Optimal-in-expectation redistribution mechanisms

AbstractMany important problems in multiagent systems involve the allocation of multiple resources among the agents. If agents are self-interested, they will lie about their valuations for the resources if they perceive this to be in their interest. The well-known VCG mechanism allocates the items efficiently, is strategy-proof (agents have no incentive to lie), and never runs a deficit. Nevertheless, the agents may have to make large payments to a party outside the system of agents, leading to decreased utility for the agents. Recent work has investigated the possibility of redistributing some of the payments back to the agents, without violating the other desirable properties of the VCG mechanism.Previous research on redistribution mechanisms has resulted in a worst-case optimal redistribution mechanism, that is, a mechanism that maximizes the fraction of VCG payments redistributed in the worst case. In contrast, in this paper, we assume that a prior distribution over the agents' valuations is available, and our goal is to maximize the expected total redistribution.In the first part of this paper, we study multi-unit auctions with unit demand. We analytically solve for a mechanism that is optimal among linear redistribution mechanisms. We also propose discretized redistribution mechanisms. We show how to automatically solve for the optimal discretized redistribution mechanism for a given discretization step size, and show that the resulting mechanisms converge to optimality as the step size goes to zero. We present experimental results showing that for auctions with many bidders, the optimal linear redistribution mechanism redistributes almost everything, whereas for auctions with few bidders, we can solve for the optimal discretized redistribution mechanism with a very small step size.In the second part of this paper, we study multi-unit auctions with nonincreasing marginal values. We extend the notion of linear redistribution mechanisms, previously defined only in the unit demand setting, to this more general setting. We introduce a linear program for finding the optimal linear redistribution mechanism. This linear program is unwieldy, so we also introduce one simplified linear program that produces relatively good linear redistribution mechanisms. We conjecture an analytical solution for the simplified linear program

Undominated Groves Mechanisms

The family of Groves mechanisms, which includes the well-known VCG mechanism (also known as the Clarke mechanism), is a family of efficient and strategy-proof mechanisms. Unfortunately, the Groves mechanisms are generally not budget balanced. That is, under such mechanisms, payments may flow into or out of the system of the agents, resulting in deficits or reduced utilities for the agents. We consider the following problem: within the family of Groves mechanisms, we want to identify mechanisms that give the agents the highest utilities, under the constraint that these mechanisms must never incur deficits. We adopt a prior-free approach. We introduce two general measures for comparing mechanisms in prior-free settings. We say that a non-deficit Groves mechanism $M$ {\em individually dominates} another non-deficit Groves mechanism $M'$ if for every type profile, every agent's utility under $M$ is no less than that under $M'$, and this holds with strict inequality for at least one type profile and one agent. We say that a non-deficit Groves mechanism $M$ {\em collectively dominates} another non-deficit Groves mechanism $M'$ if for every type profile, the agents' total utility under $M$ is no less than that under $M'$, and this holds with strict inequality for at least one type profile. The above definitions induce two partial orders on non-deficit Groves mechanisms. We study the maximal elements corresponding to these two partial orders, which we call the {\em individually undominated} mechanisms and the {\em collectively undominated} mechanisms, respectively.Comment: 34 pages. To appear in Journal of AI Research (JAIR

Undominated Groves Mechanisms

The family of Groves mechanisms, which includes the well-known VCG mechanism (also known as the Clarke mechanism), is a family of efficient and strategy-proof mechanisms. Unfortunately, the Groves mechanisms are generally not budget balanced. That is, under such mechanisms, payments may flow into or out of the system of the agents, resulting in deficits or reduced utilities for the agents. We consider the following problem: within the family of Groves mechanisms, we want to identify mechanisms that give the agents the highest utilities, under the constraint that these mechanisms must never incur deficits. We adopt a prior-free approach. We introduce two general measures for comparing mechanisms in prior-free settings. We say that a non-deficit Groves mechanism M in- dividually dominates another non-deficit Groves mechanism M′ if for every type profile, every agent’s utility under M is no less than that under M′, and this holds with strict inequality for at least one type profile and one agent. We say that a non-deficit Groves mechanism M collectively dominates another non-deficit Groves mechanism M′ if for every type profile, the agents’ total utility under M is no less than that under M′, and this holds with strict inequality for at least one type profile. The above definitions induce two partial orders on non-deficit Groves mechanisms. We study the maximal elements corresponding to these two partial orders, which we call the individually undominated mechanisms and the collectively undominated mechanisms, respectively

Exposing market mechanism design trade-offs via multi-objective evolutionary search

Market mechanisms are a means by which resources in contention can be allocated between contending parties, both in human economies and those populated by software agents. Designing such mechanisms has traditionally been carried out by hand, and more recently by automation. Assessing these mechanisms typically involves them being evaluated with respect to multiple conflicting objectives, which can often be nonlinear, noisy, and expensive to compute. For typical performance objectives, it is known that designed mechanisms often fall short on being optimal across all objectives simultaneously. However, in all previous automated approaches, either only a single objective is considered, or else the multiple performance objectives are combined into a single objective. In this paper we do not aggregate objectives, instead considering a direct, novel application of multi-objective evolutionary algorithms (MOEAs) to the problem of automated mechanism design. This allows the automatic discovery of trade-offs that such objectives impose on mechanisms. We pose the problem of mechanism design, specifically for the class of linear redistribution mechanisms, as a naturally existing multi-objective optimisation problem. We apply a modified version of NSGA-II in order to design mechanisms within this class, given economically relevant objectives such as welfare and fairness. This application of NSGA-II exposes tradeoffs between objectives, revealing relationships between them that were otherwise unknown for this mechanism class. The understanding of the trade-off gained from the application of MOEAs can thus help practitioners with an insightful application of discovered mechanisms in their respective real/artificial markets

Almost Budget Balanced Mechanisms with Scalar Bids For Allocation of a Divisible Good

This paper is about allocation of an infinitely divisible good to several rational and strategic agents. The allocation is done by a social planner who has limited information because the agents' valuation functions are taken to be private information known only to the respective agents. We allow only a scalar signal, called a bid, from each agent to the social planner. Yang and Hajek [Jour. on Selected Areas in Comm., 2007] as well as Johari and Tsitsiklis [Jour. of Oper. Res., 2009] proposed a scalar strategy Vickrey-Clarke-Groves (SSVCG) mechanism with efficient Nash equilibria. We consider a setting where the social planner desires minimal budget surplus. Example situations include fair sharing of Internet resources and auctioning of certain public goods where revenue maximization is not a consideration. Under the SSVCG framework, we propose a mechanism that is efficient and comes close to budget balance by returning much of the payments back to the agents in the form of rebates. We identify a design criterion for {\em almost budget balance}, impose feasibility and voluntary participation constraints, simplify the constraints, and arrive at a convex optimization problem to identify the parameters of the rebate functions. The convex optimization problem has a linear objective function and a continuum of linear constraints. We propose a solution method that involves a finite number of constraints, and identify the number of samples sufficient for a good approximation.Comment: Accepted for publication in the European Journal of Operational Research (EJOR

Designing Redistribution Mechanisms for Reducing Transaction Fees in Blockchains

Blockchains deploy Transaction Fee Mechanisms (TFMs) to determine which user transactions to include in blocks and determine their payments (i.e., transaction fees). Increasing demand and scarce block resources have led to high user transaction fees. As these blockchains are a public resource, it may be preferable to reduce these transaction fees. To this end, we introduce Transaction Fee Redistribution Mechanisms (TFRMs) -- redistributing VCG payments collected from such TFM as rebates to minimize transaction fees. Classic redistribution mechanisms (RMs) achieve this while ensuring Allocative Efficiency (AE) and User Incentive Compatibility (UIC). Our first result shows the non-triviality of applying RM in TFMs. More concretely, we prove that it is impossible to reduce transaction fees when (i) transactions that are not confirmed do not receive rebates and (ii) the miner can strategically manipulate the mechanism. Driven by this, we propose \emph{Robust} TFRM (\textsf{R-TFRM}): a mechanism that compromises on an honest miner's individual rationality to guarantee strictly positive rebates to the users. We then introduce \emph{robust} and \emph{rational} TFRM (\textsf{R}$^2$\textsf{-TFRM}) that uses trusted on-chain randomness that additionally guarantees miner's individual rationality (in expectation) and strictly positive rebates. Our results show that TFRMs provide a promising new direction for reducing transaction fees in public blockchains.Comment: Full Paper (AAMAS '24

Maximizing social welfare in congestion games via redistribution

It is well-known that efficient use of congestible resources can be achieved via marginal pricing; however, payments collected from the agents generate a budget surplus, which reduces social welfare. We show that an asymptotically first-best solution in the number of agents can be achieved by the appropriate redistribution of the budget surplus back to the agents