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

TL;DR

This paper formalizes a three-layer model-platform-user market game and identifies conditions for the existence of pure Nash equilibrium, and examines welfare outcomes and shows that market structure depends not only on models' global average performance but also on their localized attraction to user groups.

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 (12)

• 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.
• 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 \ref{['sec:calex1']}.
• Figure 3: $\pi_{{\bm{\theta}}}^{\star}$ versus $\frac{\Gamma}{\rho}$.
• 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 \ref{['subsec:EquilibriumWelfare']}.
• 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.

Theorems & Definitions (44)

• Definition 2.1: Nash Equilibrium
• Proposition 2.2
• Definition 2.3: Best-Response Cycle
• Definition 2.4: Coverage Value
• Definition 2.5: User Welfare
• Definition 2.6: Social Optimum Welfare
• Definition 2.7: Herfindahl-Hirschman Index (HHI) Diversity
• Definition 2.8: Support Diversity
• Definition 3.1: Average Score
• Definition 3.2: Attraction Term and Deviation Advantage