Mechanism design for large language models
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Mechanism design for large language models
February 13, 2025<br>Paul Duetting and Song Zuo, Research Scientists
We investigate the design of auction mechanisms for aggregating the output of multiple self-interested LLMs into one joint output. We argue that this comes with a number of unique challenges, and we propose a simple token auction mechanism and illustrate our design through demonstration with an off-the-shelf LLM.
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Generative AI and large language models (LLMs) facilitate the automated generation of assets across a variety of domains. For many use cases, several LLM agents may need to collaborate to create a joint output. A potential example is in the context of Internet ads, where advertisers might be represented by LLM agents capable of producing ads in reply to a user query. Or it could be that the LLMs represent stakeholders of a company, working together to write a joint report.<br>Consider an example situation where there is a single space on a webpage to be filled with an ad creative in reply to a user searching for “Vacations in Hawaii”. Suppose there are two advertisers interested in this search query, Alpha Airlines and Beta Resort, each represented by an LLM agent. Each LLM agent is capable of producing an ad creative in reply to the search query. For example: “Fly to Hawaii with Alpha Airlines” and “Enjoy the beauty of Hawaii at Beta Resort”. However, in this case, a suitable auction design would be flexible enough to enable the creation of a joint ad creative, such as “Alpha Airlines flies you to Hawaii where you can enjoy a magic weeklong experience at Beta Resort”.
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An illustrative example, consider separate LLM agents representing two hypothetical advertisers, Alpha Airlines and Beta Resort, which are tasked to collaborate to produce a joint ad creative.
In applications like this, each LLM agent has (potentially diverging) preferences for the joint output. For example, advertisers prefer to have their products or services mentioned, while also caring about different aspects that they wish to mention more prominently. Problems in which multiple agents collaborate to select a joint output naturally call for a mechanism design (i.e., auction design) approach.<br>In “Mechanism Design for Large Language Models”, which won the WWW 2024 Best Paper Award, we argue that the problem of joint output generation through multiple LLM agents comes with several unique challenges, and we present a new class of auction mechanisms tailored to address the key challenges of this novel application domain. We describe theoretical results that inform the design of auctions[ab829e] from that class, and we show how these insights lead to practical auction designs that yield promising outcomes when deployed with real-world LLMs.
The token auction model
At a high-level, our approach — which we dub the token auction model — mimics the mechanics of LLMs as closely as possible. The token auction operates on a token-by-token basis and functions like one giant LLM, while also defining some payment function, monetary or otherwise. We illustrate the key ideas and concepts in the context of text creation, but the same ideas apply to the creation of other media types (such as images or videos). In this context, a token is simply an individual word, a sequence of words, punctuation mark, etc. There is also a special “end” token signifying the end of the creation process.<br>Let’s first look at how an individual LLM works. On an abstract level, an LLM defines for any sequence of input tokens, a distribution over tokens. For example, the input sequence could be “Mechanism Design for”, and the output distribution could be [(“Large”, 0.8), (“Generative”, 0.2)], meaning that the next token should be “Large” with 80% probability and “Generative” with 20%. This functionality can then be used for so-called auto-regressive text generation. The process starts with an initial prompt, which is just a sequence of tokens. Then a token is sampled from the distribution over tokens defined by the LLM. This token is appended to the sequence being generated. Then the process is repeated with the resulting expanded sequence of tokens until the special “end” token is sampled.<br>The token auction performs two key tasks: it expands the shared token sequence and determines agent payments. Both of these tasks are achieved through functions, which we refer to as the distribution aggregation function and the payment function. Both functions take as input the distributions of the individual LLMs and a bid by each agent. The distribution aggregation function maps this to a distribution over tokens, while the output of the payment function is a vector of payments.
The...