SearcharxivSearch

arXiv · 2411.02661

Pricing and Competition for Generative AI

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.

Explore related subjects

Keep this discovery

BibTeXRIS

Rafid Mahmood. 2024-11-04. Pricing and Competition for Generative AI. https://arxiv.org/abs/2411.02661

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

MMS Allocation for Chores with Online Agent Arrivals

We study the fair allocation of $m$ indivisible chores to $n$ agents with subadditive cost functions arriving online in an arbitrary order. Upon an agent's arrival, we are informed of her cost function and must irrevocably assign her a set of chores. We focus on the Maximin Share (MMS) fairness notion and aim to compute an allocation in which all items are assigned, and no agent incurs a cost more than $\alpha$ times her MMS. Without any prior information about the instance (other than $n$ and $m$), we design an algorithm with a competitive ratio of $O(\min\{n, k\log^{1+\epsilon}k, \log m\})$ for any constant $\epsilon > 0$, where $k$ denotes the number of cost function types. Our bound matches the best known offline approximation guarantees for MMS under subadditive costs and is nearly optimal with respect to all three parameters: we show that even for binary additive cost functions, no online algorithm can achieve a competitive ratio of $o(\min\{n, k\log k, \log m\})$. We then consider the setting in which the $k$ cost function types are known in advance (though the realized types of arriving agents are not). For additive cost functions, we provide an algorithm with a competitive ratio of $O(\min\{\log k, \log(kn)/\log\log(kn)\})$, and show that constant-competitive algorithms do not exist for general $k$, even for the binary additive setting. For binary additive functions when $k \le n$, we propose a $3$-competitive algorithm and establish a lower bound of $2$.

cs.GT

Truncated Noisy Best-Response Algorithms: Toward Game Theoretic Learning with Safety Guarantees

We consider a game theoretic approach to solve multi-agent coordination problems with submodular maximization objectives. It is known for such problems that the Nash equilibria for the corresponding game are always within 50% of the optimal, but that the equilibria which achieve this worst-case bound are not stable. To exploit this instability, we propose a family of algorithms which we call Truncated Noisy Best-Response (TNBR) Algorithms. These algorithms are flexibly characterized by agents asynchronously and stochastically selecting actions from a neighbourhood of their best response payoffs. We compute bounds on the recurrent classes of TNBR algorithms' associated Markov chains. Our bounds fall into two categories: first, "Performance" bounds ensure that TNBR algorithms always have a high-value recurrent state; second, "Safety" bounds ensure that TNBR algorithms never have arbitrarily-bad recurrent states. Furthermore, these two types of bounds are linked by a waterbed-like effect: every game with a poor Safety guarantee necessarily has a favorable Performance guarantee.

cs.GT

Existence of the Core in Approval-Based Committee Elections

We settle the main open question in the theory of approval-based multi-winner elections: we show that there always exists a committee in the core. The core is a stability and group fairness concept. The proof introduces a new voting rule that optimizes an entropy-like objective function over committees and payment systems. All local optima of this objective function lie in the core, which implies that a core committee can be found in polynomial time.

cs.GT