Specialists Hold, Generalists Discount: Asymmetric Equilibrium in LLM Routing Auctions

Abstract

Routing systems for large language models, such as MasRouter, RouteLLM, FrugalGPT, and others, match queries to suppliers based on cost-quality tradeoffs. Most prior work optimizes this problem from the demand side, while the supplier-side question of how LLM suppliers should price their services within a routing mechanism has received little formal treatment. We provide the first systematic analysis of this problem. In our setup, the LLM is the priced commodity: supplier organizations set price functions for the services they offer, rather than acting as strategic agents that generate bids per query. We model supplier-side pricing as a sealed-bid first-price reverse auction over a router that allocates each query to one supplier based on cost and quality. This framework applies to any cost-quality routing system rather than to a specific implementation. Using calibrated profiles from 12 open-weight models and MasRouter as a case-study router, we characterize equilibrium behavior. Our main finding is that the Bayesian Nash equilibrium is asymmetric: capability-differentiated suppliers adopt flat, non-discounted strategies, while marginal-quality suppliers compete primarily on price. A mechanism-baseline experiment, where the case-study router is replaced by an analytical rational-decision rule, confirms that this pattern is a property of the auction mechanism rather than an artifact of router training. We further observe that price differentiation can emerge in equilibrium even under capability symmetry, because private-cost types alone produce nontrivial bid functions. The practical implication is that auction-based pricing alone does not discipline specialist rents. Achieving that goal requires additional mechanism elements, such as reserve prices or capability-blind tie-breaking.