{"type":"ScholarlyArticle","title":"Combinatorial Cost Sharing","authors":[{"name":"Shahar Dobzinski","slug":"shahar-dobzinski","given":"Shahar","family":"Dobzinski","affiliation":"Weizmann Institute of Science"},{"name":"Shahar Ovadia","slug":"shahar-ovadia","given":"Shahar","family":"Ovadia","affiliation":"Weizmann Institute of Science"}],"abstract":"We introduce a combinatorial variant of the cost sharing problem: several services can be provided to each player and each player values every combination of services differently. A publicly known cost function specifies the cost of providing every possible combination of services. A combinatorial cost sharing mechanism is a protocol that decides which services each player gets and at what price. We look for dominant strategy mechanisms that are (economically) efficient and cover the cost, ideally without overcharging (i.e., budget balanced). Note that unlike the standard cost sharing setting, combinatorial cost sharing is a multi-parameter domain. This makes designing dominant strategy mechanisms with good guarantees a challenging task.\r\n\r\nWe present the Potential Mechanism -- a combination of the VCG mechanism and a well-known tool from the theory of cooperative games: Hart and Mas-Colell's potential function. The potential mechanism is a dominant strategy mechanism that always covers the incurred cost. When the cost function is subadditive the same mechanism is also approximately efficient. Our main technical contribution shows that when the cost function is submodular the potential mechanism is approximately budget balanced in three settings: supermodular valuations, symmetric cost function and general symmetric valuations, and two players with general valuations.","doi":"10.24963/ijcai.2018/728","url":"https://ijcai.org/proceedings/2018/728","pdf":"https://ijcai.org/proceedings/2018/0728.pdf","markdown":"https://ijcai.org/proceedings/2018/728.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/728","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Sister Conferences Best Papers","track":"Best Sister Conferences","number":728,"pages":{"first":5234,"last":5238},"keywords":["Agent-based and Multi-agent Systems: Economic Paradigms, Auctions and Market-Based Systems","Agent-based and Multi-agent Systems: Algorithmic Game Theory","Agent-based and Multi-agent Systems: Cooperative Games"],"videos":[],"references":[{"position":1,"raw":"[Ausubel and Milgrom, 2006] Lawrence M. Ausubel and Paul Milgrom. The lovely but lonely vickrey auction. In Combinatorial Auctions, chapter 1. MIT Press, 2006.","title":"The lovely but lonely vickrey auction","authors":"Lawrence M Ausubel, Paul Milgrom","year":"2006","venue":"Combinatorial Auctions","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Bleischwitz and Schoppmann, 2008] Yvonne Bleischwitz and Florian Schoppmann. Group-strategyproof cost sharing for metric fault tolerant facility location. In International Symposium on Algorithmic Game Theory, pages 350-361. Springer, 2008.","title":"Yvonne Bleischwitz and Florian Schoppmann. Group-strategyproof cost sharing for metric fault tolerant facility location","authors":"Schoppmann Bleischwitz","year":"2008","venue":"International Symposium on Algorithmic Game Theory","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bleischwitz et al., 2007] Yvonne Bleischwitz, Burkhard Monien, and Florian Schoppmann. To be or not to be (served). In International Workshop on Web and Internet Economics, pages 515-528. Springer, 2007.","title":"To be or not to be","authors":"Yvonne Bleischwitz, Burkhard Monien, Florian Schoppmann","year":"2007","venue":"International Workshop on Web and Internet Economics","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Blumrosen and Dobzinski, 2014] Liad Blumrosen and Sha- har Dobzinski. Reallocation mechanisms. In Proceedings of the Fifteenth ACM Conference on Economics and Com- putation, EC '14, pages 617-617, New York, NY, USA, 2014. ACM.","title":"Reallocation mechanisms","authors":"Liad Blumrosen, Shahar Dobzinski","year":"2014","venue":"Proceedings of the Fifteenth ACM Conference on Economics and Computation, EC '14","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Cavallo, 2006] Ruggiero Cavallo. Optimal decision-making with minimal waste: Strategyproof redistribution of vcg payments. In Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems, pages 882-889. ACM, 2006.","title":"Optimal decision-making with minimal waste: Strategyproof redistribution of vcg payments","authors":"Ruggiero Cavallo","year":"2006","venue":"Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Deb and Razzolini, 1999] Rajat Deb and Laura Razzolini. Voluntary cost sharing for an excludable public project. Mathematical Social Sciences, 37(2):123-138, 1999.","title":"Voluntary cost sharing for an excludable public project","authors":"Rajat Deb, Laura Razzolini","year":"1999","venue":"Mathematical Social Sciences","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Dobzinski and Ovadia, 2017] Shahar Dobzinski and Shahar Ovadia. Combinatorial cost sharing. In Proceedings of the 2017 ACM Conference on Economics and Computation, pages 387-404. ACM, 2017.","title":"Combinatorial cost sharing","authors":"Ovadia Dobzinski, Shahar Dobzinski, Shahar Ovadia","year":"2017","venue":"Proceedings of the 2017 ACM Conference on Economics and Computation","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Dobzinski et al., 2008] Shahar Dobzinski, Aranyak Mehta, Tim Roughgarden, and Mukund Sundararajan. Is shapley cost sharing optimal? In International Symposium on Al- gorithmic Game Theory, pages 327-336. Springer, 2008.","title":"Is shapley cost sharing optimal?","authors":"Shahar Dobzinski, Aranyak Mehta, Tim Roughgarden, Mukund Sundararajan","year":"2008","venue":"International Symposium on Algorithmic Game Theory","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Feigenbaum et al., 2002] Joan Feigenbaum, Arvind Krish- namurthy, Rahul Sami, and Scott Shenker. Hardness re- sults for multicast cost sharing. In International Confer- ence on Foundations of Software Technology and Theoret- ical Computer Science, pages 133-144. Springer, 2002.","title":"Hardness results for multicast cost sharing","authors":"Joan Feigenbaum, Arvind Krishnamurthy, Rahul Sami, Scott Shenker","year":"2002","venue":"International Conference on Foundations of Software Technology and Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Georgiou and Swamy, 2013] Konstantinos Georgiou and Chaitanya Swamy. Black-box reductions for cost-sharing mechanism design. Games and Economic Behavior, 2013.","title":"Black-box reductions for cost-sharing mechanism design","authors":"Swamy ; Georgiou, Chaitanya Georgiou, Swamy","year":"2013","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Guo and Conitzer, 2009] Mingyu Guo and Vincent Conitzer. Worst-case optimal redistribution of vcg payments in multi-unit auctions. Games and Economic Behavior, 67(1):69-98, 2009.","title":"Worst-case optimal redistribution of vcg payments in multi-unit auctions","authors":"Conitzer Guo, Mingyu Guo, Vincent Conitzer","year":"2009","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Hart and Mas-Colell, 1989] Sergiu Hart and Andreu Mas- Colell. Potential, value, and consistency. Econometrica: Journal of the Econometric Society, pages 589-614, 1989.","title":"Potential, value, and consistency","authors":"Sergiu Hart, Andreu Mas-Colell","year":"1989","venue":"Econometrica: Journal of the Econometric Society","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Hashimoto and Saitoh, 2015] Kazuhiko Hashimoto and Hi- roki Saitoh. Strategy-proof cost sharing under increasing returns: Improvement of the supremal welfare loss. Games and Economic Behavior, 89:101-121, 2015.","title":"Strategy-proof cost sharing under increasing returns: Improvement of the supremal welfare loss","authors":"Saitoh Hashimoto, Kazuhiko Hashimoto, Hiroki Saitoh","year":"2015","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Littlechild and Owen, 1973] Stephen C Littlechild and Guillermo Owen. A simple expression for the shap- ley value in a special case. Management Science, 20(3):370-372, 1973.","title":"A simple expression for the shapley value in a special case","authors":"C Stephen, Guillermo Littlechild, Owen","year":"1973","venue":"Management Science","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Mehta et al., 2007] Aranyak Mehta, Tim Roughgarden, and Mukund Sundararajan. Beyond moulin mechanisms. In Proceedings of the 8th ACM Conference on Electronic Commerce, pages 1-10. ACM, 2007.","title":"Beyond moulin mechanisms","authors":"Mehta","year":"2007","venue":"Proceedings of the 8th ACM Conference on Electronic Commerce","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Moulin and Shenker, 2001] Hervé Moulin and Scott Shenker. Strategyproof sharing of submodular costs: budget balance versus efficiency. Economic Theory, 18(3):511-533, 2001.","title":"Strategyproof sharing of submodular costs: budget balance versus efficiency","authors":"Shenker Moulin, Hervé Moulin, Scott Shenker","year":"2001","venue":"Economic Theory","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Moulin, 1999] Hervé Moulin. Incremental cost sharing: Characterization by coalition strategy-proofness. Social Choice and Welfare, 16(2):279-320, 1999.","title":"Incremental cost sharing: Characterization by coalition strategy-proofness","authors":"Hervé Moulin","year":"1999","venue":"Social Choice and Welfare","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Moulin, 2009] Hervé Moulin. Almost budget-balanced VCG mechanisms to assign multiple objects. Journal of Economic Theory, 144(1):96 -119, 2009.","title":"Almost budget-balanced VCG mechanisms to assign multiple objects","authors":"Hervé Moulin, Moulin","year":"2009","venue":"Journal of Economic Theory","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Roberts, 1979] Kevin Roberts. Aggregation and revelation of preferences. The Characterization of Implementable Choice Rules, pages 321-348, 1979.","title":"Aggregation and revelation of preferences","authors":"Kevin Roberts","year":"1979","venue":"The Characterization of Implementable Choice Rules","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Roughgarden and Sundararajan, 2009] Tim Roughgarden and Mukund Sundararajan. Quantifying inefficiency in cost-sharing mechanisms. Journal of the ACM (JACM), 56(4):23, 2009.","title":"Quantifying inefficiency in cost-sharing mechanisms","authors":"Sundararajan Roughgarden, Tim Roughgarden, Mukund Sundararajan","year":"2009","venue":"Journal of the ACM (JACM)","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Shapley, 1953] Lloyd S Shapley. A value for n-person games. Contributions to the Theory of Games, 2(28):307- 317, 1953.","title":"A value for n-person games","authors":"S Lloyd, Shapley","year":"1953","venue":"Contributions to the Theory of Games","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}