Competition and Diversity in Generative AI

Manish Raghavan

cs.GTDec 11, 2024

Competition and Diversity in Generative AI

Authors: Manish Raghavan

Organizations: MIT Sloan School of Management & Department of Electrical Engineering and Computer Science.

Abstract

Recent evidence, both in the lab and in the wild, suggests that the use of generative artificial intelligence reduces the diversity of content produced. The use of the same or similar AI models appears to lead to more homogeneous behavior. Our work begins with the observation that there is a force pushing in the opposite direction: competition. When producers compete with one another (e.g., for customers or attention), they are incentivized to create novel or unique content. We explore the impact competition has on both content diversity and overall social welfare. Through a formal game-theoretic model, we show that competitive markets select for diverse AI models, mitigating monoculture. We further show that a generative AI model that performs well in isolation (i.e., according to a benchmark) may fail to provide value in a competitive market. Our results highlight the importance of evaluating generative AI models across the breadth of their output distributions, particularly when they will be deployed in competitive environments. We validate our results empirically by using language models to play Scattergories, a word game in which players are rewarded for answers that are both correct and unique. Overall, our results suggest that homogenization due to generative AI is unlikely to persist in competitive markets, and instead, competition in downstream markets may drive diversification in AI model development.

Figures & tables

Figure 1: Description of game mechanics.

Panel of Figure 2 — Figure 2: Sample score functions $s_{\gamma}(x)=x^{\gamma}$ .

Panel of Figure 3 — Figure 3: For further intuition on Lemma 4.7 , we show how $\mathbf{p}_{\textsc{opt}}(n,\mathbf{d},s_{\gamma})_{1}$ and $\mathbf{p}_{\textsc{eq}}(n,\mathbf{d},s_{\gamma})_{1}$ respectively vary with both $n$ and $\gamma$ for the instance given by $\mathbf{d}=[5;~2]$ . For $\gamma<1$ , both $\mathbf{p}_{\textsc{opt}}$ and $\mathbf{p}_{\textsc{eq}}$ converge to $\mathbf{p}^{\dagger}(\gamma)$ , shown as a magenta line in each panel. For $\gamma\geq 1$ , $\mathbf{p}_{\textsc{opt}}$ converges to the uniform distribution, with a discontinuity at $\gamma=1$ . Further, while $\mathbf{p}_{\textsc{eq}}$ is monotone in both $n$ and $\gamma$ ( Theorems 4.4 and 4.5 ), $\mathbf{p}_{\textsc{opt}}$ is not. Increasing $n$ can lead to a less diverse symmetric socially optimal strategy.

Figure 4: Empirical setup for Section 6.1 . At low temperatures, collisions are likely. Higher temperatures reduce collisions, but they increase the chance of errors (e.g., “Sandal”).

Role	Content
System	You are a helpful assistant. Answer in as few words as possible, with no explanations.
User	We are playing a game of Scattegories. I will give you a letter and a category, and you will give me a word or short phrase that starts with that letter and matches the category. For example, if I say "Fruit" and "A," you could say "Apple" or "Apricot."
Assistant	I understand.
User	Letter: C\nCategory: Countries
Assistant	Canada
User	Letter: X\nCategory: Instruments

Table 1: Default prompt

Figure 5: Per-player utility as a function of $\tau$ for different values of $n$ . The highest line corresponds to $n=1$ , and the lowest corresponds to $n=15$ . $\gamma=1.0$ .

Figure 6: Average accuracy (as verified by qwen2.5 ) vs entropy for each LLM. Each point represents a different temperature, using darker circles for higher temperatures. As one might expect, entropy increases monotonically with temperature. The left panel shows average entropy for the unconditional distribution, while the right panel shows entropy conditional on correctness. Observe that llama3.1 falls from the accuracy-entropy frontier at high temperatures when we only consider correct answers.

Figure 7: Socially optimal and equilibrium temperatures for each language model as a function of $n$ . Observe that (1) all curves are increasing in $n$ , and (2) equilibrium temperatures are lower than their socially optimal counterparts. $\gamma=1.0$

Figure 8: Socially optimal and equilibrium welfare (per player) for each language model as a function of $n$ . Observe that (1) welfare is decreasing in $n$ , and (2) equilibrium welfare is not too far from optimal. phi3.5 and gemma2 perform better in the presence of stronger competition. $\gamma=1.0$ .

Panel of Figure 9 — Figure 9: Each dot represents a possible pair $(m_{1},m_{2})$ of equilibrium market shares for each language model. Dashed lines connect points with the same total number of players $n$ , with a maximum of $n=15$ . $\gamma=1.0$ .

Figure 10: Illustration of our setup for Section 6.3 . We compute distributions over answers for multiple LLMs and prompts (at a variety of temperatures). We compute distances between distributions based on how “mis-ranked” they are relative to one another. In this example, while the two rankings from phi3.5 are not identical, they are “close” in the sense that they can be made identical by shifting a small amount of probability mass. At a high level, we find that differences across prompts are much less salient than differences across tools. We use prompts that are quite different to capture potential strategic behavior—for example, one explicitly mentions Scattergories and provides examples of less “obvious” answers, whereas the other does not. Our experiments use different in-context examples for each prompt. See Section D.4 for further details.

Figure 11: Distance matrix $D$ defined in ( 6 ).

Figure 12: Confusion matrix from spectral clustering.

Figure 13: Illustration of our setting for Section 7 . A user arrives with an intent

I

, instantiated as a text description of their desired image

\omega^{*}

. Each producer samples an output, using their chosen GAIT. In this example, each producer chooses a different GAIT. The user selects the closest image as measured by

\sigma

(in this case,

\omega_{2}

). Player 2 gets utility 1, and the others get utility 0.

Model	Average Distance
cogview4	0.413
FLUX.1-dev	0.428
pixart-sigma	0.462
stable-diffusion3.5	0.442

Table 2: Average distance to target image ( DreamSim )

Figure 14: Market shares for equilibrium and optimal strategies. There is no pure strategy equilibrium for $n=7$ .

Figure 15: Image diversity with optimal and equilibrium strategies, as measured by average pairwise distance. Equilibria generally yield lower pairwise distances (more visual similarity) than socially optimal strategies, though competition (larger $n$ ) increases distances.

Appendix figures & tables27 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 16 — Figure 16: Social welfare as a function of $\tau$ for different values of $n$ . $\gamma=1.0$ .

Figure 17: Socially optimal and equilibrium temperatures for each language model as a function of $\gamma$ . Observe that (1) all curves are increasing in $\gamma$ , and (2) equilibrium temperatures are lower than their socially optimal counterparts. Optimal and equilibrium temperatures converge for large $\gamma$ , as predicted by Lemma 4.8 . Note that llama3.1 appears to have higher equilibrium temperature than optimal temperature for $\gamma\geq 5$ . This is an artifact of discretization of the temperature space. $n=3$ .

Figure 18: Social welfare for each language model at optimal and equilibrium temperatures as a function of $\gamma$ . Note that for $\gamma\geq 1$ , optimal social welfare is constant. Observe that (1) social welfare is decreasing in $\gamma$ for $\gamma\leq 1$ , and (2) equilibrium welfare is not too far from optimal. The nonmonotonicity at $\gamma=1$ is due to the fact that our social welfare changes at this point. Interestingly, social welfare for gemma2 , phi3.5 , and llama3.1 are nearly identical for large values of $\gamma$ despite the fact that they yield very different per-player utilities ( Figure 19 ). $n=3$ .

Figure 19: Socially optimal and equilibrium utility (per player) for each language model as a function of $\gamma$ . Note that for $\gamma>1$ , social welfare ( Figure 18 ) is strictly larger than the sum of player utilities. Observe that (1) utility is decreasing in $\gamma$ , and (2) equilibrium welfare is not too far from optimal. Note that phi3.5 and gemma2 seem to perform relatively better in the presence of stronger competition. $n=3$ .

Figure 20: Pairwise equilibria for all pairs of GAITs. $\gamma=1.0$ .

Figure 21: Probability mass captured by our sample at different temperatures.

Letter	Category	Letter	Category
B	Fish	L	Things With Tails
C	Spicy Foods	M	Crimes
D	Things That Can Kill You	O	Things With Tails
D	Words With Double Letters	Q	Game Terms
E	Bad Habits	R	Junk Food
E	Birds	R	Software

Appendix

Table 4: Instances in our sample

Figure 22: 2D spectral embedding of the similarity matrix $S$ . Points are colored according the clusters learned via spectral clustering, which correspond exactly to the LLMs that generated them.

Role	Content
System	You are a helpful assistant. Answer in as few words as possible, with no explanations.
User	You are judging a Scattergories game. I will give you a category and an answer. You will tell me whether that answer fits the given category. You are strict but fair. You do not accept incomplete answers. Answer with either the word ’yes’ or ’no’.
Assistant	I understand.
User	Category: Things that are red\nAnswer: blood
Assistant	yes
User	Category: Animals\nAnswer: rock

Appendix

Table 5: Verification prompt

Role	Content
System	You are a concise and clever word generator. Respond with a single word or short phrase that fits the request. No explanations.
User	We are playing a word game. I’ll give you a letter and a category. You respond with something that starts with that letter and fits the category. For example, if I say "Fruit" and "A," your answer could be "Apple" or "Avocado."
Assistant	Got it.
User	Letter: A\nCategory: Animals
Assistant	Alligator
User	Letter: B\nCategory: Things you find in a bathroom

Appendix

Table 6: ChatGPT prompt #1

Role	Content
System	You are playing a game of Scattergories. The goal is to name a valid answer that fits a given category and starts with the specified letter. Your answer should be unique, plausible, and as specific as possible. Only respond with the answer-no explanations or extra text.
User	Letter: {letter}\nCategory: {category}

Appendix

Table 7: ChatGPT prompt #2

Role	Content
System	You are a Scattegories expert. Provide single-word or very brief answers that start with the specified letter. Be creative, original, and avoid common responses.
User	We’re playing Scattegories. I’ll give you a letter and category, and you’ll respond with an interesting word or short phrase starting with that letter. For example, if I say ’Letter: A, Category: Fruit,’ you might answer ’Ackee’ or ’Asian pear’ rather than the more obvious ’Apple.’
Assistant	Ready to play!
User	Letter: P\nCategory: U.S. Cities
Assistant	Philadelphia
User	Letter: S\nCategory: Superheroes

Appendix

Table 8: Claude prompt #1

Role	Content
System	You are playing Scattergories! Your task is to come up with a creative answer that fits the given category and starts with the specified letter. Follow these rules:\n\n1. Your answer must start with the given letter\n2. Your answer must fit the category\n3. Be creative and try to think of unique answers\n4. Give only ONE answer\n5. Respond with just the answer, no explanation needed\n\nExample:\nLetter: B\nCategory: Things in a kitchen\nAnswer: Blender
User	Letter: S\nCategory: Animals
Assistant	Squirrel
User	Letter: {letter}\nCategory: {category}

Appendix

Table 9: Claude prompt #2

Role	Content
System	You are a competitive Scattergories champion. Respond with only valid answers - single words or very short phrases that perfectly match the category and start with the given letter. No explanations, no apologies.
User	Let’s play Scattergories! I’ll give you a letter and category, and you’ll respond with the first valid answer that comes to mind. Quick, creative, and strictly following the rules. For example:
Assistant	Ready to play.
User	Letter: F\nCategory: Famous people
Assistant	Franklin
User	Letter: D\nCategory: Hobbies

Appendix

Table 10: deepseek prompt #1

Role	Content
User	You’re playing Scattergories, the word game where players brainstorm unique words fitting categories. For each round, I’ll provide a starting letter and a category. Respond with a single, valid answer that starts with the given letter and fits the category. Be creative but keep answers realistic and category-appropriate.
Assistant	Understood! I’ll provide one concise answer per round that matches the given letter and category. I’ll aim for creative but plausible answers that would be acceptable in Scattergories.
User	Letter: {letter}\nCategory: {category}

Appendix

Table 11: deepseek prompt #2

Role	Content
System	You are a Scattegories master. Provide a single, concise word or short phrase that fits the given letter and category. No explanations, no extra words.
User	Let’s play Scattegories! I’ll give you a letter and a category. You respond with a valid answer that starts with that letter and fits the category. For example, if I say "Fruit" and "A," you could respond with "Apple" or "Apricot."
Assistant	Understood. I’m ready.
User	Letter: C\nCategory: Countries
Assistant	China
User	Letter: V\nCategory: Instruments

Appendix

Table 12: Gemini prompt #1

Role	Content
System	You are an expert Scattergories player. Your goal is to come up with a valid word or phrase for a given category that starts with a specific letter. Your responses must be a single word or a short phrase. If you cannot think of a valid answer, respond with ’N/A’. Do not include any other text or explanations.
User	Letter: C\nCategory: Things you find in a classroom
Assistant	Chalkboard
User	Letter: P\nCategory: Types of fruit
Assistant	Pineapple
User	Letter: Z\nCategory: Animals

Appendix

Table 13: Gemini prompt #2

Role	Content
System	You are a creative assistant. Provide a single word or short phrase in response, no explanations.
User	We’re playing Scattergories! I’ll give you a letter and a category. Respond with a word or short phrase starting with that letter, fitting the category. For example, ’Fruit’ and ’B’ could be ’Banana’ or ’Blueberry.’
Assistant	Got it! Ready to play.
User	Letter: M\nCategory: Brands of cars
Assistant	Mazda
User	Letter: T\nCategory: Things you can eat for breakfast

Appendix

Table 14: Grok prompt #1

Role

Content

System

You are a creative and quick-thinking assistant playing Scattergories. Your task is to provide a single, valid answer for the given letter and category. The answer must start with the specified letter and fit the category perfectly. Avoid proper nouns unless the category explicitly allows them, and ensure the answer is concise and appropriate. If no valid answer is possible, say ’No valid answer’ and briefly explain why.

User

Letter: {letter}\nCategory: {category}

Appendix

Table 15: Grok prompt #2

Role	Content
System	You are playing Scattergories competitively. Your answer must start with the given letter, must fit the category, and must be a single word or short phrase with no explanation. Choose a valid answer that other players are less likely to choose.
User	We are playing Scattergories. I will give you a letter and a category. Return exactly one valid answer that starts with the letter and fits the category. Prefer an uncommon but still clearly valid answer.
Assistant	Understood.
User	Letter: C\nCategory: Countries
Assistant	Comoros
User	Letter: H\nCategory: Hobbies

Appendix

Table 16: Strategic prompt #1.

Role	Content
System	You are playing Scattergories competitively. Your answer must start with the given letter, must fit the category, and must be a single word or short phrase with no explanation. Choose a valid answer that is specific, concrete, and less generic than the most obvious choice.
User	I will give you a letter and a category. Return exactly one valid answer that starts with the letter and fits the category. Prefer a specific answer over a broad or generic one.
Assistant	Ready.
User	Letter: V\nCategory: Instruments
Assistant	Vibraphone
User	Letter: B\nCategory: Things in a kitchen

Appendix

Table 17: Strategic prompt #2.

Role	Content
System	You are playing Scattergories competitively. Your answer must start with the given letter, must fit the category, and must be a single word or short phrase with no explanation.
User	Take into account answers that other players might commonly use. Then, produce a different answer. Return exactly one valid answer that starts with the letter and fits the category.
Assistant	Got it.
User	Letter: M\nCategory: Dogs
Assistant	Mastiff
User	Letter: S\nCategory: Things in a garage

Appendix

Table 18: Strategic prompt #3.

Figure 23: Market share for equilibrium and optimal strategies, using LPIPS to measure similarity.

Figure 24: Image diversity with optimal and equilibrium strategies, as measured by average pairwise distance, using LPIPS to measure similarity.

Figure 25: Average distance ( DreamSim ) between selected image and target image for both equilibrium and optimal strategies.

Figure 26: Average distance ( LPIPS ) between selected image and target image for both equilibrium and optimal strategies.

Model	Average Distance
Model
cogview4	0.684
flux1.dev	0.672
pixart-sigma	0.678
sd3.5	0.693

Appendix

Table 20: Average distance to target image ( LPIPS )

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