📈 economics

Token Is All You Price

The paper demonstrates that token-based pricing in GenAI services is the revenue-optimal way to screen buyers with different levels of urgency by using a menu of stopping-time caps on information throughput.

Original authors: Weijie Zhong

Published 2026-04-28

📖 3 min read☕ Coffee break read

CC BY 4.0

Original authors: Weijie Zhong

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are at a high-end, all-you-can-eat buffet, but there is a catch: the chef is incredibly talented, but they can only cook so many dishes per hour because the kitchen is small.

Now, imagine there are two types of customers:

The "Hungry Professional": They are in a massive rush. They need to eat now to get back to a business meeting. They are willing to pay a premium to get food on the table immediately.
The "Leisurely Diner": They have all afternoon. They don't mind waiting for the perfect dish to be prepared, as long as the food is good.

The Problem: How does the restaurant owner make the most money without making the "Hungry Professional" wait too long or making the "Leisurely Diner" feel ripped off?

The Old Way of Thinking (The "Menu of Different Foods" Approach)

In traditional economics, a business usually tries to separate these customers by offering different products. They might give the hungry person a quick, mediocre sandwich and the patient person a slow-cooked, gourmet steak. This is called "distorting the product." It’s not ideal because the hungry person doesn't actually want a mediocre sandwich—they want the gourmet steak, just faster.

The Paper’s Big Discovery (The "Timer" Approach)

This paper, written by Weijie Zhong, argues that for modern AI services (like ChatGPT or Claude), the smartest way to make money isn't to change what the AI says, but to change how long you are allowed to talk to it.

Instead of offering a "dumb" AI for fast people and a "smart" AI for slow people, the paper says the optimal strategy is to:

Use one "Super-Chef" (The Greedy Process): Use the best possible AI model that works as fast and efficiently as possible to find the answer. This is what computer scientists call "preference-aligned"—it’s the version of the AI that is most helpful to a human.
Use a "Stopwatch" (The Token Cap): Instead of changing the AI, you just give people different "time limits" or "token quotas."

The hungry professional pays a high price for a "Short Burst" pass (e.g., "You can use the Super-Chef for 5 minutes"). The patient diner pays a lower price for a "Long Session" pass (e.g., "You can use the Super-Chef for 5 hours").

Why This Matters for AI (The "Token" Connection)

If you’ve ever used an AI and seen messages like "You have 40 messages left for the next 3 hours," or if you've seen B2B companies paying for different "API Tiers" (Priority vs. Batch), you are seeing this exact math in action.

The paper explains that:

The AI doesn't need to be "dumbed down" for cheaper tiers. It stays high-quality.
The "Price" is actually a "Speed Limit." You aren't just paying for information; you are paying for the right to keep the information flowing before the system cuts you off.

The "Magic" of the Math

The most surprising part of the paper is that the "best" way to serve everyone is actually the "best" way to serve a single person who has no time limit at all.

In most businesses, the owner has to "cheat" the customer a little bit to make a profit (by giving them lower quality). But in the world of AI information, the owner can maximize their profit by being perfectly honest with the quality and only being "strict" with the clock.

In short: The paper proves that in the age of AI, you don't sell "intelligence"—you sell "time to think."

Technical Summary: Token Is All You Price: Screening Urgency via Information Design

1. Problem Statement

The paper addresses a mechanism design problem in the context of dynamic information services (e.g., Generative AI, expert networks, or legal retainers). The seller provides a real-time information process (a sequence of posterior beliefs) to buyers who wish to learn an unknown state $\theta$ .

The core tension arises from two constraints:

Information-Throughput Constraint: The seller has a physical or technological limit on how much information (entropy) can be generated per unit of time ( $\chi$ ).
Private Urgency (Heterogeneous Types): Buyers differ in their private discount rates $r$ , representing how much they value learning the state quickly. A higher $r$ indicates higher urgency.

The seller's objective is to design a menu of mechanisms (belief processes and transfers) that maximizes expected revenue while satisfying Incentive Compatibility (IC) and Individual Rationality (IR).

2. Methodology

The author employs tools from dynamic information design, Bayesian persuasion, and nonlinear pricing theory.

The Design Space: The principal can choose any càdlàg martingale process $\langle\mu_t\rangle$ that satisfies a generalized entropy-based throughput constraint. This is an infinite-dimensional optimization problem.
Pointwise Reduction: Using the Envelope Theorem, the author reduces the complex revenue maximization problem to a series of pointwise maximization problems. The goal is to maximize a "virtual time preference" $\rho_r(t)$ , which adjusts the buyer's utility to account for the information rent they would receive.
Duality Machinery: The paper utilizes the duality framework developed by Sannikov and Zhong (2024) to characterize the optimal stopping-time distributions under martingale constraints.
Greedy Exploration Construction: The author proposes a specific recursive construction for the belief process, where the seller allocates the entire throughput budget to the states currently "closest" to the current belief in terms of Bregman divergence.

3. Key Results

The paper yields several mathematically sharp results:

The Greedy Exploration Process (Proposition 1): For any positive, decreasing, convex time preference, the optimal belief process is the "greedy exploration process." This process is myopically optimal: it maximizes the instantaneous arrival rate of a revealing signal by focusing all throughput on the most likely states.
Uniform Non-Distortion (Theorem 1): Unlike classical Mussa–Rosen screening (where a monopolist distorts product quality downward for lower types), the optimal mechanism here does not distort the belief process itself. The same "preference-aligned" process is used for all buyers.
The Token-Price Menu: Screening is achieved solely through a one-dimensional menu of stopping-time caps $T(r)$ . The seller offers the same high-quality information process to everyone but limits the duration (or number of tokens) for more urgent/low-value types.
Extension to Reasoning Quality: If the model allows for endogenous reasoning quality (where the "depth" of thought can vary), the optimal mechanism involves a tradeoff: more urgent types receive faster but lower-quality answers, effectively creating "soft caps" where output quality degrades as the time limit approaches.

4. Key Contributions

Theoretical Innovation: It bridges the gap between static screening (Mussa–Rosen) and dynamic information acquisition. It proves that in dynamic settings with convex time preferences, the infinite-dimensional design problem collapses into a one-dimensional screening problem.
Economic Rationale for AI Alignment: It provides a profit-maximizing justification for "preference alignment" in LLMs. The process that maximizes user utility (the "aligned" process) is the same process that maximizes the seller's revenue, provided the seller screens via caps rather than quality distortion.
Characterization of "Tokenized" Pricing: It provides a formal mathematical foundation for why modern AI companies (OpenAI, Anthropic) use rolling-window message quotas and tiered API access (Priority vs. Batch) rather than offering different "intelligence levels" for different price points.

5. Significance

The paper is highly significant for both economic theory and the AI industry.

For Theory: It identifies a unique class of screening problems where "quality" is not a tradable dimension, but "time" is. It demonstrates that convexity in time preferences preserves the optimality of a single, non-distorted product.
For Industry: It explains the prevailing business models of GenAI providers. It clarifies that tiered pricing (e.g., ChatGPT Plus vs. Enterprise API) is not necessarily about the "smartness" of the model, but about the latency and throughput allowed to the user. It also suggests that "Batch API" services (which are cheaper but slower) are the mathematically optimal way to capture users with low urgency.