{"type":"ScholarlyArticle","title":"Pure Nash Equilibria in Online Fair Division","authors":[{"name":"Martin Aleksandrov","slug":"martin-aleksandrov","given":"Martin","family":"Aleksandrov","affiliation":"UNSW Sydney Data61 , CSIRO TU Berlin"},{"name":"Toby Walsh","slug":"toby-walsh","given":"Toby","family":"Walsh","affiliation":"UNSW Sydney Data61 , CSIRO TU Berlin"}],"abstract":"We consider a fair division setting in which items arrive one by one and are allocated to agents via two existing mechanisms: LIKE and BALANCED LIKE. The LIKE mechanism is strategy-proof whereas the BALANCED LIKE mechanism is not. Whilst LIKE is strategy-proof, we show that it is not group strategy-proof. Indeed, our first main result is that no online mechanism is group strategy-proof. We then focus on pure Nash equilibria of these two mechanisms. Our second main result is that computing a pure Nash equilibrium is tractable for LIKE and intractable for BALANCED LIKE. Our third main result is that there could be multiple such profiles and counting them is also intractable even when we restrict our attention to equilibria with a specific property (e.g. envy-freeness, Pareto efficiency).","doi":"10.24963/ijcai.2017/7","url":"https://ijcai.org/proceedings/2017/7","pdf":"https://ijcai.org/proceedings/2017/0007.pdf","markdown":"https://ijcai.org/proceedings/2017/7.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/7","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":7,"pages":{"first":42,"last":48},"keywords":["Agent-based and Multi-agent Systems: Agent Theories and Models","Agent-based and Multi-agent Systems: Social Choice Theory"],"videos":[],"references":[{"position":1,"raw":"[Aleksandrov et al., 2015] Martin Aleksandrov, Haris Aziz, Serge Gaspers, and Toby Walsh. Online fair division: Analysing a food bank problem. In Proc. of IJCAI 2015, Buenos Aires, Argentina, July 25-31, 2015, pages 2540- 2546, 2015.","title":"Online fair division: Analysing a food bank problem","authors":"Martin Aleksandrov, Haris Aziz, Serge Gaspers, Toby Walsh","year":"2015","venue":"Proc. of IJCAI 2015","doi":null,"url":null,"internal_url":"/proceedings/2015/360"},{"position":2,"raw":"[Aziz et al., 2015] Haris Aziz, Serge Gaspers, Simon Mackenzie, Nicholas Mattei, Nina Narodytska, and Toby Walsh. Equilibria under the probabilistic serial rule. In Proc. of IJCAI 2015, Buenos Aires, Argentina, July 25-31, 2015, pages 1105-1112, 2015.","title":"Equilibria under the probabilistic serial rule","authors":"Haris Aziz, Serge Gaspers, Simon Mackenzie, Nicholas Mattei, Nina Narodytska, Toby Walsh","year":"2015","venue":"Proc. of IJCAI 2015","doi":null,"url":null,"internal_url":"/proceedings/2015/160"},{"position":3,"raw":"[Budish and Cantillon, 2012] Eric Budish and Estelle Cantil- lon. The multi-unit assignment problem: Theory and ev- idence from course allocation at Harvard. American Eco- nomic Review, 102(5):2237-2271, 2012.","title":"The multi-unit assignment problem: Theory and evidence from course allocation at Harvard","authors":"Cantillon Budish","year":"2012","venue":"American Economic Review","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Conitzer and Sandholm, 2008] Vincent Conitzer and Tuo- mas Sandholm. New complexity results about nash equi- libria. Games and Economic Behavior, 63(2):621-641, 2008.","title":"Vincent Conitzer and Tuomas Sandholm. New complexity results about nash equilibria","authors":"Sandholm Conitzer","year":"2008","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Dagum and Luby, 1992] Paul Dagum and Michael Luby. Approximating the permanent of graphs with large factors. Theoretical Computer Science, 102(2):283-305, 1992.","title":"Approximating the permanent of graphs with large factors","authors":"Luby Dagum, Paul Dagum, Michael Luby","year":"1992","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Demange and Ekim, 2008] Marc Demange and Tinaz Ekim. Minimum maximal matching is NP-hard in regular bipartite graphs. In 5th International TAMC 2008, Xi'an, China, April 25-29, 2008. Proceedings, pages 364-374, 2008.","title":"Minimum maximal matching is NP-hard in regular bipartite graphs","authors":"Ekim Demange, Marc Demange, Tinaz Ekim","year":"2008","venue":"5th International TAMC 2008, Xi'an","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Dickhaut and Kaplan, 1993] John Dickhaut and Todd Ka- plan. A Program for Finding Nash Equilibria, pages 148- 166. Springer New York, New York, NY, 1993.","title":"A Program for Finding Nash Equilibria","authors":"Kaplan Dickhaut","year":"1993","venue":null,"doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Downey and Fellows, 2013] Rodney G. Downey and Michael R. Fellows. Fundamentals of Parameterized Complexity. Texts in Computer Science. Springer, 2013.","title":"Fundamentals of Parameterized Complexity","authors":"Rodney G Downey, Michael R Fellows","year":"2013","venue":"Texts in Computer Science","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Garey and Johnson, 1979] M. R. Garey and David S. John- son. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979.","title":"Computers and Intractability: A Guide to the Theory of NP-Completeness","authors":"M R Garey, David S Johnson","year":"1979","venue":null,"doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Gilboa and Zemel, 1989] Itzhak Gilboa and Eitan Zemel. Nash and correlated equilibria: Some complexity con- siderations. Games and Economic Behavior, 1(1):80-93, 1989.","title":"Nash and correlated equilibria: Some complexity considerations","authors":"Zemel Gilboa, Itzhak Gilboa, Eitan Zemel","year":"1989","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Hopcroft and Karp, 1973] John E. Hopcroft and Richard M. Karp. An n 5/2 algorithm for maximum matchings in bi- partite graphs. SIAM J. of Comp., 2(4):225-231, 1973.","title":"An n 5/2 algorithm for maximum matchings in bipartite graphs","authors":"John E Hopcroft, Richard M Karp","year":"1973","venue":"SIAM J. of Comp","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Jerrum and Sinclair, 1989] Mark Jerrum and Alistair Sin- clair. Approximating the permanent. SIAM J. of Comp., 18(6):1149-1178, 1989.","title":"Approximating the permanent","authors":"Mark Jerrum, Alistair Sinclair","year":"1989","venue":"SIAM J. of Comp","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Martínez et al., 2004] Ruth Martínez, Jordi Massó, Alejan- dro Neme, and Jorge Oviedo. On group strategy-proof mechanisms for a many-to-one matching model. Int. J. Game Theory, 33(1):115-128, 2004.","title":"On group strategy-proof mechanisms for a many-to-one matching model","authors":"Martínez","year":"2004","venue":"Int. J. Game Theory","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Porter et al., 2008] Ryan Porter, Eugene Nudelman, and Yoav Shoham. Simple search methods for finding a nash equilibrium. Games and Economic Behavior, 63(2):642- 662, 2008.","title":"Simple search methods for finding a nash equilibrium","authors":"Ryan Porter, Eugene Nudelman, Yoav Shoham","year":"2008","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Pountourakis and Vidali, 2012] Emmanouil Pountourakis and Angelina Vidali. A complete characterization of group-strategyproof mechanisms of cost-sharing. Algorithmica, 63(4):831-860, 2012.","title":"Emmanouil Pountourakis and Angelina Vidali. A complete characterization of group-strategyproof mechanisms of cost-sharing","authors":"Vidali Pountourakis","year":"2012","venue":"Algorithmica","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Sabán and Sethuraman, 2013] Daniela Sabán and Jay Sethuraman. The complexity of computing the random priority allocation matrix. In Proc. of WINE 2013, Cambridge, MA, USA, December 11-14, page 421, 2013.","title":"The complexity of computing the random priority allocation matrix","authors":"Sethuraman Sabán, Daniela Sabán, Jay Sethuraman","year":"2013","venue":"Proc. of WINE 2013","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Sandholm et al., 2005] Tuomas Sandholm, Andrew Gilpin, and Vincent Conitzer. Mixed-integer programming meth- ods for finding nash equilibria. In Proceedings, The Twen- tieth National Conference on Artificial Intelligence and the Seventeenth Innovative Applications of Artificial Intelli- gence Conference, July 9-13, 2005, Pittsburgh, Pennsyl- vania, USA, pages 495-501, 2005.","title":"Mixed-integer programming methods for finding nash equilibria","authors":"Sandholm","year":"2005","venue":"Proceedings, The Twentieth National Conference on Artificial Intelligence and the Seventeenth Innovative Applications of Artificial Intelligence Conference","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Shapley and Rigby, 1959] L. S. Shapley and Fred D. Rigby. Equilibrium points in games with vector payoffs. Naval Research Logistics Quarterly, 6(1):57-61, 1959.","title":"Equilibrium points in games with vector payoffs","authors":"L S Shapley, Fred D Rigby","year":"1959","venue":"Naval Research Logistics Quarterly","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Tomala, 1998] Tristan Tomala. Pure equilibria of repeated games with public observation. International Journal of Game Theory, 27(1):93-109, 1998.","title":"Tristan Tomala. Pure equilibria of repeated games with public observation","authors":"Tomala","year":"1998","venue":"International Journal of Game Theory","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Turing, 1936] Alan M. Turing. On computable numbers, with an application to the Entscheidungsproblem. J. Proc. of the London Math. Soc., 2(42):230-265, 1936.","title":"On computable numbers, with an application to the Entscheidungsproblem","authors":"Alan M Turing","year":"1936","venue":"J. Proc. of the London Math. Soc","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Ummels and Wojtczak, 2009] Michael Ummels and Do- minik Wojtczak. Decision problems for nash equilibria in stochastic games. In Computer Science Logic, 23rd in- ternational Workshop, CSL 2009, 18th Annual Conference of the EACSL, Coimbra, Portugal, September 7-11, 2009. Proceedings, pages 515-529, 2009.","title":"Michael Ummels and Dominik Wojtczak. Decision problems for nash equilibria in stochastic games","authors":"Wojtczak Ummels","year":"2009","venue":"Computer Science Logic, 23rd international Workshop, CSL 2009, 18th Annual Conference of the EACSL","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Valiant, 1979] Leslie G. Valiant. The complexity of comput- ing the permanent. Theor. Comp. Sc., 8:189-201, 1979.","title":"The complexity of computing the permanent","authors":"Leslie G Valiant","year":"1979","venue":"Theor. Comp. Sc","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Walsh, 2014] Toby Walsh. Allocation in practice. In Proc. of 37th KI 2014, Stuttgart, Germany, September 22-26, 2014, pages 13-24, 2014.","title":"Allocation in practice","authors":"Toby Walsh","year":"2014","venue":"Proc. of 37th KI 2014","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Walsh, 2015] Toby Walsh. Challenges in resource and cost allocation. In Proc. of 29th AAAI 2015, Austin, Texas, USA, January 25-30, pages 4073-4077, 2015.","title":"Challenges in resource and cost allocation","authors":"Toby Walsh","year":"2015","venue":"Proc. of 29th AAAI 2015","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}