UI (the size of $K$).

Limitations

The model assumes a reverse-chronological feed, which is increasingly rare in the age of AI-driven "For You" pages (e.g., TikTok/Instagram). In those systems, the "shift" isn't strictly caused by every new arrival, but by a ranking algorithm.

Future Outlook

The framework provides a rigorous mathematical baseline. Subsequent research could integrate User Engagement (e.g., likes/shares extending a post's life) into the Markov model, transforming it from a simple queue into a priority queue based on content quality.