Double Auctions in Markets for Multiple Kinds of Goods

Motivated by applications such as stock exchanges and spectrum auctions, there is a growing interest in mechanisms for arranging trade in two-sided markets. Existing mechanisms are either not truthful, or do not guarantee an asymptotically-optimal gain-from-trade, or rely on a prior on the traders' valuations, or operate in limited settings such as a single kind of good. We extend the random market-halving technique used in earlier works to markets with multiple kinds of goods, where traders have gross-substitute valuations. We present MIDA: a Multi Item-kind Double-Auction mechanism. It is prior-free, truthful, strongly-budget-balanced, and guarantees near-optimal gain from trade when market sizes of all goods grow to $\infty$ at a similar rate.Comment: Full version of IJCAI-18 paper, with 2 figures. Previous names: "MIDA: A Multi Item-type Double-Auction Mechanism", "A Random-Sampling Double-Auction Mechanism". 10 page

Multi-unit Bilateral Trade

We characterise the set of dominant strategy incentive compatible (DSIC), strongly budget balanced (SBB), and ex-post individually rational (IR) mechanisms for the multi-unit bilateral trade setting. In such a setting there is a single buyer and a single seller who holds a finite number k of identical items. The mechanism has to decide how many units of the item are transferred from the seller to the buyer and how much money is transferred from the buyer to the seller. We consider two classes of valuation functions for the buyer and seller: Valuations that are increasing in the number of units in possession, and the more specific class of valuations that are increasing and submodular. Furthermore, we present some approximation results about the performance of certain such mechanisms, in terms of social welfare: For increasing submodular valuation functions, we show the existence of a deterministic 2-approximation mechanism and a randomised e/(1-e) approximation mechanism, matching the best known bounds for the single-item setting

Social Welfare in One-sided Matching Markets without Money

We study social welfare in one-sided matching markets where the goal is to efficiently allocate n items to n agents that each have a complete, private preference list and a unit demand over the items. Our focus is on allocation mechanisms that do not involve any monetary payments. We consider two natural measures of social welfare: the ordinal welfare factor which measures the number of agents that are at least as happy as in some unknown, arbitrary benchmark allocation, and the linear welfare factor which assumes an agent's utility linearly decreases down his preference lists, and measures the total utility to that achieved by an optimal allocation. We analyze two matching mechanisms which have been extensively studied by economists. The first mechanism is the random serial dictatorship (RSD) where agents are ordered in accordance with a randomly chosen permutation, and are successively allocated their best choice among the unallocated items. The second mechanism is the probabilistic serial (PS) mechanism of Bogomolnaia and Moulin [8], which computes a fractional allocation that can be expressed as a convex combination of integral allocations. The welfare factor of a mechanism is the infimum over all instances. For RSD, we show that the ordinal welfare factor is asymptotically 1/2, while the linear welfare factor lies in the interval [.526, 2/3]. For PS, we show that the ordinal welfare factor is also 1/2 while the linear welfare factor is roughly 2/3. To our knowledge, these results are the first non-trivial performance guarantees for these natural mechanisms

Chain: A Dynamic Double Auction Framework for Matching Patient Agents

In this paper we present and evaluate a general framework for the design of truthful auctions for matching agents in a dynamic, two-sided market. A single commodity, such as a resource or a task, is bought and sold by multiple buyers and sellers that arrive and depart over time. Our algorithm, Chain, provides the first framework that allows a truthful dynamic double auction (DA) to be constructed from a truthful, single-period (i.e. static) double-auction rule. The pricing and matching method of the Chain construction is unique amongst dynamic-auction rules that adopt the same building block. We examine experimentally the allocative efficiency of Chain when instantiated on various single-period rules, including the canonical McAfee double-auction rule. For a baseline we also consider non-truthful double auctions populated with zero-intelligence plus"-style learning agents. Chain-based auctions perform well in comparison with other schemes, especially as arrival intensity falls and agent valuations become more volatile

Designing Coalition-Proof Reverse Auctions over Continuous Goods

This paper investigates reverse auctions that involve continuous values of different types of goods, general nonconvex constraints, and second stage costs. We seek to design the payment rules and conditions under which coalitions of participants cannot influence the auction outcome in order to obtain higher collective utility. Under the incentive-compatible Vickrey-Clarke-Groves mechanism, we show that coalition-proof outcomes are achieved if the submitted bids are convex and the constraint sets are of a polymatroid-type. These conditions, however, do not capture the complexity of the general class of reverse auctions under consideration. By relaxing the property of incentive-compatibility, we investigate further payment rules that are coalition-proof without any extra conditions on the submitted bids and the constraint sets. Since calculating the payments directly for these mechanisms is computationally difficult for auctions involving many participants, we present two computationally efficient methods. Our results are verified with several case studies based on electricity market data

Mechanism design for dynamic double auctions

Cette thèse a pour objet de concevoir des mécanismes d'allocation dans le contexte des enchères doubles dynamiques (achats groupés, bourses électroniques). Le principal défi inhérent à la conception de tels mécanismes est d'aboutir à un résultat socialement optimal alors que la dynamique induit une incertitude sur les arrivées et départs des participants de l'enchère ainsi que sur les valuations qui peuvent être fluctuantes. Dans cette thèse, nous proposons des mécanismes qui sont efficaces, incitatifs et garantissant l'équilibre du budget. La définition de ces mécanismes s'appuient sur les algorithmes d'appareillage pour des graphes bipartis (technique d'augmentation et réduction) ainsi que sur une méthode générale prenant en compte le comportement des participants.This thesis addresses the problem of designing mechanisms that lead to socially desirable outcomes in dynamic double auction markets such as stock exchanges and group buying. The main challenge of the design is dealing with the uncertainty posed by the participants who are dynamically arriving and departing and their valuations vary over time. The thesis demonstrates the difficulties in designing mechanisms with desirable properties such as truthfulness, efficiency and budget balance. It also provides dedicated mechanisms satisfying those properties by using augmentation, reduction and behaviour-based approaches