Proceedings of the 2017 ACM Conference on Economics and Computation最新文献

{"title":"Pricing and Optimization in Shared Vehicle Systems: An Approximation Framework","authors":"Siddhartha Banerjee, Daniel Freund, Thodoris Lykouris","doi":"10.1145/3033274.3085099","DOIUrl":"https://doi.org/10.1145/3033274.3085099","url":null,"abstract":"Optimizing shared vehicle systems (bike-sharing/car-sharing/ride-sharing) is more challenging compared to traditional resource allocation settings due to the presence of complex network externalities. In particular, changes in the demand/supply at any location (via dynamic pricing, rebalancing of empty vehicles, etc.) affect future supply throughout the system within short timescales. Such externalities are well captured by steady-state Markovian models, which are therefore widely used to analyze and design shared vehicle systems. However, using such models to design pricing/control policies is computationally difficult since the resulting optimization problems are high-dimensional and non-convex. To this end, we develop a general approximation framework for designing pricing policies in shared vehicle systems, based on a novel convex relaxation which we term elevated flow relaxation. Our approach provides the first efficient algorithms with rigorous approximation guarantees for a wide range of objective functions (throughput, revenue, welfare). For any shared vehicle system with $n$ stations and m vehicles, our framework provides a pricing policy with an approximation ratio of 1+(n-1)/m. This guarantee is particularly meaningful when m/n, the average number of vehicles per station is large, as is often the case in practice. Further, the simplicity of our approach allows us to extend it to more complex settings. Apart from pricing, shared vehicle systems enable other control levers for modulating demand and supply, e.g. rebalancing empty vehicles, redirecting riders to nearby vehicles, etc. Our approach yields efficient algorithms with the same approximation guarantees for all these problems, and in the process, obtains as special cases several existing heuristics and asymptotic guarantees. We also extend our approach to obtain bi-criterion guarantees in multi-objective settings; we illustrate this with the example of Ramsey pricing. From a technical perspective, our work develops a new approach for obtaining control policies with approximation guarantees in steady-state Markovian models. Our approach can be distilled into the following three-step program: (i) construct an upper bound via a relaxation to the original problem that encodes essential conservation laws of the system, (ii) identify a family of control policies inducing known steady-state distributions that achieve the value of the relaxed solution in an appropriate scaling limit (in our case, state-independent policies in the limit m++), and (iii) characterize the performance loss between the finite system (i.e. fixed m) and the scaling limit. This technique may be of independent interest for other settings.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128656620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multidimensional Dynamic Pricing for Welfare Maximization","authors":"Aaron Roth, Aleksandrs Slivkins, Jonathan Ullman, Zhiwei Steven Wu","doi":"10.1145/3033274.3085106","DOIUrl":"https://doi.org/10.1145/3033274.3085106","url":null,"abstract":"We study the problem of a seller dynamically pricing d distinct types of indivisible goods, when faced with the online arrival of unit-demand buyers drawn independently from an unknown distribution. The goods are not in limited supply, but can only be produced at a limited rate and are costly to produce. The seller observes only the bundle of goods purchased at each day, but nothing else about the buyer's valuation function. Our main result is a dynamic pricing algorithm for optimizing welfare (including the seller's cost of production) that runs in time and a number of rounds that are polynomial in d and the approximation parameter. We are able to do this despite the fact that (i) the price-response function is not continuous, and even its fractional relaxation is a non-concave function of the prices, and (ii) the welfare is not observable to the seller. We derive this result as an application of a general technique for optimizing welfare over divisible goods, which is of independent interest. When buyers have strongly concave, Hölder continuous valuation functions over d divisible goods, we give a general polynomial time dynamic pricing technique. We are able to apply this technique to the setting of unit demand buyers despite the fact that in that setting the goods are not divisible, and the natural fractional relaxation of a unit demand valuation is not strongly concave. In order to apply our general technique, we introduce a novel price randomization procedure which has the effect of implicitly inducing buyers to \"regularize'' their valuations with a strongly concave function. Finally, we also extend our results to a limited-supply setting in which the number of copies of each good cannot be replenished.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130575245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nash Social Welfare Approximation for Strategic Agents","authors":"Simina Brânzei, Vasilis Gkatzelis, R. Mehta","doi":"10.1145/3033274.3085143","DOIUrl":"https://doi.org/10.1145/3033274.3085143","url":null,"abstract":"The fair division of resources among strategic agents is an important age-old problem that has led to a rich body of literature. At the center of this literature lies the question of whether there exist mechanisms that can implement fair outcomes, despite the agents' strategic behavior. A fundamental objective function used for measuring the fairness of an allocation is the geometric mean of the agents' values, known as the Nash social welfare (NSW). This objective function is maximized by widely known solution concepts such as Nash bargaining and the competitive equilibrium with equal incomes. In this work we focus on the question of (approximately) implementing this objective. The starting point of our analysis is the Fisher market, a fundamental model of an economy, whose benchmark is precisely the (weighted) Nash social welfare. We begin by studying two extreme classes of valuations functions, namely perfect substitutes and perfect complements, and find that for perfect substitutes, the Fisher market mechanism yields a constant approximation: at most 2 and at least e1/e (≈ 1.44). However, for perfect complements, the Fisher market mechanism does not work well, its bound degrading linearly with the number of players. Strikingly, the Trading Post mechanism---an indirect market mechanism also known as the Shapley-Shubik game---has significantly better performance than the Fisher market on its own benchmark. Not only does Trading Post achieve an approximation of 2 for perfect substitutes, but this bound holds for any concave utilities, and it becomes essentially optimal for perfect complements, where it reaches (1+ε) for any ε>0. Moreover, we show that all the Nash equilibria of the Trading Post mechanism are pure (hence the approximation factors extend to all Nash equilibria), and satisfy an important notion of individual fairness known as proportionality.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128662711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Matching while Learning","authors":"Ramesh Johari, Vijay Kamble, Yashodhan Kanoria","doi":"10.1145/3033274.3084095","DOIUrl":"https://doi.org/10.1145/3033274.3084095","url":null,"abstract":"We consider the problem faced by a service platform that needs to match supply with demand but also to learn attributes of new arrivals in order to match them better in the future. We introduce a benchmark model with heterogeneous workers and jobs that arrive over time. Job types are known to the platform, but worker types are unknown and must be learned by observing match outcomes. Workers depart after performing a certain number of jobs. The payoff from a match depends on the pair of types and the goal is to maximize the steady-state rate of accumulation of payoff. Our main contribution is a complete characterization of the structure of the optimal policy in the limit that each worker performs many jobs. The platform faces a trade-off for each worker between myopically maximizing payoffs (exploitation) and learning the type of the worker (exploration). This creates a multitude of multi-armed bandit problems, one for each worker, coupled together by the constraint on the availability of jobs of different types (capacity constraints). We find that the platform should estimate a shadow price for each job type, and use the payoffs adjusted by these prices, first, to determine its learning goals and then, for each worker, (i) to balance learning with payoffs during the exploration phase, and (ii) to myopically match after it has achieved its learning goals during the exploitation phase.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"24 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128458501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}