{"title":"Bicriteria Nash flows over time","authors":"Tim Oosterwijk , Daniel Schmand , Marc Schröder","doi":"10.1016/j.geb.2024.06.002","DOIUrl":null,"url":null,"abstract":"<div><p>Flows over time are a natural way to incorporate flow dynamics that arise in various applications such as traffic networks. In this paper we introduce a natural variant of the deterministic fluid queuing model in which users aim to minimize their costs subject to arrival at their destination before a pre-specified deadline. We determine the existence and the structure of Nash flows over time and fully characterize the price of anarchy for this model. The price of anarchy measures the ratio of the quality of the equilibrium and the quality of the optimum flow, where we evaluate the quality using two different natural performance measures: the throughput for a given deadline and the makespan for a given amount of flow. While it turns out that both prices of anarchy can be unbounded in general, we provide tight bounds for the important subclass of parallel path graphs.</p></div>","PeriodicalId":48291,"journal":{"name":"Games and Economic Behavior","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0899825624000836/pdfft?md5=a56d3241c546f13dc49a509b94370f60&pid=1-s2.0-S0899825624000836-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Games and Economic Behavior","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0899825624000836","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ECONOMICS","Score":null,"Total":0}
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Abstract
Flows over time are a natural way to incorporate flow dynamics that arise in various applications such as traffic networks. In this paper we introduce a natural variant of the deterministic fluid queuing model in which users aim to minimize their costs subject to arrival at their destination before a pre-specified deadline. We determine the existence and the structure of Nash flows over time and fully characterize the price of anarchy for this model. The price of anarchy measures the ratio of the quality of the equilibrium and the quality of the optimum flow, where we evaluate the quality using two different natural performance measures: the throughput for a given deadline and the makespan for a given amount of flow. While it turns out that both prices of anarchy can be unbounded in general, we provide tight bounds for the important subclass of parallel path graphs.
期刊介绍：
Games and Economic Behavior facilitates cross-fertilization between theories and applications of game theoretic reasoning. It consistently attracts the best quality and most creative papers in interdisciplinary studies within the social, biological, and mathematical sciences. Most readers recognize it as the leading journal in game theory. Research Areas Include: • Game theory • Economics • Political science • Biology • Computer science • Mathematics • Psychology
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