Automated Market Making for Goods with Perishable Utility (2511.16357v1)

Abstract: We study decentralized markets for goods whose utility perishes in time, with compute as a primary motivation. Recent advances in reproducible and verifiable execution allow jobs to pause, verify, and resume across heterogeneous hardware, which allow us to treat compute as time indexed capacity rather than bespoke bundles. We design an automated market maker (AMM) that posts an hourly price as a concave function of load--the ratio of current demand to a "floor supply" (providers willing to work at a preset floor). This mechanism decouples price discovery from allocation and yields transparent, low latency trading. We establish existence and uniqueness of equilibrium quotes and give conditions under which the equilibrium is admissible (i.e. active supply weakly exceeds demand). To align incentives, we pair a premium sharing pool (base cost plus a pro rata share of contemporaneous surplus) with a Cheapest Feasible Matching (CFM) rule; under mild assumptions, providers optimally stake early and fully while truthfully report costs. Despite being simple and computationally efficient, we show that CFM attains bounded worst case regret relative to an optimal benchmark.

• The paper introduces an AMM that prices perishable compute resources via a concave load-dependent function to achieve equilibrium and price stability.
• It employs online bipartite matching algorithms (GCM, GSM, CFM) that balance feasibility and incentive compatibility with bounded supply and demand regret.
• The mechanism aligns provider incentives using staking, cryptographic verification, and dynamic floor pricing to overcome inefficiencies and ensure truthful participation.

Automated Market Making for Compute with Perishable Utility: Technical Summary

Problem Statement and Motivation

This work introduces a rigorous model and mechanism for decentralized markets trading goods with perishable utility, using computational capacity ("compute") as the primary motivating commodity. The core challenge is to price and allocate hardware resources—whose utility decays rapidly over time—across distributed, heterogeneous providers and demanders, while ensuring incentives for truthful participation and aligning allocation with welfare and utilization criteria.

Existing approaches to compute markets are encumbered by acute inefficiencies, opaque pricing, high entry barriers, and combinatorial allocation bottlenecks. The paper leverages advancements in reproducible and verifiable computing—where compute jobs can be checkpointed, verified, and resumed across heterogeneous hardware (Arun et al., 26 Feb 2025)—to simplify allocation, allowing compute to be modeled as a time-indexed, fungible, and perishable good.

Market Design and Mechanism

Market Model

The proposed market is two-sided:

• Supply: Compute providers, who bid their cost per hour and the temporal window for which they can make hardware available.
• Demand: Users (jobs) specifying budget, deadline, and minimum run length.

Time is treated discretely, and both sides lack valuable outside options for their resources/jobs.

Automated Market Maker and Pricing

A central innovation is the design of an Automated Market Maker (AMM) that posts hourly prices as a concave function of load, defined as the ratio of current demand to "floor supply"—providers willing to work at or below a pre-set floor price. Key features:

• If demand ≤ floor supply, the price is at the floor; when demand surpasses floor supply, price smoothly increases via a function $f(\alpha)$ with $\alpha = D/S_f$, where $D$ is demand, $S_f$ is floor supply.
• The pricing mechanism is continuous, increasing, and concave in load, ensuring robust equilibrium and price stability.

The paper proves existence and uniqueness of equilibrium prices (fixed points of the pricing equation), and gives conditions (regular crossing and local responsiveness) under which the market clears with active supply at least equaling demand.

Incentive Mechanisms

To align supply-side incentives and prevent cost inflation or withholding of availability, the design introduces:

• Pool Sharing: Providers staked in the network are paid the base cost plus a pro-rata share of contemporaneous market surplus. Early, long-term stakers receive a larger share as more later-demanded jobs overlap their active period.
• Cheapest-Feasible Matching (CFM): At each hour, the mechanism assigns jobs to the lowest-cost available provider who can feasibly accommodate the job length.

Under mild behavioral assumptions, it's shown that this mechanism structure makes it strictly optimal for providers to (i) stake early, (ii) reveal true cost, and (iii) offer full capacity, yielding an incentive-compatible market.

Theoretical and Algorithmic Contributions

Allocation and Matching Algorithms

The allocation problem is reduced (by operational reproducibility) to an online bipartite matching with time-indexed availability and deadlines.

Three classes of matching algorithms are studied:

• GCM (Greedy Cheapest): Ignores feasibility, matches jobs to the cheapest available provider.
• GSM (Greedy Shortest Feasible): Matches jobs to the shortest-available feasible provider, achieving maximal feasible match cardinality.
• CFM (Cheapest Feasible Matching): Matches each job to the cheapest feasible provider—balancing incentive-compatibility and feasibility.

Welfare and Regret Guarantees

CFM is shown to achieve bounded regret relative to the two optimal (but non-incentive compatible) algorithms:

• Provider-Side (Supply) Regret: At most $\lfloor n/2 \rfloor (P-P_f)$ per period, where $n$ is the number of jobs, $P$ is the current price, and $P_f$ is the floor price.
• User-Side (Demand) Regret: At most $\lfloor n/2 \rfloor$ jobs per period may fail to be assigned compared to the maximum possible, i.e. CFM achieves at least a $1/2$ competitive ratio.

In the multi-period, two-provider case, the difference in the number of infeasible matches between CFM and GSM is at most one per least common multiple of staking intervals—making the per-period excess infeasibility rate vanish as capacity increases.

Complexity Analyses

The algorithms are designed for real-time operation:

• All three (GCM, GSM, CFM) have $O(\log n)$ per-job matching complexity with appropriate data structures.

Incomplete Information Extensions

The framework is extended to handle incomplete information, including:

• Malicious/Lazy Providers: Integration of cryptographic verification games ensures that providers cannot misreport capacity without risk of slashing.
• Unknown Job Length / Strategic Misreporting: A racing protocol with collateral and tolerance ensures that only nearly truthful reports are undominated strategies, and the selected provider is fastest in expectation up to the tolerance.

Floor Price Adaptation

The paper discusses online adaptation of the floor price for sustained market health. By averaging the observed marginal cost (most expensive matched provider) over previous windows, the mechanism anchors the floor price to the long-run empirical marginal cost, thus maximizing price stability (market clears at the floor) and budget feasibility for users.

Implications and Future Directions

Practical Impact

This design provides a robust and incentive-compatible foundation for decentralized compute marketplaces, with transparent real-time pricing, verifiable execution, and low computational complexity. It offers a solution to the longstanding inefficiencies in compute resource markets, characterized by inflexible supply and opaque, non-market pricing.

Theoretical Insights

• Price discovery and allocation can be decoupled using a concave AMM, bypassing combinatorial auctions while maintaining efficiency and incentive compatibility.
• Matching greedy feasibility with provider-side cost prioritization yields tight worst-case bounds on welfare relative to the unattainable social optimum.
• The regret bounds are robust even in adversarial and dynamic settings, and diminish as the system scales.

Future Work

Several open problems remain:

• Extending the multi-period, multi-provider regret guarantees analytically beyond the two-provider case.
• Dynamic, possibly learning-based, floor pricing models to further optimize both participation and price stability.
• Stochastic job arrival modeling, job heterogeneity, preemptible jobs, and partially completed job valuation.
• Strategic robustness against sophisticated adversaries (Sybil attacks, collusion).
• Empirical evaluation with real workloads, verification overheads, and system-level deployment constraints.

Conclusion

This paper rigorously advances market mechanisms for decentralized compute, formalizing and solving the key bottlenecks of perishable utility, incentive compatibility, and real-time price discovery. The algorithms and equilibrium analysis offer a tractable and deployable template for trustless, efficient cloud and distributed resource marketplaces, with strong performance and robustness guarantees. The work contributes both to theory—by circumventing prior complexity barriers with a practical AMM—and to practice, charting a clear implementation path for decentralized compute infrastructures.

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Reference: "Automated Market Making for Goods with Perishable Utility" (2511.16357)