{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T19:35:16Z","timestamp":1760297716839},"reference-count":22,"publisher":"Association for Computing Machinery (ACM)","issue":"3","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGOPS Oper. Syst. Rev."],"published-print":{"date-parts":[[2006,7]]},"abstract":"<jats:p>\n            We consider a stylized model of content contribution in a peer-to-peer network. The model is appealing because it allows for linear-quadratic payoff functions and for very general interaction patterns among agents. Furthermore, when the model has a unique Nash equilibrium (NE) we find that it is defined by a network centrality measure (Bonacich 1987), with\n            <jats:italic>L1<\/jats:italic>\n            and\n            <jats:italic>L2<\/jats:italic>\n            norms of the Bonacich index vector providing aggregate contribution and social welfare. Furthermore, we find that NE are always (even when they are non-unique) computable by solving a linear complementarity problem. We study the network designer's problem of engineering the most efficient equilibrium outcome, proving that maximizing aggregate contribution can be reconciled with maximizing aggregate welfare. We also provide a partial characterization of optimal NE graphs and suggest different approaches for how a network designer can promote more efficient graph structures.\n          <\/jats:p>","DOI":"10.1145\/1151374.1151388","type":"journal-article","created":{"date-parts":[[2006,10,18]],"date-time":"2006-10-18T22:35:32Z","timestamp":1161210932000},"page":"61-66","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":12,"title":["A study of Nash equilibrium in contribution games for peer-to-peer networks"],"prefix":"10.1145","volume":"40","author":[{"given":"Jacomo","family":"Corbo","sequence":"first","affiliation":[{"name":"Harvard University"}]},{"given":"Antoni","family":"Calv\u00f3-Armengol","sequence":"additional","affiliation":[{"name":"Universitat Aut\u00f2noma de Barcelona"}]},{"given":"David","family":"Parkes","sequence":"additional","affiliation":[{"name":"Harvard University"}]}],"member":"320","published-online":{"date-parts":[[2006,7]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1038\/35019019"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2004.68"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.comnet.2004.03.021"},{"key":"e_1_2_1_4_1","volume-title":"Who's Who in Crime Networks. Wanted: The Key Player,\" CEPR Discussion Paper No. 4421","author":"Ballester C.","year":"2004","unstructured":"Ballester , C. , A. Calv\u00f3-Armengol , and Y. Zenou ( 2004 ) \" Who's Who in Crime Networks. Wanted: The Key Player,\" CEPR Discussion Paper No. 4421 . Ballester, C., A. Calv\u00f3-Armengol, and Y. Zenou (2004) \"Who's Who in Crime Networks. Wanted: The Key Player,\" CEPR Discussion Paper No. 4421."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1080\/15427951.2004.10129080"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1086\/228631"},{"key":"e_1_2_1_7_1","volume-title":"K. Carley and P. Pattison, Committee on Human Factors","author":"Borgatti S. P.","year":"2003","unstructured":"Borgatti , S. P. ( 2003 ): \" The Key Player Problem,\" in Dynamic Social Network Modeling and Analysis: Workshop Summary and Papers, ed. by R. Breiger , K. Carley and P. Pattison, Committee on Human Factors , National Research Council , 241--252. Borgatti, S. P. (2003): \"The Key Player Problem,\" in Dynamic Social Network Modeling and Analysis: Workshop Summary and Papers, ed. by R. Breiger, K. Carley and P. Pattison, Committee on Human Factors, National Research Council, 241--252."},{"key":"e_1_2_1_8_1","volume-title":"The Role of Bilateral Consent in Strategic Network Formation,\" Harvard Working Paper Series","author":"Corbo J.","year":"2005","unstructured":"Corbo , J. , D. Parkes ( 2005 ): \" The Role of Bilateral Consent in Strategic Network Formation,\" Harvard Working Paper Series . Corbo, J., D. Parkes (2005): \"The Role of Bilateral Consent in Strategic Network Formation,\" Harvard Working Paper Series."},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1080\/03081089008818026"},{"key":"e_1_2_1_10_1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139086547","volume-title":"Eigenspaces of Graphs","author":"Cvetkovi\u0107 D.","year":"1997","unstructured":"Cvetkovi\u0107 , D. , P. Rowlinson , and S. Simi\u0107 ( 1997 ): Eigenspaces of Graphs . Cambridge : Cambridge University Press . Cvetkovi\u0107, D., P. Rowlinson, and S. Simi\u0107 (1997): Eigenspaces of Graphs. Cambridge: Cambridge University Press."},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.2307\/1907925"},{"key":"e_1_2_1_12_1","volume-title":"Neighborhood Effects,\" in Handbook of Regional and Urban Economics","author":"Durlauf S. E.","year":"2004","unstructured":"Durlauf , S. E. ( 2004 ): \" Neighborhood Effects,\" in Handbook of Regional and Urban Economics Vol. 4 , ed. by J. V. Henderson and J-F. Thisse . Amsterdam : Elsevier Science , 2173--2242. Durlauf, S. E. (2004): \"Neighborhood Effects,\" in Handbook of Regional and Urban Economics Vol. 4, ed. by J. V. Henderson and J-F. Thisse. Amsterdam: Elsevier Science, 2173--2242."},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0899-8256(02)00562-6"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.89.248701"},{"key":"e_1_2_1_15_1","volume-title":"A Survey of Models of Network Formation: Stability and Efficiency,\" in Group Formation in Economics: Networks, Clubs and Coalitions, ed. by G. Demange and M. Wooders","author":"Jackson M. O.","year":"2005","unstructured":"Jackson , M. O. ( 2005 ): \" A Survey of Models of Network Formation: Stability and Efficiency,\" in Group Formation in Economics: Networks, Clubs and Coalitions, ed. by G. Demange and M. Wooders . Cambridge : University Press. Jackson, M. O. (2005): \"A Survey of Models of Network Formation: Stability and Efficiency,\" in Group Formation in Economics: Networks, Clubs and Coalitions, ed. by G. Demange and M. Wooders. Cambridge: University Press."},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02289026"},{"key":"e_1_2_1_17_1","volume-title":"Graphical Models for Game Theory,\" UAI","author":"Kearns M.","year":"2001","unstructured":"Kearns M. , M. Littman , and S. Singh ( 2001 ): \" Graphical Models for Game Theory,\" UAI . Kearns M., M. Littman, and S. Singh (2001): \"Graphical Models for Game Theory,\" UAI."},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548302005424"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.51.R1"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2003.12.002"},{"key":"e_1_2_1_21_1","volume-title":"Generalized Simulated Annealing,\" in Annual Review of Computational Physics II","author":"Tsallis C.","year":"1995","unstructured":"Tsallis C. , D. A. Stariolo ( 1995 ): \" Generalized Simulated Annealing,\" in Annual Review of Computational Physics II . Tsallis C., D. A. Stariolo (1995): \"Generalized Simulated Annealing,\" in Annual Review of Computational Physics II."},{"key":"e_1_2_1_22_1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511815478","volume-title":"Social Network Analysis. Methods and Applications","author":"Wasserman S.","year":"1994","unstructured":"Wasserman , S. , And K. Faust ( 1994 ): Social Network Analysis. Methods and Applications . Cambridge : Cambridge University Press . Wasserman, S., And K. Faust (1994): Social Network Analysis. Methods and Applications. Cambridge: Cambridge University Press."}],"container-title":["ACM SIGOPS Operating Systems Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1151374.1151388","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T21:03:08Z","timestamp":1672261388000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1151374.1151388"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,7]]},"references-count":22,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2006,7]]}},"alternative-id":["10.1145\/1151374.1151388"],"URL":"https:\/\/doi.org\/10.1145\/1151374.1151388","relation":{},"ISSN":["0163-5980"],"issn-type":[{"value":"0163-5980","type":"print"}],"subject":[],"published":{"date-parts":[[2006,7]]},"assertion":[{"value":"2006-07-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}