07261 Abstracts Collection -- Fair Division

From 24.06. to 29.06.2007, the Dagstuhl Seminar 07261 % generate automatically ``Fair Division\u27\u27 % generate automatically was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Assignment problems and their application in economics

Four assignment problems are introduced in this thesis, and they are approached based on the context they are presented in. The underlying graphs of the assignment problems in this thesis are in most cases bipartite graphs with two sets of vertices corresponding to the agents and the resources. An edge might show the interest of an agent in a resource or willingness of a manufacturer to produce the corresponding product of a market, to name a few examples. The rst problem studied in this thesis is a two-stage stochastic matching problem in both online and oine versions. In this work, which is presented in Chapter 2 of this thesis, a coordinator tries to benet by having access to the statistics of the future price discounts which can be completely unpredictable for individual customers. In our model, individual risk-averse customers want to book hotel rooms for their future vacation; however, they are unwilling to leave booking to the last minute which might result in huge savings for them since they have to take the risk of all the hotel rooms being sold out. Instead of taking this risk, individual customers make contracts with a coordinator who can spread the risk over many such cases and also has more information on the probability distribution of the future prices. In the rst stage, the coordinator agrees to serve some buyers, and then in the second stage, once the nal prices have been revealed, he books rooms for them just as he promised. An agreement between the coordinator and each buyer consists of a set of acceptable hotels for the customer and a single price. Two models for this problem are investigated. In the rst model, the details of the agreements are proposed by the buyer, and we propose a bicriteria-style approximation algorithm that gives a constant-factor approximation to the objective function by allowing a bounded fraction of our hotel bookings to overlap. In the second model, the details of the agreements are proposed by the coordinator, and we show the prices yielding the optimal prot up to a small additive loss can be found by a polynomial time algorithm. In the third chapter of this thesis, two versions of the online matching problem are analyzed with a similar technique. Online matching problems have been studied by many researchers recently due to their direct application in online advertisement systems such as Google Adwords. In the online bipartite matching problem, the vertices of one side are known in advance; however, the vertices of the other side arrive one by one, and reveal their adjacent vertices on the oine side only upon arrival. Each vertex can only be matched to an unmatched vertex once it arrives and we cannot match or rematch the online vertex in the future. In the online matching problem with free disposal, we have the option to rematch an already matched oine vertex only if we eliminate its previous online match from the graph. The goal is to maximize the expected size of the matching. We propose a randomized algorithm that achieves a ratio greater than 0:5 if the online nodes have bounded degree. The other problem studied in the third chapter is the edge-weighted oblivious matching in which the weights of all the edges in the underlying graph are known but existence of each edge is only revealed upon probing that edge. The weighted version of the problem has applications in pay-per-click online advertisements, in which the revenue for a click on a particular ad is known, but it is unknown whether the user will actually click on that ad. Using a similar technique, we develop an algorithm with approximation factor greater than 0:5 for this problem too. In Chapter 4, a generalized version of the Cournot Competition (a foundational model in economics) is studied. In the traditional version, rms are competing in a single market with one heterogeneous good, and their strategy is the quantity of good they produce. The price of the good is an inverse function of the total quantity produced in the market, and the cost of production for each rm in each market increases with the quantity it produces. We study Cournot Competition on a bipartite network of rms and markets. The edges in this network demonstrate access of a rm to a market. The price of the good in each market is again an inverse function of the quantity of the good produced by the rms, and the cost of production for each rm is a function of its production in dierent markets. Our goal is to give polynomial time algorithms to nd the quantity produced by rms in each market at the equilibrium for generalized cost and price functions. The nal chapter of this thesis is on analyzing a problem faced by online marketplaces such as Amazon and ebay which deal with huge datasets registering transaction of merchandises between many buyers and sellers. As the size of datasets grow, it is important that the algorithms become more selective in the amount of data they store. Our goal is to develop pricing algorithms for social welfare (or revenue) maximization that are appropriate for use with the massive datasets in these networks. We specially focus on the streaming setting, the common model for big data analysis. Furthermore, we include hardness results (lower bounds) on the minimum amount of memory needed to calculate the exact prices and also present algorithms which are more space ecient than the given lower bounds but approximate the optimum prices for the goods besides the revenue or the social welfare of the mechanism

Market-based allocation of airport slots : the PAUSE auction mechanism and extensions

During the past several months, passenger air transport has been recovering from its significant retraction during the two years Covid pandemics. If the recent significant drop in air traffic due do the Covid pandemics acted as an external mitigating factor to airport traffic congestion in several major airports around the world, with the post-pandemics air traffic recovery it is likely that airport capacity will, once again, fall short of demand and not keep pace with the growth in air traffic. That is why close to two hundred major airports worldwide, most of them in Europe, face capacity constraints and are “coordinated”. Eurocontrol predicts Europe's capacity shortage in 2050 at 500,000 flights/year in the baseline scenario, which could rise to 2.7 million in an optimistic scenario. The allocation of airport slots in Europe and elsewhere is still ruled by administrative processes, based on the IATA (International Air Transport Association) Worldwide Airport Slot Guidelines (WASG), which follow historical precedence and time adjustments of historical slots. Market mechanisms in slot allocation, as an alternative to administrative processes, are still rarely used. Several authors have highlighted the inefficiency of the current airport slot administrative allocation system, based on the IATA’s Guidelines. Several authors have suggested improvements in this administrative system, such as congestion pricing mechanisms and other market mechanisms involving auction procedures. Among the various auction mechanisms, scoring auctions and the PAUSE methodology have been suggested in the literature. In this paper, and following our previous work, we explore and extend the application of the PAUSE auction mechanism with bidding based on a score function for the auctioneer, that includes another variable in addition to the total revenue, where this variable can represent e.g., quality of the service provided. We study the application of this auction mechanism, in a gradual fashion, p.e. to the year round three level 3 international airports operating in Portugal. The different airlines using these airports would still follow the current IATA slot allocation guidelines in their use of other airports, including the slot exchange protocols. We show that some of PAUSE auction mechanism’s desirable properties, such as computability, transparency, absence of envy, and the mitigation of the “price-jump problem”, “threshold problem”, “exposure problem”, and “winner’s curse problem”, still hold.info:eu-repo/semantics/publishedVersio

Essays on Online Learning and Resource Allocation

This thesis studies four independent resource allocation problems with different assumptions on information available to the central planner, and strategic considerations of the agents present in the system. We start off with an online, non-strategic agents setting in Chapter 1, where we study the dynamic pricing and learning problem under the Bass demand model. The main objective in the field of dynamic pricing and learning is to study how a seller can maximize revenue by adjusting price over time based on sequentially realized demand. Unlike most existing literature on dynamic pricing and learning, where the price only affects the demand in the current period, under the Bass model, price also influences the future evolution of demand. Finding arevenue-maximizing dynamic pricing policy in this model is non-trivial even in the full information case, where model parameters are known. We consider the more challenging incomplete information problem where dynamic pricing is applied in conjunction with learning the unknown model parameters, with the objective of optimizing the cumulative revenues over a given selling horizon of length . Our main contribution is an algorithm that satisfies a high probability regret guarantee of order ²/³; where the market size is known a priori. Moreover, we show that no algorithm can incur smaller order of loss by deriving a matching lower bound. We then switch our attention to a single round, strategic agents setting in Chapter 2, where we study a multi-resource allocation problem with heterogeneous demands and Leontief utilities. Leontief utility function captures the idea that for certain resource allocation settings, the utility of marginal increase in one resource depends on the availabilities of other resources. We generalize the existing literature on this model formulation to incorporate more constraints faced in real applications, which in turn requires new algorithm design and analysis techniques. The main contribution of this chapter is an allocation algorithm that satisfies Pareto optimality, envy-freenss, strategy-proofness, and a notion of sharing incentive. In Chapter 3, we study a single round, non-strategic agent setting, where the central planner tries to allocate a pool of items to a set of agents who each has to receive a prespecified fraction of all items. Additionally, we want to ensure fairness by controlling the amount of envy that agents have with the final allocations. We make the observation that this resource allocation setting can be formulated as an Optimal Transport problem, and that the solution structure displays a surprisingly simple structure. Using this insight, we are able to design an allocation algorithm that achieves the optimal trade-off between efficiency and envy. Finally, in Chapter 4 we study an online, strategic agent setting, where similar to the previous chapter, the central planner needs to allocate a pool of items to a set of agents who each has to receive a prespecified fraction of all items. Unlike in the previous chapter, the central planner has no a priori information on the distribution of items. Instead, the central planner needs to implicitly learn these distributions from the observed values in order to pick a good allocation policy. Additionally, an added challenge here is that the agents are strategic with incentives to misreport their valuations in order to receive better allocations. This sets our work apart both from the online auction mechanism design settings which typically assume known valuation distributions and/or involve payments, and from the online learning settings that do not consider strategic agents. To that end, our main contribution is an online learning based allocation mechanism that is approximately Bayesian incentive compatible, and when all agents are truthful, guarantees a sublinear regret for individual agents' utility compared to that under the optimal offline allocation policy

A Classification Scheme for Local Energy Trading

The current trend towards more renewable and sustainable energy generation leads to an increased interest in new energy management systems and the concept of a smart grid. One important aspect of this is local energy trading, which is an extension of existing electricity markets by including prosumers, who are consumers also producing electricity. Prosumers having a surplus of energy may directly trade this surplus with other prosumers, which are currently in demand. In this paper, we present an overview of the literature in the area of local energy trading. In order to provide structure to the broad range of publications, we identify key characteristics, define the various settings, and cluster the considered literature along these characteristics. We identify three main research lines, each with a distinct setting and research question. We analyze and compare the settings, the used techniques, and the results and findings within each cluster and derive connections between the clusters. In addition, we identify important aspects, which up to now have to a large extent been neglected in the considered literature and highlight interesting research directions, and open problems for future work.Comment: 38 pages, 1 figure, This work has been submitted and accepted at OR Spectru

Pricing in Non-Convex Markets: How to Price Electricity in the Presence of Demand Response

A Walrasian competitive equilibrium defines a set of linear and anonymous prices where no coalition of market participants wants to deviate. Walrasian prices do not exist in non-convex markets in general, with electricity markets as an important real-world example. However, the availability of linear and anonymous prices is important for derivatives markets and as a signal for scarcity. Prior literature on electricity markets assumed price-inelastic demand and introduced numerous heuristics to compute linear and anonymous prices on electricity markets. At these prices market participants often make a loss. As a result, market operators provide out-of-market side-payments (so-called make-whole payments) to cover these losses. Make-whole payments dilute public price signals and are a significant concern in electricity markets. Besides, demand-side flexibility becomes increasingly important with growing levels of renewable energy sources. Demand response implies that different flexibility options come at different prices, and the proportion of price-sensitive demand that actively bids on power exchanges will further increase. We show that with price-inelastic demand there are simple pricing schemes that are individually rational (participants do not make a loss), clear the market, support an efficient solution and do not require make-whole payments. With the advent of demand-side bids, budget balanced prices (no subsidies are necessary) cannot exist anymore, and we propose a pricing rule that minimizes make-whole payments. We describe design desiderata that different pricing schemes satisfy and report results of experiments that evaluate the level of subsidies required for linear and anonymous prices on electricity spot markets with price-sensitive demand

The Rank Pricing Problem: models and branch-and-cut algorithms

International audienceOne of the main concerns in management and economic planning is to sell the right product to the right customer for the right price. Companies in retail and manufacturing employ pricing strategies to maximize their revenues. The Rank Pricing Problem considers a unit-demand model with unlimited supply and uniform budgets in which customers have a rank-buying behavior. Under these assumptions, the problem is first analyzed from the perspective of bilevel pricing models and formulated as a non linear bilevel program with multiple independent followers. We also present a direct non linear single level formulation bearing in mind the aim of the problem. Two different linearizations of the models are carried out and two families of valid inequalities are obtained which, embedded in the formulations by implementing a branch-and-cut algorithm, allow us to tighten the upper bound given by the linear relaxation of the models. We also study the polyhedral structure of the models, taking advantage of the fact that a subset of their constraints constitutes a special case of the Set Packing Problem, and characterize all the clique facets. Besides, we develop a preprocessing procedure to reduce the size of the instances. Finally, we show the efficiency of the formulations, the branch-and-cut algorithms and the preprocessing through extensive computational experiments

ALLOCATIONS IN LARGE MARKETS

Rapid growth and popularity of internet based services such as online markets and online advertisement systems provide a lot of new algorithmic challenges. One of the main challenges is the limited access to the input. There are two main reasons that algorithms have limited data accessibility. 1) The input is extremely large, and hence having access to the whole data at once is not practical. 2) The nature of the system forces us to make decisions before observing the whole input. Internet-enabled marketplaces such as Amazon and eBay deal with huge datasets registering transaction of merchandises between lots of buyers and sellers. It is important that algorithms become more time and space efficient as the size of datasets increase. An algorithm that runs in polynomial time may not have a reasonable running time for such large datasets. In the first part of this dissertation, we study the development of allocation algorithms that are appropriate for use with massive datasets. We especially focus on the streaming setting which is a common model for big data analysis. In the graph streaming, the algorithm has access to a sequence of edges, called a stream. The algorithm reads edges in the order in which they appear in the stream. The goal is to design an algorithm that maintains a large allocation, using as little space as possible. We achieve our results by developing powerful sampling techniques. Indeed, one can implement our sampling techniques in the streaming setting as well as other distributed settings such as MapReduce. Giant online advertisement markets such as Google, Bing and Facebook raised up several interesting allocation problems. Usually, in these applications, we need to make the decision before obtaining the full information of the input graph. This enforces an uncertainty on our belief about the input, and thus makes the classical algorithms inapplicable. To address this shortcoming online algorithms have been developed. In online algorithms again the input is a sequence of items. Here the algorithm needs to make an irrevocable decision upon arrival of each item. In the second part of this dissertation, we aim to achieve two main goals for each allocation problem in the market. Our first goal is to design models to capture the uncertainty of the input based on the properties of problems and the accessible data in real applications. Our second goal is to design algorithms and develop new techniques for these market allocation problems