Pricing and Competition for Generative AI

TL;DR

This work develops a comparison of two different models for a specific task with respect to user cost-effectiveness and finds that if the different tasks are sufficiently similar, the first-to-market model may become cost-ineffective on all tasks regardless of how this technology is priced.

Abstract

Compared to classical machine learning (ML) models, generative models offer a new usage paradigm where (i) a single model can be used for many different tasks out-of-the-box; (ii) users interact with this model over a series of natural language prompts; and (iii) the model is ideally evaluated on binary user satisfaction with respect to model outputs. Given these characteristics, we explore the problem of how developers of new generative AI software can release and price their technology. We first develop a comparison of two different models for a specific task with respect to user cost-effectiveness. We then model the pricing problem of generative AI software as a game between two different companies who sequentially release their models before users choose their preferred model for each task. Here, the price optimization problem becomes piecewise continuous where the companies must choose a subset of the tasks on which to be cost-effective and forgo revenue for the remaining tasks. In particular, we reveal the value of market information by showing that a company who deploys later after knowing their competitor's price can always secure cost-effectiveness on at least one task, whereas the company who is the first-to-market must price their model in a way that incentivizes higher prices from the latecomer in order to gain revenue. Most importantly, we find that if the different tasks are sufficiently similar, the first-to-market model may become cost-ineffective on all tasks regardless of how this technology is priced.

Figures (3)

• Figure 1: Overview of the competitive pricing problem for generative AI models.
• Figure 2: (Left) Three tasks with three different exponential demand functions $D_1(p) = 100e^{-0.5p}$, $D_2(p) = 200e^{-0.5p}$, $D_3(p) = 400e^{-0.5p}$. (Right) The corresponding revenue from each task along with the total revenue function for a firm $R_B(p)$. The vertical lines correspond to $\kappa_1q$, $\kappa_2q$, and $\kappa_3q$, where $\kappa_1 > \kappa_2 > \kappa_3$. For $p < \kappa_3q$, revenue is obtained from all three tasks, for $p \in (\kappa_3q, \kappa_2q]$, revenue is obtained from only the first two tasks, and for $p \in (\kappa_2q, \kappa_1q]$, revenue is only obtained from the first task. No revenue can be obtained if $p > \kappa_1 q$.
• Figure 3: The relationship between $\kappa_2/\kappa_1$ and $a_1/(a_1 + a_2)$ for firm A. In the blue region, firm B will always set a price that is competitive on both tasks and firm A will acquire zero revenue. In the orange region, the maximum price that firm A can set is upper bounded (see problem \ref{['eq:two_player_exp_demand_prob2']}). In the green region, the maximum price that firm A can set has a higher upper bound (see problem \ref{['eq:two_player_exp_demand_prob1']}).

Theorems & Definitions (14)

• Theorem 1
• Theorem 2
• Theorem 3
• Corollary 1
• Theorem 4
• Proposition 1
• Proposition 2
• proof : Proof of Theorem \ref{['thm:general_one_player']}
• proof : Proof of Theorem \ref{['thm:firm_A_problem']}
• proof : Proof of Theorem \ref{['thm:one_player_exp_demand']}