Optimal Mechansim Design and Money Burning (0804.2097v1)

Abstract: Mechanism design is now a standard tool in computer science for aligning the incentives of self-interested agents with the objectives of a system designer. There is, however, a fundamental disconnect between the traditional application domains of mechanism design (such as auctions) and those arising in computer science (such as networks): while monetary transfers (i.e., payments) are essential for most of the known positive results in mechanism design, they are undesirable or even technologically infeasible in many computer systems. Classical impossibility results imply that the reach of mechanisms without transfers is severely limited. Computer systems typically do have the ability to reduce service quality--routing systems can drop or delay traffic, scheduling protocols can delay the release of jobs, and computational payment schemes can require computational payments from users (e.g., in spam-fighting systems). Service degradation is tantamount to requiring that users burn money}, and such ``payments'' can be used to influence the preferences of the agents at a cost of degrading the social surplus. We develop a framework for the design and analysis of money-burning mechanisms to maximize the residual surplus--the total value of the chosen outcome minus the payments required.

• The paper introduces a theoretical framework for money-burning mechanisms that maximize residual surplus by replacing monetary transfers with service degradation.
• It characterizes Bayesian optimal mechanisms using ironed virtual valuations to overcome non-monotonicity in single-parameter agent settings.
• The study demonstrates that a $k$-unit (p,q)-lottery approximates optimal surplus and quantifies efficiency loss through a logarithmic social cost measure.

Optimal Mechanism Design and Money Burning

The paper "Optimal Mechanism Design and Money Burning," authored by Jason D. Hartline and Tim Roughgarden, explores the adaptation of mechanism design for environments, particularly in computer systems, where traditional monetary transfers are infeasible. This research extends mechanism design theory to address contexts where "payments" correspond to service degradation or computational penalties, rather than financial transactions.

Key Contributions

1. Framework for Money-Burning Mechanisms: The paper establishes a theoretical framework for designing money-burning mechanisms aimed at maximizing residual surplus, which is the value of the outcome minus the cost of burnt payments. This adjusts traditional mechanism design paradigms, which typically focus on monetary transfers.
2. Characterization of Optimal Mechanisms: The authors characterize Bayesian optimal money-burning mechanisms within single-parameter agent settings. They present an innovative approach to optimize using "ironed" virtual valuations, which rectify issues with non-monotonicity that arise in such settings. Notably, the paper extends this analysis to complex non-MHR distributions, offering a more comprehensive understanding than previous economic literature.
3. Approximation by Prior-Free Mechanisms: For multi-unit auctions, a significant outcome is the derivation of a near-optimal, prior-free mechanism. This mechanism achieves expected residual surplus close to that of Bayesian optimal mechanisms. The authors introduce the concept of a $k$-unit $(p,q)$-lottery for achieving this result, showing robustness against unpredictable valuation distributions.
4. Quantifying the Cost of Money Burning: The paper investigates how much efficiency is lost when implementing money-burning as opposed to traditional monetary transfers. They demonstrate that the social cost of burnt money results in a logarithmic fraction of potential surplus under certain worst-case conditions for multi-unit auctions. This quantifies the practical implications when substituting monetary exchanges with service degradation.

Implications and Future Directions

The implications of the research are both theoretical and practical. Theoretically, it broadens the foundational understanding of mechanism design by reconciling prior-free and Bayesian approaches, offering a robust framework to address settings where money burning is necessary. Practically, it suggests how computer systems—where real monetary transfers are cumbersome or impossible—can still leverage mechanism design principles effectively through service quality adjustments.

In terms of future work, several directions are notable. First, exploring generalizations beyond symmetric settings could provide insights into more diverse practical scenarios. Furthermore, extending the analysis to multi-parameter settings, where agents have private values for both service and degradation, presents a challenging yet potentially rewarding frontier that could open the paper to multi-dimensional agent preferences. Finally, improving the approximation bounds for prior-free mechanisms with a small number of agents and identifying better benchmarks in non-symmetric settings could refine the practical utility of these mechanisms.

Through this work, Hartline and Roughgarden pave the way for mechanism design applications in technologically constrained environments, spanning beyond the theoretical confines of traditional economic models. Their approach reflects a nuanced understanding of computational systems' unique challenges, setting the stage for innovative applications in the field.