Market Games for Generative Models: Equilibria, Welfare, and Strategic Entry

Xiukun Wei; Min Shi; Xueru Zhang

cs.GTFeb 19, 2026

Market Games for Generative Models: Equilibria, Welfare, and Strategic Entry

Authors: Xiukun Wei, Min Shi, Xueru Zhang

Organizations: The Ohio State University

Abstract

Generative model ecosystems increasingly operate as competitive multi-platform markets, where platforms strategically select models from a shared pool and users with heterogeneous preferences choose among them. Understanding how platforms interact, when market equilibria exist, how outcomes are shaped by model-providers, platforms, and user behavior, and how social welfare is affected is critical for fostering a beneficial market environment. In this paper, we formalize a three-layer model-platform-user market game and identify conditions for the existence of pure Nash equilibrium. Our analysis shows that market structure, whether platforms converge on similar models or differentiate by selecting distinct ones, depends not only on models' global average performance but also on their localized attraction to user groups. We further examine welfare outcomes and show that expanding the model pool does not necessarily increase user welfare or market diversity. Finally, we design novel best-response training schemes that allow model providers to strategically introduce new models into competitive markets.

Figures & tables

Figure 1: The three-layer model-platform-user market structure. Model providers develop generative models, platforms select models to deploy, and heterogeneous users choose platforms.

	$S_{1}({\bm{\theta}})$	$S_{2}({\bm{\theta}})$
${\bm{\theta}}_{A}$	0.90	0.85
${\bm{\theta}}_{B}$	0.35	0.80

Figure 2: Two scenarios with the same average score gap

|T_{2}-T_{1}|=0.20

but different deviation advantage

(\delta_{1},\delta_{2})

for

N=2

and

M=2

, resulting in opposite equilibrium outcomes. In Scenario A, although

g_{1}

has a lower average score (

T_{1}<T_{2}

), it is still chosen in equilibrium because its strong advantage on the high-weight type

{\bm{\theta}}_{A}

satisfies the differentiation condition. Removing this type-specific advantage in Scenario B breaks the condition, leading to a homogeneous equilibrium on

g_{2}

. These scenarios demonstrate that market structure is not determined solely by average performance; a strong local advantage in high-weight user segments can sustain a model’s presence in equilibrium. Full calculation details are provided in Section C.4 .

Figure 3:

\pi_{{\bm{\theta}}}^{\star}

versus

\frac{\Gamma}{\rho}

	$S_{1}({\bm{\theta}})$	$S_{2}({\bm{\theta}})$
${\bm{\theta}}_{A}$	0.90	0.85
${\bm{\theta}}_{B}$	0.35	0.80

Figure 4: An example where enlarging the model pool decreases welfare. In Scenario A, with models

g_{1}

and

d_{2}

, the equilibrium is fully differentiated with the welfare

W=0.85

. Adding a new model

g_{3}

in Scenario B shifts the equilibrium to the homogeneous

(g_{3},g_{3})

, where welfare decreases to

W=0.84

. It pulls both platforms toward homogenization, thereby sacrificing the welfare of minority types. The calculation details are provided in Section C.9 .

Table 5

Panel of Figure 5 — Figure 5: When enlarging either the model pool (a,b) with $3$ players or the number of platforms (d,e) with $5$ models, the change of HHI diversity ((a,d), where larger values indicate more homogenization) and coverage value ((b,e), where larger values are better). (c,f) provide examples of utility trajectories across best-response steps, where filled markers denote the player taking the action at each step. (c) shows best-response cycle and (d) shows an equilibrium.

Figure 6: Performance of new models generated by the direct-gradient method $M_{\mathrm{grad}}$ and the resampling method $M_{\mathrm{samp}}$ . (a) Left: equilibrium outcomes and utilities of three players when competing over the original pool, after introducing $M_{\mathrm{grad}}$ and $M_{\mathrm{samp}}$ . (b) Middle: diversity $D_{\mathrm{HHI}}$ and welfare $W_{\mathrm{eq}}$ under the three equilibrium. (c) Right: comparison between the best original model $M_{5}$ and the new entrants $M_{\mathrm{grad}}$ , $M_{\mathrm{samp}}$ on user scores.

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Model	$b_{j}$	$\mu_{jr}$	$A_{jr}$	$\sigma_{jr}$
1	0.12	(1.5, 0.0)	0.90	1.20
2	0.05	(0.0, 0.0)	1.30	0.35
3	0.08	(3.0, 0.0)	1.00	0.50
4	0.06	(0.0,0.0), (3.0,0.0)	0.70, 0.70	0.70, 0.70
5	0.05	(1.5, 0.6)	1.00	0.40
6	0.05	(1.5,-0.6)	1.00	0.40

Appendix

Table 3: Simulation model pool.

Weight $w_{q}$	Mean $\mu_{q}$	Covariance $\Sigma_{q}$
0.6	(0.0, 0.0)	[[0.25, 0.0], [0.0, 0.25]]
0.4	(3.0, 0.0)	[[0.25, 0.0], [0.0, 0.25]])

Appendix

Table 4: User distribution parameters.

Panel of Figure 7 — Figure 7: Best-response simulations under different settings.

Panel of Figure 8 — Figure 8: The average performance $T_{i}$ of the five models in model pool in Table 2 and their user-specific performance $S_{i}({\bm{\theta}})$ in Table 2 .

Table 12

User Pool	$f$	$D_{\text{supp}}$	$D_{\text{HHI}}$	$W_{\text{eq}}$
Pool 1	$(M5,M5,M5)$	1	0.3333	0.2110
Pool 2	$(M5,M5,M1)$	2	0.3349	0.2117
Pool 3	$(M5,M3,M1)$	3	0.3335	0.1615
Pool 4	$(M5,M5,M5)$	1	0.3333	0.2366
Pool 5	$(M5,M1,M1)$	2	0.3856	0.1932
Pool 6	$(M1,M1,M1)$	1	0.3333	0.1715

Appendix

Table 7: Outcomes of a 3-player setting under different user pools.

Figure 9: Label distributions of

2,000

generated samples from three models: (a) left:

M2

from the original model pool (b) middle:

M_{\mathrm{samp}}

by redampling method. (c) right:

M_{\mathrm{grad}}

by direct-gradient method.

Panel of Figure 10 — Figure 10: Different performance of model scores across user groups under different $\beta$ and $\gamma$ compared to each user group’s best score $\bar{S}$ .

Panel of Figure 11 — Figure 11: Different performance of model scores across user groups under different $\lambda$ compared to each user group’s best score $\bar{S}$ .

Model	HEval	Multi-language	Overall	Math	IFEval
M0: CodeLlama-34B	0.5079	0.4297	0.1721	0.0413	0.4604
M1: Qwen2.5-Coder-32B	0.5710	0.6497	0.3326	0.3089	0.4363
M2: Nxcode-CQ-7B-orpo	0.8723	0.6688	0.1237	0.4007	0.4007
M3: Qwen2.5-Coder-32B-Instruct	0.8320	0.7723	0.3989	0.4955	0.7265

Appendix

Table 8: Performance of four models on coding and reasoning benchmarks.

Table 18

User Pool	$f$	$D_{\text{supp}}$	$D_{\text{HHI}}$	$W_{\text{eq}}$
Pool 1	$(M3,M3,M3)$	1	0.3333	0.65945
Pool 2	$(M3,M2,M2)$	2	0.375	0.75949
Pool 3	$(M3,M3,M2)$	2	0.33375	0.73080

Appendix

Table 11: Outcomes of a 3-player setting under different user pools.

Panel of Figure 12 — Figure 12: Best-response simulations under different settings of language tasks.

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