We study a large language model (LLM) service in which a provider chooses a per-token price and a default reasoning-token allocation, while a user may accept the default, customize the allocation, or exit. Larger allocations can improve accuracy but increase token cost and latency. We model this interaction as a Stackelberg game and derive the user's unique optimal customized allocation in closed form. For any price, the acceptable defaults form either an empty set or a compact interval. We characterize the provider's optimal default through a three-regime rule, reduce equilibrium computation to a one-dimensional price optimization, and prove the existence of the equilibrium. We further show that defaults affect the implemented reasoning allocation only when users value the convenience of avoiding customization; otherwise, every service-providing outcome implements the user's optimal customized allocation. Experiments with two compact open-weight reasoning models on five mathematics and science benchmarks support the accuracy-token model and show how model and task characteristics determine equilibrium prices, defaults, and reasoning allocations.
We extend the standard Principal-Agent framework to scenarios where the Agent selects from a suite of technologies, each characterized by a distinct cost-capability profile. This framework is increasingly critical in the era of Large Language Models (LLMs), where Agents choose both a model and an associated effort leve...
When auction bidders misperceive their rivals, a seller can change not only the amount of information rent but also the states in which it is delivered. We ask when this payment-design opportunity survives a finite bidding interface, nonnegative-payment restrictions, and comparison with conventional auctions under the...
The case does not show that guardrails are ineffective; it shows their apparent value is unidentified until the simulated agents and protocol pass these checks, and contributes a construct-validity contract separating incentive validity, protocol isolation, stochastic stability, and welfare accounting.
Static evaluations credit a language model for naming the right move, but an agent must carry a plan through to a verified outcome while an opponent responds. We introduce XiangqiBench, an executable benchmark that measures this difference in Chinese chess: starting from 119 tactical endgames with forced mates supporte...
Extending the Price-and-Choose (P&C) mechanism of Echenique and Nunez (2025), we propose the Price-Accept-and-Choose (PA&C) mechanism, which preserves efficiency while eliminating P&C's first-mover advantage. We then analyze randomized and bidding variants and show that the resulting equilibrium payoffs correspond to s...
Yukihiko Funaki, Yukio Koriyama, Matías Núñez et al.· 0 citations
The random-order interpretation of the Shapley value specifies both a terminal allocation and a payment path: each entrant is paid her marginal contribution at the time of entry. We embed this path in a finite dynamic entry problem in which a selected player may accept immediately or defer and allow another outsider to...
Tongseok Lim· 0 citations
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