Bayesian algorithmic mechanism design

The seminal impossibility result of Myerson and Satterthwaite [1983] states that for bilateral trade, there is no mechanism that is individually rational (IR), incentive compatible (IC), weakly budget balanced, and efficient. This has led follow-up work on two-sided trade settings to weaken the efficiency requirement and consider approximately efficient simple mechanisms, while still demanding the other properties. The current state-of-the-art of such mechanisms for two-sided markets can be categorized as giving one (but not both) of the following two types of approximation guarantees on the gains from trade : a constant ex-ante guarantee, measured with respect to the second-best efficiency benchmark, or an asymptotically optimal ex-post guarantee, measured with respect to the first-best efficiency benchmark. Here the second-best efficiency benchmark refers to the highest gains from trade attainable by any IR, IC and weakly budget balanced mechanism, while the first-best efficiency benchmark refers to the maximum gains from trade (attainable by the VCG mechanism, which is not weakly budget balanced).In this paper, we construct simple mechanisms for double-auction and matching markets that simultaneously achieve both types of guarantees: these are ex-post IR, Bayesian IC, and ex-post weakly budget balanced mechanisms that 1) ex-ante guarantee a constant fraction of the gains from trade of the second-best, and 2) ex-post guarantee a realization-dependent fraction of the gains from trade of the first-best, such that this realization-dependent fraction converges to 1 (full efficiency) as the market grows large.We believe that mechanisms that not only provide a worst-case guarantee, but also provide a guarantee of performing very well on easy instances are appealing and more likely to be used. In our setting, we implement this agenda by postulating that nice instances are large-market instances, and we are able to achieve the best of both worlds: a guaranteed constant approximation on one hand, and asymptotic optimality when the markets are large on the other hand. We believe that presenting similar results in other settings is an interesting research direction.

On the Coexistence Of Stability and Incentive Compatibility in Fractional Matchings

Previous chapter Next chapter Full AccessProceedings Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)A deterministic truthful PTAS for scheduling related machines.George Christodoulou and Annamária KovácsGeorge Christodoulou and Annamária Kovácspp.1005 - 1016Chapter DOI:https://doi.org/10.1137/1.9781611973075.81PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract Scheduling on related machines (Q‖Cmax) is one of the most important problems in the field of Algorithmic Mechanism Design. Each machine is controlled by a selfish agent and her valuation can be expressed via a single parameter, her speed. Archer and Tardos [4] showed that, in contrast to other similar problems, a (non-polynomial) allocation that minimizes the makespan can be truthfully implemented. On the other hand, if we leave out the game-theoretic issues, the complexity of the problem has been completely settled — the problem is strongly NP-hard, while there exists a PTAS [9, 8]. This problem is the most well-studied in single-parameter Algorithmic Mechanism Design. It gives an excellent ground to explore the boundary between truthfulness and efficient computation. Since the work of Archer and Tardos, quite a lot of deterministic and randomized mechanisms have been suggested. Recently, a breakthrough result [7] showed that a randomized, truthful-in-expectation PTAS exists. On the other hand, for the deterministic case, the best known approximation factor is 2.8 [10, 11]. It has been a major open question whether there exists a deterministic truthful PTAS, or whether truthfulness has an essential, negative impact on the computational complexity of the problem. In this paper we give a definitive answer to this important question by providing a truthful deterministic PTAS. Previous chapter Next chapter RelatedDetails Published:2010ISBN:978-0-89871-701-3eISBN:978-1-61197-307-5 https://doi.org/10.1137/1.9781611973075Book Series Name:ProceedingsBook Code:PR135Book Pages:xviii + 1667

We show that efficient anonymous incentive compatible (dominant strategy) mechanisms for public goods eliminate externalities, i.e., each individual is unable to change the welfare of anyone else. The characterization is used to derive existence and non-existence results for models with a finite number of individuals and to explain existence results in the continuum. A similar characterization and conclusions are demonstrated for private goods in (J Econ Theory 85:169–225, 1999). However, unlike private goods, elimination of externalities with public goods implies that individuals cannot change the outcome. Hence, such mechanisms provide only weak incentives for truth-telling.

This paper concerns the mechanism design for online scheduling in a strategic setting. In this setting, each job is owned by a self-interested agent who may misreport the release time, deadline, length, and value of her job, while we need to determine not only the schedule of the jobs, but also the payment of each agent. We focus on the design of incentive compatible (IC) mechanisms, and study the maximization of social welfare (i.e., the aggregated value of completed jobs) by competitive analysis. We first derive two lower bounds on the competitive ratio of any deterministic IC mechanism to characterize the landscape of our research. We then propose a deterministic IC mechanism and show that such a simple mechanism works very well for both the preemption-restart model and the preemption-resume model. We show the mechanism can achieve the optimal competitive ratio of 5 for equal-length jobs and a near optimal competitive ratio (within a constant factor) for unequal-length jobs.

We explore the consequences of weakening the notion of incentive compatibility from strategy-proofness to ordinal Bayesian incentive compatibility (OBIC) in the random assignment model. If the common prior of the agents is the uniform prior, then a large class of random mechanisms are OBIC with respect to this prior—this includes the probabilistic serial mechanism. We then introduce a robust version of OBIC: a mechanism is locally robust OBIC if it is OBIC with respect all independent and identical priors in some neighborhood of a given independent and identical prior. We show that every locally robust OBIC mechanism satisfying a mild property called elementary monotonicity is strategy-proof. This leads to a strengthening of the impossibility result in Bogomolnaia and Moulin (J Econ Theory 100:295–328, 2001): if there are at least four agents, there is no locally robust OBIC and ordinally efficient mechanism satisfying equal treatment of equals.

Wireless power transfer (WPT) technology enables a cost-effective and sustainable energy supply in wireless networks, where energy users (EUs) can remotely harvest energy from the wireless signal transmitted by energy transmitters (ETs). However, the broadcast nature of wireless signal makes wireless power a non-excludable public good, which renders the traditional market mechanisms inefficient due to the possibility of the free-riders. In this study, we formulate the transmit power provision problem in a single-channel WPT network as a public good provision problem, aiming to maximize the social welfare of all the ET and EUs considering their private information and selfish behaviors. The considered problem also brings both economic and technical challenges in ensuring voluntary participation and distributed algorithm design. To this end, we propose a two- phase all-or-none procedure involving a low-complexity Power And Taxation (PAT) Nash mechanism, which ensures voluntary participation, incentive compatibility, and budget balance, and yields the socially optimal transmit power at all Nash equilibria. We further propose a distributed D-PAT Algorithm and prove its convergence by exploiting the connection between the structure of Nash equilibria and that of the optimal solutions to a related optimization problem. Finally, our simulation results validate the PAT Mechanism and the practical algorithm. We show that our design can significantly improve the social welfare compared to the benchmark market mechanism, especially when there are many and relatively comparable EUs.

When agents have quasi-linear preferences, every incentive compatible social choice function can be implemented by a simple extensive form mechanism, even if agents are allowed to use mixed strategies. The second stage of the mechanism, which is used to elicit the agents' true preferences, is not reached in equilibrium; it gives agents strict dominant strategies, so equilibrium outcomes are not sensitive to agents' beliefs off the equilibrium path. This solves the multiple equilibrium problem of a principal facing several agents: the mechanism implements any solution to the principal's second best maximization problem. The specification of incentive compatibility constraints in the principal's problem presupposes a precise knowledge of the agents' beliefs. However, the above mechanism can be modified to implement the principal's second best (to within arbitrarily small perturbations of transfers), regardless of the agents' conditional beliefs.

Generalized second price auction is optimal for discrete types

In this paper, we focus on mechanism design for single leader Stackelberg problems, which are a special case of hierarchical decision making problems in which a distinguished agent, known as the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">leader</i> , makes the first move and this action is followed by the actions of the remaining agents, which are known as the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">followers</i> . These problems are also known as <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">single</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">leader</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rest</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">follower</i> (SLRF) problems. There are many examples of such problems in the areas of electronic commerce, supply chain management, manufacturing systems, distributed computing, transportation networks, and multiagent systems. The game induced among the agents for these problems is a Bayesian Stackelberg game, which is more general than a Bayesian game. For this reason, classical mechanism design, which is based on Bayesian games, cannot be applied as is for solving SLRF mechanism design problems. In this paper, we extend classical mechanism design theory to the specific setting of SLRF problems. As a significant application of the theory developed, we explore two examples from the domain of electronic commerce- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first-price</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">and</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">second-price</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">electronic</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">procurement</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">auctions</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">with</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">reserve</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">prices</i> . Using an SLRF model for these auctions, we derive certain key results using the SLRF mechanism design framework developed in this paper. The theory developed has many promising applications in modeling and solving emerging game theoretic problems in engineering.

The Group Steiner Tree (GST) problem is a classical problem in combinatorial optimization and theoretical computer science. In the Edge-Weighted Group Steiner Tree (EW-GST) problem, we are given an undirected graph G = (V, E) on n vertices with edge costs c : E → ℝ≥ 0, a source vertex s and a collection of subsets of vertices, called groups, S1, . . . , Sk ⊆ V. The goal is to find a minimum-cost tree H ⊆ G that connects s to some vertex from each group Si, for all i = 1, 2, . . . , k. The Node-Weighted Group Steiner Tree (NW-GST) problem has the same setting, but the costs are associated with nodes. The goal is to find a minimum-cost node set X ⊆ V such that G[X] connects every group to the source.When G is a tree, both EW-GST and NW-GST admit a polynomial-time O(log n log k) approximation algorithm due to the seminal result of [Garg et al., SODA'98 and J. Algorithm]. The matching hardness of log2−ϵn is known even for tree instances of EW-GST and NW-GST [Halperin and Krauthgamer STOC'03]. In general graphs, most of polynomial-time approximation algorithms for EW-GST reduce the problem to a tree instance using the metric-tree embedding, incurring a loss of O(log n) on the approximation factor [Bartal, FOCS'96; Fakcharoenphol et al., FOCS'03 and JCSS]. This yields an approximation ratio of O(log2n log k) for EW-GST. Using metric-tree embedding, this factor cannot be improved: The loss of Ω(log n) is necessary on some input graphs (e.g., grids and expanders). There are alternative approaches that avoid metric-tree embedding, e.g., the algorithm of [Chekuri and Pal, FOCS'05], which gives a tight approximation ratio, but none of which achieves polylogarithmic approximation in polynomial-time. This state of the art shows a clear lack of understanding of GST in general graphs beyond the metric-tree embedding technique. For NW-GST (for which the metric-tree embedding does not apply), not even a polynomial-time polylogarithmic approximation algorithm is known.In this paper, we present O(log n log k) approximation algorithms that run in time nO(tw(G)2) for both NW-GST and EW-GST1, where tw(G) denotes the treewidth of graph G. The key to both results is a different type of "tree-embedding" that produces a tree of much bigger size, but does not cause any loss on the approximation factor. Our embedding is inspired by dynamic programming, a technique which is typically not applicable to Group Steiner problems.

This book is intended to be used as a textbook for graduate students studying theoretical computer science. It can also be used as a reference book for researchers in the area of design and analysis of approximation algorithms. Design and Analysis of Approximation Algorithms is a graduate course in theoretical computer science taught widely in the universities, both in the United States and abroad. There are, however, very few textbooks available for this course. Among those available in the market, most books follow a problem-oriented format; that is, they collected many important combinatorial optimization problems and their approximation algorithms, and organized them based on the types, or applications, of problems, such as geometric-type problems, algebraic-type problems, etc. Such arrangement of materials is perhaps convenient for a researcher to look for the problems and algorithms related to his/her work, but is difficult for a student to capture the ideas underlying the various algorithms. In the new book proposed here, we follow a more structured, technique-oriented presentation. We organize approximation algorithms into different chapters, based on the design techniques for the algorithms, so that the reader can study approximation algorithms of the same nature together. It helps the reader to better understand the design and analysis techniques for approximation algorithms, and also helps the teacher to present the ideas and techniques of approximation algorithms in a more unified way.

Dominant strategy implementation of Bayesian incentive compatible allocation rules

Reliable Blockchain Transaction Fee Mechanisms with Revenue Guarantees In the paper “Bayesian Mechanism Design for Blockchain Transaction Fee Allocation” by Xi Chen, David Simchi-Levi, Zishuo Zhao, and Yuan Zhou, the authors address the critical challenge of designing reliable blockchain transaction fee mechanisms (TFMs) that ensure truthfulness, collusion-proofness, and desirable miner revenues. By proposing an innovative “auxiliary mechanism method,” the authors establish connections between Bayesian Nash Incentive Compatible (BNIC) and Dominant Strategy Incentive Compatible (DSIC) mechanisms through an “auxiliary-variation decomposition.” This breakthrough allows the proposed mechanism to bypass previous limitations in TFM design via the Bayesian game setting, achieving constant-ratio approximations of optimal miner revenues while providing strong incentive guarantees. The research not only advances the theoretical understanding of blockchain fee mechanisms but also demonstrates the potential versatility of the auxiliary mechanism method for designing and optimizing BNIC mechanisms across broader applications. This work represents a significant contribution to both blockchain economics and mechanism design, offering a pathway toward more reliable and efficient blockchain ecosystems.

The Stochastic Boolean Function Evaluation problem for symmetric Boolean functions