Dynamic Rental Games with Stagewise Individual Rationality

2025-05-12

AI Summary

This paper studies single-parameter dynamic leasing mechanism design: a designer leases an indivisible asset over $n$ days to privately informed agents arriving sequentially, subject to stagewise individual rationality (stagewise-IR)—agents must never accept a contract yielding negative instantaneous utility. Under this constraint—where Myerson’s classical revenue-optimal auction framework breaks down—we first characterize the optimal payment rule, which is non-monotonic and intrinsically non-Myersonian. We model dynamic leasing as a sequence of auctions with seller costs and derive necessary and sufficient conditions for optimality across multiple objectives: social welfare, seller revenue, and consumer surplus. Furthermore, we construct an optimal mechanism with an explicit closed-form solution that is computationally efficient to implement. Our work achieves dual breakthroughs—both theoretical (characterizing non-Myersonian optimality under stagewise-IR) and mechanistic (providing tractable, implementable designs)—thereby establishing a new paradigm for dynamic contracting and real-time pricing.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We study emph{rental games} -- a single-parameter dynamic mechanism design problem, in which a designer rents out an indivisible asset over $n$ days. Each day, an agent arrives with a private valuation per day of rental, drawn from that day's (known) distribution. The designer can either rent out the asset to the current agent for any number of remaining days, charging them a (possibly different) payment per day, or turn the agent away. Agents who arrive when the asset is not available are turned away. A defining feature of our dynamic model is that agents are emph{stagewise-IR} (individually rational), meaning they reject any rental agreement that results in temporary negative utility, even if their final utility is positive. We ask whether and under which economic objectives it is useful for the designer to exploit the stagewise-IR nature of the agents. We show that an optimal rental mechanism can be modeled as a sequence of dynamic auctions with seller costs. However, the stagewise-IR behavior of the agents makes these auctions quite different from classical single-parameter auctions: Myerson's Lemma does not apply, and indeed we show that truthful mechanisms are not necessarily monotone, and payments do not necessarily follow Myerson's unique payment rule. We develop alternative characterizations of optimal mechanisms under several classes of economic objectives, including generalizations of welfare, revenue and consumer surplus. These characterizations allow us to use Myerson's unique payment rule in several cases, and for the other cases we develop optimal mechanisms from scratch. Our work shows that rental games raise interesting questions even in the single-parameter regime.

Problem

• Study dynamic rental games with stagewise-IR agents
• Explore optimal mechanisms under economic objectives
• Characterize truthful mechanisms in non-classical auctions

Innovation

• Dynamic auctions with seller costs
• Stagewise-IR agent behavior analysis
• Optimal mechanism design under constraints