{"type":"ScholarlyArticle","title":"A Complete Landscape of EFX Allocations on Graphs: Goods, Chores and Mixed Manna","authors":[{"name":"Yu Zhou","slug":"yu-zhou","given":"Yu","family":"Zhou","affiliation":"Department of Computer Science , City University of Hong Kong , Hong Kong , China"},{"name":"Tianze Wei","slug":"tianze-wei","given":"Tianze","family":"Wei","affiliation":"Department of Computer Science , City University of Hong Kong , Hong Kong , China"},{"name":"Minming Li","slug":"minming-li","given":"Minming","family":"Li","affiliation":"Department of Computer Science , City University of Hong Kong , Hong Kong , China"},{"name":"Bo Li","slug":"bo-li","given":"Bo","family":"Li","affiliation":"Department of Computing , The Hong Kong Polytechnic University , Hong Kong , China"}],"abstract":"We study envy-free up to any item (EFX) allocations on graphs where vertices and edges represent agents and items respectively. An agent is only interested in items that are incident to her and all other items have zero marginal values to her. Christodoulou et al. first proposed this setting and studied the case of goods. We extend this setting to the case of mixed manna where an item may be liked or disliked by its endpoint agents. In our problem, an agent has an arbitrary valuation over her incident items such that the items she likes have non-negative marginal values to her and those she dislikes have non-positive marginal values. We provide a complete study of the four notions of EFX for mixed manna in the literature, which differ by whether the removed item can have zero marginal value. We prove that an allocation that satisfies the notion of EFX where the virtually-removed item could always have zero marginal value may not exist and determining its existence is NP-complete, while one that satisfies any of the other three notions always exists and can be computed in polynomial time. We also prove that an orientation (i.e., a special allocation where each edge must be allocated to one of its endpoint agents) that satisfies any of the four notions may not exist, and determining its existence is NP-complete.","doi":"10.24963/ijcai.2024/338","url":"https://ijcai.org/proceedings/2024/338","pdf":"https://ijcai.org/proceedings/2024/0338.pdf","markdown":"https://ijcai.org/proceedings/2024/338.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/338","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":338,"pages":{"first":3049,"last":3056},"keywords":["Game Theory and Economic Paradigms: GTEP: Computational social choice","Game Theory and Economic Paradigms: GTEP: Fair division"],"videos":[],"references":[{"position":1,"raw":"[Aleksandrov and Walsh, 2019] Martin Aleksandrov and Toby Walsh. Greedy algorithms for fair division of mixed manna. CoRR, abs/1911.11005, 2019.","title":"Greedy algorithms for fair division of mixed manna","authors":"Aleksandrov, Walsh ;, Martin Aleksandrov, Toby Walsh","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Aleksandrov and Walsh, 2020] Martin Aleksandrov and Toby Walsh. Two algorithms for additive and fair division of mixed manna. In Proceedings of the 43rd German Conference on Artificial Intelligence, pages 3-17, 2020.","title":"Two algorithms for additive and fair division of mixed manna","authors":"Aleksandrov, Walsh ;, Martin Aleksandrov, Toby Walsh","year":"2020","venue":"Proceedings of the 43rd German Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Amanatidis et al., 2021] Georgios Amanatidis, Georgios Birmpas, Aris Filos-Ratsikas, Alexandros Hollender, and Alexandros A. Voudouris. Maximum nash welfare and other stories about EFX. Theoretical Computer Science, 863:69-85, 2021.","title":"Maximum nash welfare and other stories about EFX","authors":"Georgios Amanatidis, Georgios Birmpas, Aris Filos-Ratsikas, Alexandros Hollender, Alexandros A Voudouris","year":"2021","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":"/proceedings/2020/4"},{"position":4,"raw":"[Aziz and Mackenzie, 2016] Haris Aziz and Simon Macken- zie. A discrete and bounded envy-free cake cutting pro- tocol for any number of agents. In Proceedings of the 57th IEEE Symposium on Foundations of Computer Sci- ence, pages 416-427, 2016.","title":"A discrete and bounded envy-free cake cutting protocol for any number of agents","authors":"Haris Aziz, Simon Mackenzie","year":"2016","venue":"Proceedings of the 57th IEEE Symposium on Foundations of Computer Science","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Aziz et al., 2022] Haris Aziz, Ioannis Caragiannis, Ayumi Igarashi, and Toby Walsh. Fair allocation of indivisible goods and chores. Autonomous Agents and Multi-Agent Systems, 36(1):3, 2022.","title":"Fair allocation of indivisible goods and chores","authors":"Haris Aziz, Ioannis Caragiannis, Ayumi Igarashi, Toby Walsh","year":"2022","venue":"Autonomous Agents and Multi-Agent Systems","doi":null,"url":null,"internal_url":"/proceedings/2019/8"},{"position":6,"raw":"[Bei et al., 2022] Xiaohui Bei, Ayumi Igarashi, Xinhang Lu, and Warut Suksompong. The price of connectivity in fair division. SIAM J. Discret. Math., 36(2):1156-1186, 2022.","title":"The price of connectivity in fair division","authors":"Xiaohui Bei, Ayumi Igarashi, Xinhang Lu, Warut Suksompong","year":"2022","venue":"SIAM J. Discret. Math","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Bérczi et al., 2020] Kristóf Bérczi, Erika R. Bérczi- Kovács, Endre Boros, Fekadu Tolessa Gedefa, Naoyuki Kamiyama, Telikepalli Kavitha, Yusuke Kobayashi, and Kazuhisa Makino. Envy-free relaxations for goods, chores, and mixed items. CoRR, abs/2006.04428, 2020.","title":"Envy-free relaxations for goods, chores, and mixed items","authors":"Kristóf Bérczi, Erika R Bérczi-Kovács, Endre Boros, Fekadu Tolessa Gedefa, Naoyuki Kamiyama, Telikepalli Kavitha, Yusuke Kobayashi, Kazuhisa Makino","year":"2020","venue":null,"doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Berman et al., 2007] Piotr Berman, Marek Karpinski, and Alexander D. Scott. Computational complexity of some restricted instances of 3-sat. Discrete Applied Mathemat- ics, 155(5):649-653, 2007.","title":"Computational complexity of some restricted instances of 3-sat","authors":"Piotr Berman, Marek Karpinski, Alexander D Scott","year":"2007","venue":"Discrete Applied Mathematics","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Bilò et al., 2022] Vittorio Bilò, Ioannis Caragiannis, Michele Flammini, Ayumi Igarashi, Gianpiero Monaco, Dominik Peters, Cosimo Vinci, and William S. Zwicker. Almost envy-free allocations with connected bundles. Games Econ. Behav., 131:197-221, 2022.","title":"Almost envy-free allocations with connected bundles","authors":"Vittorio Bilò, Ioannis Caragiannis, Michele Flammini, Ayumi Igarashi, Gianpiero Monaco, Dominik Peters, Cosimo Vinci, William S Zwicker","year":"2022","venue":"Games Econ. Behav","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Bouveret et al., 2017] Sylvain Bouveret, Katarína Cechlárová, Edith Elkind, Ayumi Igarashi, and Do- minik Peters. Fair division of a graph. In Proceedings of the 26th International Joint Conference on Artificial Intelligence, pages 135-141, 2017.","title":"Fair division of a graph","authors":"Sylvain Bouveret, Katarína Cechlárová, Edith Elkind, Ayumi Igarashi, Dominik Peters","year":"2017","venue":"Proceedings of the 26th International Joint Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Caragiannis et al., 2019] Ioannis Caragiannis, Nick Gravin, and Xin Huang. Envy-freeness up to any item with high nash welfare: The virtue of donating items. In Proceedings of the 20th ACM Conference on Economics and Computa- tion, pages 527-545, 2019.","title":"Envy-freeness up to any item with high nash welfare: The virtue of donating items","authors":"Ioannis Caragiannis, Nick Gravin, Xin Huang","year":"2019","venue":"Proceedings of the 20th ACM Conference on Economics and Computation","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Chaudhury et al., 2020] Bhaskar Ray Chaudhury, Jugal Garg, and Kurt Mehlhorn. Efx exists for three agents. In Proceedings of the 21st ACM Conference on Economics and Computation, pages 1-19, 2020.","title":"Efx exists for three agents","authors":"Ray Bhaskar, Jugal Chaudhury, Kurt Garg, Mehlhorn","year":"2020","venue":"Proceedings of the 21st ACM Conference on Economics and Computation","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Christodoulou et al., 2023] George Christodoulou, Amos Fiat, Elias Koutsoupias, and Alkmini Sgouritsa. Fair al- location in graphs. In Proceedings of the 24th ACM Con- ference on Economics and Computation, pages 473-488, 2023.","title":"Fair allocation in graphs","authors":"George Christodoulou, Amos Fiat, Elias Koutsoupias, Alkmini Sgouritsa","year":"2023","venue":"Proceedings of the 24th ACM Conference on Economics and Computation","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Dehghani et al., 2018] Sina Dehghani, Alireza Farhadi, Mohammad Taghi Hajiaghayi, and Hadi Yami. Envy-free chore division for an arbitrary number of agents. In Pro- ceedings of the 29th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 2564-2583, 2018.","title":"Envy-free chore division for an arbitrary number of agents","authors":"Sina Dehghani, Alireza Farhadi, Mohammad Taghi Hajiaghayi, Hadi Yami","year":"2018","venue":"Proceedings of the 29th Annual ACM-SIAM Symposium on Discrete Algorithms","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Hosseini et al., 2021] Hadi Hosseini, Sujoy Sikdar, Rohit Vaish, and Lirong Xia. Fair and efficient allocations un- der lexicographic preferences. In Proceedings of the 35th AAAI Conference on Artificial Intelligence, pages 5472- 5480, 2021.","title":"Fair and efficient allocations under lexicographic preferences","authors":"Hadi Hosseini, Sujoy Sikdar, Rohit Vaish, Lirong Xia","year":"2021","venue":"Proceedings of the 35th AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Hummel and Hetland, 2022] Halvard Hummel and Mag- nus Lie Hetland. Fair allocation of conflicting items. Au- tonomous Agents and Multi-Agent Systems, 36(1):8, 2022.","title":"Halvard Hummel and Magnus Lie Hetland. Fair allocation of conflicting items","authors":"Hetland Hummel","year":"2022","venue":"Autonomous Agents and Multi-Agent Systems","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Igarashi and Peters, 2019] Ayumi Igarashi and Dominik Pe- ters. Pareto-optimal allocation of indivisible goods with connectivity constraints. In AAAI, pages 2045-2052. AAAI Press, 2019.","title":"Ayumi Igarashi and Dominik Peters. Pareto-optimal allocation of indivisible goods with connectivity constraints","authors":"Peters Igarashi","year":"2019","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Karp et al., 1975] Richard M Karp, Raymond E Miller, and James W Thatcher. Reducibility among combinatorial problems. Journal of Symbolic Logic, 40(4), 1975.","title":"Reducibility among combinatorial problems","authors":"Raymond E Richard M Karp, James W Miller, Thatcher","year":"1975","venue":"Journal of Symbolic Logic","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Li et al., 2022] Bo Li, Yingkai Li, and Xiaowei Wu. Almost (weighted) proportional allocations for indivisible chores. In Proceedings of the ACM Web Conference 2022, pages 122-131, 2022.","title":"Almost (weighted) proportional allocations for indivisible chores","authors":"Bo Li, Yingkai Li, Xiaowei Wu","year":"2022","venue":"Proceedings of the ACM Web Conference 2022","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Liu et al., 2023] Shengxin Liu, Xinhang Lu, Mashbat Suzuki, and Toby Walsh. Mixed fair division: A survey. CoRR, abs/2306.09564, 2023.","title":"Mixed fair division: A survey","authors":"Liu","year":"2023","venue":null,"doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Madathil, 2023] Jayakrishnan Madathil. Fair division of a graph into compact bundles. In Proceedings of the 32nd International Joint Conference on Artificial Intelligence, pages 2835-2843, 2023.","title":"Fair division of a graph into compact bundles","authors":"Jayakrishnan Madathil","year":"2023","venue":"Proceedings of the 32nd International Joint Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/2023/316"},{"position":22,"raw":"[Payan et al., 2023] Justin Payan, Rik Sengupta, and Vig- nesh Viswanathan. Relaxations of envy-freeness over graphs. In Proceedings of the 2023 International Con- ference on Autonomous Agents and Multiagent Systems, pages 2652-2654, 2023.","title":"Relaxations of envy-freeness over graphs","authors":"Justin Payan, Rik Sengupta, Vignesh Viswanathan","year":"2023","venue":"Proceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Plaut and Roughgarden, 2020] Benjamin Plaut and Tim Roughgarden. Almost envy-freeness with general val- uations. SIAM Journal on Discrete Mathematics, 34(2):1039-1068, 2020.","title":"Almost envy-freeness with general valuations","authors":"Benjamin Plaut, Tim Roughgarden","year":"2020","venue":"SIAM Journal on Discrete Mathematics","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Suksompong, 2019] Warut Suksompong. Fairly allocating contiguous blocks of indivisible items. Discret. Appl. Math., 260:227-236, 2019.","title":"Warut Suksompong. Fairly allocating contiguous blocks of indivisible items","authors":"Suksompong","year":"2019","venue":"Discret. Appl. Math","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}