Capacitated network design games with weighted players
We consider network design games with weighted players and uniform edge capacities and study their Nash equilibria. In these games, each player has to choose a path from her source to her sink through a network subject to the constraint that the total weight of all players using an edge within their...
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| Vydáno v: | Networks Ročník 68; číslo 2; s. 141 - 158 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Blackwell Publishing Ltd
01.09.2016
Wiley Subscription Services, Inc |
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| ISSN: | 0028-3045, 1097-0037 |
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| Abstract | We consider network design games with weighted players and uniform edge capacities and study their Nash equilibria. In these games, each player has to choose a path from her source to her sink through a network subject to the constraint that the total weight of all players using an edge within their chosen path does not exceed the capacity of the edge. The fixed cost of each edge that is used by some player is shared among the players using the edge by charging each player a fraction of the edge's cost equal to the ratio of her weight to the total weight of all players using the edge. We show that there exist instances of capacitated network design games with weighted players and uniform capacities that do not admit a Nash equilibrium even in the case that all players share the same source and sink. Moreover, we show that it is strongly
N
P
‐hard to decide whether a given instance admits a Nash equilibrium even if a feasible solution for the underlying network design problem is guaranteed to exist. In contrast, we prove that, for series‐parallel graphs, there always exists a Nash equilibrium whose total cost equals the cost of an optimal solution of the corresponding network design problem and provide an (exponential‐time) algorithm to compute this equilibrium. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 68(2), 141–158 2016 |
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| AbstractList | We consider network design games with weighted players and uniform edge capacities and study their Nash equilibria. In these games, each player has to choose a path from her source to her sink through a network subject to the constraint that the total weight of all players using an edge within their chosen path does not exceed the capacity of the edge. The fixed cost of each edge that is used by some player is shared among the players using the edge by charging each player a fraction of the edge's cost equal to the ratio of her weight to the total weight of all players using the edge. We show that there exist instances of capacitated network design games with weighted players and uniform capacities that do not admit a Nash equilibrium even in the case that all players share the same source and sink. Moreover, we show that it is strongly
‐hard to decide whether a given instance admits a Nash equilibrium even if a feasible solution for the underlying network design problem is guaranteed to exist. In contrast, we prove that, for series‐parallel graphs, there always exists a Nash equilibrium whose total cost equals the cost of an optimal solution of the corresponding network design problem and provide an (exponential‐time) algorithm to compute this equilibrium. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 68(2), 141–158 2016 We consider network design games with weighted players and uniform edge capacities and study their Nash equilibria. In these games, each player has to choose a path from her source to her sink through a network subject to the constraint that the total weight of all players using an edge within their chosen path does not exceed the capacity of the edge. The fixed cost of each edge that is used by some player is shared among the players using the edge by charging each player a fraction of the edge's cost equal to the ratio of her weight to the total weight of all players using the edge. We show that there exist instances of capacitated network design games with weighted players and uniform capacities that do not admit a Nash equilibrium even in the case that all players share the same source and sink. Moreover, we show that it is strongly N P ‐hard to decide whether a given instance admits a Nash equilibrium even if a feasible solution for the underlying network design problem is guaranteed to exist. In contrast, we prove that, for series‐parallel graphs, there always exists a Nash equilibrium whose total cost equals the cost of an optimal solution of the corresponding network design problem and provide an (exponential‐time) algorithm to compute this equilibrium. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 68(2), 141–158 2016 We consider network design games with weighted players and uniform edge capacities and study their Nash equilibria. In these games, each player has to choose a path from her source to her sink through a network subject to the constraint that the total weight of all players using an edge within their chosen path does not exceed the capacity of the edge. The fixed cost of each edge that is used by some player is shared among the players using the edge by charging each player a fraction of the edge's cost equal to the ratio of her weight to the total weight of all players using the edge. We show that there exist instances of capacitated network design games with weighted players and uniform capacities that do not admit a Nash equilibrium even in the case that all players share the same source and sink. Moreover, we show that it is strongly N P -hard to decide whether a given instance admits a Nash equilibrium even if a feasible solution for the underlying network design problem is guaranteed to exist. In contrast, we prove that, for series-parallel graphs, there always exists a Nash equilibrium whose total cost equals the cost of an optimal solution of the corresponding network design problem and provide an (exponential-time) algorithm to compute this equilibrium. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 68(2), 141-158 2016 We consider network design games with weighted players and uniform edge capacities and study their Nash equilibria. In these games, each player has to choose a path from her source to her sink through a network subject to the constraint that the total weight of all players using an edge within their chosen path does not exceed the capacity of the edge. The fixed cost of each edge that is used by some player is shared among the players using the edge by charging each player a fraction of the edge's cost equal to the ratio of her weight to the total weight of all players using the edge. We show that there exist instances of capacitated network design games with weighted players and uniform capacities that do not admit a Nash equilibrium even in the case that all players share the same source and sink. Moreover, we show that it is strongly [Formulaomitted] -hard to decide whether a given instance admits a Nash equilibrium even if a feasible solution for the underlying network design problem is guaranteed to exist. In contrast, we prove that, for series-parallel graphs, there always exists a Nash equilibrium whose total cost equals the cost of an optimal solution of the corresponding network design problem and provide an (exponential-time) algorithm to compute this equilibrium. NETWORKS, Vol. 68(2), 141-158 2016 |
| Author | Thielen, Clemens Chassein, André Krumke, Sven O. |
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| References_xml | – reference: R.K. Ahuja, T.L. Magnanti, and J.B. Orlin, Network flows, Prentice Hall, Upper Saddle River, New Jersey, USA, 1993. – reference: E. Anshelevich, A. Dasgupta, J. Kleinberg, É. Tardos, T. Wexler, and T. Roughgarden, The price of stability for network design with fair cost allocation, SIAM J Comput 38 (2008), 1602-1623. – reference: W.W. Bein, P. Brucker, and A. Tamir, Minimum cost flow algorithms for series-parallel networks, Discrete Appl Math 10 (1985), 117-124. – reference: S. Fortune, J. Hopcroft, and J. Wyllie, The directed subgraph homeomorphism problem, Theor Comput Sci 10 (1980), 111-121. – reference: H.L. Chen and T. Roughgarden, Network design with weighted players, Theory Comput Syst 45 (2009), 302-324. – reference: J.M.V. de Carvalho, Exact solution of bin-packing problems using column generation and branch-and-bound, Ann Oper Res 86 (1999), 629-659. – volume: 86 start-page: 629 year: 1999 end-page: 659 article-title: Exact solution of bin‐packing problems using column generation and branch‐and‐bound publication-title: Ann Oper Res – start-page: 37 year: 2014 end-page: 48 – start-page: 132 year: 2012 end-page: 143 – volume: 10 start-page: 117 year: 1985 end-page: 124 article-title: Minimum cost flow algorithms for series‐parallel networks publication-title: Discrete Appl Math – start-page: 9 year: 2006 end-page: 18 – volume: 38 start-page: 1602 year: 2008 end-page: 1623 article-title: The price of stability for network design with fair cost allocation publication-title: SIAM J Comput – volume: 45 start-page: 302 year: 2009 end-page: 324 article-title: Network design with weighted players publication-title: Theory Comput Syst – start-page: 86 year: 2003 end-page: 87 – year: 1993 – volume: 10 start-page: 111 year: 1980 end-page: 121 article-title: The directed subgraph homeomorphism problem publication-title: Theor Comput Sci – start-page: 651 year: 2013 end-page: 658 – start-page: 446 year: 2008 end-page: 453 – ident: e_1_2_8_8_1 doi: 10.1007/978-3-662-44803-8_4 – ident: e_1_2_8_3_1 doi: 10.1137/070680096 – ident: e_1_2_8_5_1 doi: 10.1109/IPDPS.2006.1639283 – ident: e_1_2_8_7_1 doi: 10.1023/A:1018952112615 – ident: e_1_2_8_12_1 – ident: e_1_2_8_10_1 doi: 10.1016/0304-3975(80)90009-2 – ident: e_1_2_8_11_1 – ident: e_1_2_8_9_1 doi: 10.1007/978-3-642-33996-7_12 – ident: e_1_2_8_13_1 doi: 10.1007/978-3-540-92185-1_50 – ident: e_1_2_8_6_1 doi: 10.1007/s00224-008-9128-8 – volume-title: Network flows year: 1993 ident: e_1_2_8_2_1 – ident: e_1_2_8_4_1 doi: 10.1016/0166-218X(85)90006-X |
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| SubjectTerms | Charging computational complexity Feasibility Game theory Games Mathematical models Nash equilibrium network design games Networks Optimization Players price of stability series-parallel graphs |
| Title | Capacitated network design games with weighted players |
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