Contests with Spillovers: Incentivizing Content Creation with GenAI

The Big Picture: The "Copycat" Problem

Imagine a bustling digital town square where people (creators) write stories, make videos, or post art to get attention from the crowd. In the past, if you wanted to win the crowd's love, you had to work hard and create something unique.

But now, we have GenAI (like advanced robots that can write and draw). These robots are trained on everything that has ever been posted in the town square.

Here is the twist: The more one person works hard, the easier it becomes for everyone else to do good work.

The Analogy: Imagine a baker who invents a secret, delicious recipe. In the old days, only she could sell those cookies. But now, a robot chef learns her recipe instantly. Suddenly, every other baker in town can use that robot to make almost-as-good cookies with half the effort.
The Problem: If I know I can just copy your hard work using the robot, why should I bother working hard myself? I'll just "free-ride." If everyone thinks this way, everyone stops trying, the quality of the town square drops, and the crowd gets bored.

The paper asks: How do we design a system that keeps people motivated to create high-quality work, even when they can easily copy each other?

Part 1: Why Old Rules Don't Work

The researchers looked at how platforms usually reward creators. They tried two common methods, and both failed in this new GenAI world.

The "Winner-Takes-All" Contest:
- The Idea: Only the single best creator gets all the attention (like a gold medal).
- Why it failed: Because of the robots, the "best" person keeps changing. If I try to be the best, you can just copy my work and beat me. If you try to beat me, I copy you. It creates a chaotic game of "chicken" where no one settles down to create; they just keep trying to out-catch each other. There is no stable point where everyone is happy.
The "Proportional" Contest (Tullock):
- The Idea: You get attention based on how much you contribute relative to others.
- Why it failed: Similar to above. Because one person's effort boosts everyone else's quality (the "spillover"), the math gets messy. People realize that if they stop working, they can still ride on the coattails of others. The system becomes unstable, and the "best" outcome never actually happens.

The Lesson: In a world where copying is easy, standard competitions create chaos, not quality.

Part 2: The New Solution – "Provisional Allocation"

The authors propose a new way to run the town square, called Provisional Allocation (PRA).

The Analogy: Imagine the town square has a fixed number of "spotlights" (attention). Instead of fighting over who gets the brightest spotlight, the town manager hands out personal contracts to each baker.
- "Baker A, you get 10% of the total spotlights, but only if you actually bake cookies."
- "Baker B, you get 10%, but only if you bake."
How it works:
- Your reward is tied directly to your own quality, not how much better you are than your neighbor.
- If you work hard, your quality goes up, and you get more of your 10%.
- If your neighbor works hard, their quality goes up, and they get more of their 10%.
- Crucially: Your neighbor's success doesn't steal your spotlight. It just means the whole town looks better, and the platform might decide to turn on more spotlights for everyone.

Why this is genius: It removes the fear of being "stolen from." It turns the game from a "fight for a single prize" into a "team effort where everyone gets a guaranteed slice of the pie if they contribute." This creates a stable environment where everyone is motivated to work hard.

Part 3: The Math Problem (The "Budget" Puzzle)

Now that we have a stable system, the platform needs to decide: Who gets what percentage of the spotlights?

The Goal: Maximize the total happiness (Social Welfare) of the crowd.
The Challenge: This is incredibly hard to calculate. It's like trying to solve a Jigsaw Puzzle where the pieces keep changing shape depending on how you fit them together.
- The paper proves that finding the perfect solution is mathematically impossible to do quickly (it's "NP-Hard"). It's like trying to find the absolute best route for a delivery truck visiting 1,000 cities; the computer would need to run for years to find the perfect answer.

The Good News: The authors didn't give up. They created smart shortcuts (algorithms) that get us 99% of the way to the perfect answer, very quickly.

For Simple Towns (Bounded Spillovers): If the "copying" effect isn't too crazy, they have a fast algorithm that works almost perfectly.
For Tree-Like Towns: If the creators are connected in a family-tree structure (A influences B, B influences C), they have a "Hierarchical" algorithm that solves it efficiently.
For Random Towns (The Real World): In a chaotic, random network of creators, they invented a "Greedy Cost Selection" algorithm.
- The Metaphor: Imagine you have a limited budget of spotlights. Instead of guessing who is best, you simply look at who is cheapest to motivate. You give the spotlights to the bakers who need the least amount of encouragement to start baking.
- The Result: Surprisingly, this simple "pick the cheapest" strategy works amazingly well in the real world, especially when there are many creators.

The Takeaway

This paper is a guide for the future of the internet.

The Warning: If we keep using old "winner-takes-all" rules in a world of AI, creators will stop trying, and the internet will fill with low-quality, copied content.
The Fix: We need to change the rules. We should reward creators based on their own contribution, guaranteeing them a share of the attention so they aren't afraid of being copied.
The Result: By using these new "Provisional Allocation" rules and smart algorithms, we can build a digital ecosystem where humans and AI work together, keeping content fresh, high-quality, and full of human effort.

In short: Don't make creators fight to the death for a single prize. Give them a guaranteed slice of the pie if they bake, and let the AI help them bake better cakes. Everyone wins.

1. Problem Statement

The paper addresses a critical economic challenge in the era of Generative AI (GenAI): the erosion of creator incentives due to positive spillovers.

Context: In GenAI ecosystems, Large Language Models (LLMs) are trained on vast amounts of user-generated content. When a creator produces high-quality content, it improves the training data or inference capabilities of the LLM. Consequently, other creators can leverage this improved model to produce high-quality content at a lower cost.
The Conflict: While these spillovers increase the total ecosystem value, they create a "free-rider" problem. Creators may reduce their own effort, relying on the improvements generated by others.
The Failure of Standard Mechanisms: The authors demonstrate that traditional contest mechanisms (e.g., Winner-Takes-All or Tullock contests), which allocate rewards based on relative performance, become unstable in the presence of strong positive spillovers. In many game instances, these mechanisms fail to yield a Pure Nash Equilibrium (PNE), leading to volatile dynamics or a collapse in content quality.
Objective: The platform (mechanism designer) aims to maximize Social Welfare (the aggregate quality of content consumed by users) while ensuring the existence of a stable equilibrium where creators are incentivized to invest genuine effort.

2. Methodology and Model

The authors introduce the Content Creation with Spillovers (CCS) game model.

Players & Strategies: $N$ creators choose an effort level $x_i \in [0, 1]$ .
Costs: Effort incurs a convex cost $c_i(x_i)$ .
Quality Function: The quality $Q_i(x)$ $Q_{i} (x)$ of creator $i$ $i$ depends on their own effort and the efforts of all other creators ( $x_{-i}$ $x_{- i}$ ) due to spillovers.
- Assumption 1 (Effort Complementarities): The marginal gain from one's own effort is non-decreasing in the efforts of others ( $\frac{\partial^2 Q_i}{\partial x_i \partial x_j} \geq 0$ ). This captures the intuition that a better ecosystem (more data) makes individual effort more productive.
Observability: The platform observes the resulting quality $Q$ but cannot observe the underlying effort $x$ . Therefore, rewards must be based on $Q$ .
Social Welfare: Defined as the sum of all content qualities: $SW(x) = \sum Q_i(x)$ .

3. Key Contributions

A. Instability of Standard Mechanisms

The paper proves that canonical mechanisms like Winner-Takes-All (WTA) and Tullock contests are unstable under positive spillovers.

Proof Sketch: In a WTA setting, a small increase in one player's effort can drastically shift the winner, creating discontinuous incentives. In Tullock contests, the interdependence of quality functions can create cycles where no strategy profile is a best response to the others, leading to the non-existence of a PNE.

B. Provisional Allocation (PRA) Mechanisms

To resolve instability, the authors propose a new family of mechanisms called Provisional Allocation (PRA).

Definition: A PRA mechanism is defined by a vector of allocation shares $p = (p_1, \dots, p_N)$ where $\sum p_i \leq 1$ . The utility for creator $i$ is:
$U_i(x) = p_i \cdot Q_i(x) - c_i(x_i)$
Key Feature: The reward is absolute (scaled by a fixed share $p_i$ ) rather than relative. A creator's reward depends on their own quality and their assigned cap, not on how they compare to others.
Theoretical Guarantees (Theorem 5):
1. Stability: Any PRA mechanism induces a Supermodular Game.
2. Existence: A Pure Nash Equilibrium (PNE) always exists.
3. Selection: There exists a unique Greatest PNE (denoted $\bar{x}$ ) that Pareto-dominates all other equilibria (higher welfare and higher utility for all players) and is reachable via best-response dynamics.
Axiomatic Characterization (Theorem 6): The authors prove that any mechanism satisfying "Strategic Complementarities" (a necessary condition for stability in this setting) must essentially take the separable form of PRA ( $M_i(Q) = b_i f_i(Q)$ ).

C. Algorithmic Results for Welfare Maximization

The platform's goal is to choose the vector $p$ to maximize $SW(\bar{x}(p))$ .

Hardness: The optimization problem is NP-hard (reduction from Maximum Clique) and hard to approximate within a constant factor.
Approximation Algorithms:
1. Bounded Spillovers: If spillovers are bounded by a factor $\beta$ , an algorithm based on the No-Spillovers Relaxation (NSR) achieves a $(1+\beta)$ -approximation in polynomial time.
2. Tree-Structured Spillovers: If the interaction graph is a tree, a dynamic programming algorithm (HOP) computes a near-optimal mechanism in polynomial time.
3. Random Graphs (Average Case): For random interaction graphs (Erdős–Rényi), the Greedy Cost Selection (GCS) algorithm runs in $O(N^2)$ $O (N^{2})$ time. It sorts players by cost and allocates shares to the cheapest players first.
  - Result: GCS achieves an approximation ratio of $(1 - O(N^{-1/4}))$ with high probability, which is asymptotically optimal.

4. Experimental Validation

The authors validate the Greedy Cost Selection (GCS) algorithm through simulations on random instances.

Setup: Compared GCS against an "Equal Allocation" baseline (giving everyone $1/N$ ).
Findings:
- GCS significantly outperforms Equal Allocation in Social Welfare across varying numbers of players ( $N$ ), edge probabilities ( $r$ ), and quality bounds ( $q^*$ ).
- GCS successfully incentivizes a larger number of active players, particularly those with lower costs, whereas Equal Allocation often fails to incentivize high-cost players even when their participation is socially beneficial due to spillovers.
- Empirical results align with the theoretical prediction that the number of incentivized players scales linearly with $N$ .

5. Significance and Implications

Theoretical Foundation: This is the first game-theoretic framework specifically addressing incentive design in GenAI-assisted content creation with positive spillovers.
Mechanism Design: It demonstrates that decoupling rewards from relative performance is crucial for stability in ecosystems with knowledge spillovers. By capping rewards (PRA), the platform prevents the "race to the bottom" or instability caused by free-riding.
Preventing Model Collapse: By providing a mechanism to sustain human effort, the work offers a theoretical solution to the risk of "Model Collapse" (where AI models degrade because they are trained on AI-generated data). Incentivizing genuine human content ensures a continuous supply of high-quality, diverse data.
Practical Application: The proposed algorithms (especially GCS) are computationally efficient and offer a blueprint for platform designers (e.g., social media, content marketplaces) to structure their reward systems in the age of AI.

In summary, the paper argues that to sustain a healthy content ecosystem in the GenAI era, platforms must move away from competitive, relative ranking systems and adopt absolute, provisional allocation mechanisms that align individual incentives with the collective benefit of the ecosystem.