Chakrabarti, Subhadip; Tangsangasaksri, Supanit Network topology, higher orders of stability and efficiency. (English) Zbl 1304.91042 Int. Game Theory Rev. 16, No. 4, Article ID 1450010, 21 p. (2014). Summary: Stable networks of order \(r\) where \(r\) is a natural number refer to those networks that are immune to coalitional deviation of size \(r\) or less. In this paper, we introduce stability of a finite order and examine its relation with efficient networks under anonymous and component additive value functions and the component-wise egalitarian allocation rule. In particular, we examine shapes of networks or network architectures that would resolve the conflict between stability and efficiency in the sense that if stable networks assume those shapes they would be efficient and if efficient networks assume those shapes, they would be stable with minimal further restrictions on value functions. MSC: 91A43 Games involving graphs 91A12 Cooperative games 90B18 Communication networks in operations research Keywords:stability of order \(r\); efficiency; network architecture PDFBibTeX XMLCite \textit{S. Chakrabarti} and \textit{S. Tangsangasaksri}, Int. Game Theory Rev. 16, No. 4, Article ID 1450010, 21 p. (2014; Zbl 1304.91042) Full Text: DOI References: [1] DOI: 10.1111/j.1468-2354.2004.00130.x · doi:10.1111/j.1468-2354.2004.00130.x [2] DOI: 10.1007/s10058-007-0026-3 · Zbl 1274.91358 · doi:10.1007/s10058-007-0026-3 [3] DOI: 10.1016/j.mathsocsci.2006.08.001 · Zbl 1151.91745 · doi:10.1016/j.mathsocsci.2006.08.001 [4] DOI: 10.1007/s00182-006-0023-8 · Zbl 1109.91016 · doi:10.1007/s00182-006-0023-8 [5] Harary F., Graph Theory (1969) [6] DOI: 10.1006/jeth.1996.0108 · Zbl 0871.90144 · doi:10.1006/jeth.1996.0108 [7] DOI: 10.1016/j.geb.2004.08.004 · Zbl 1099.91011 · doi:10.1016/j.geb.2004.08.004 [8] DOI: 10.1287/moor.2.3.225 · Zbl 0402.90106 · doi:10.1287/moor.2.3.225 [9] DOI: 10.1137/0607025 · Zbl 0651.90109 · doi:10.1137/0607025 [10] DOI: 10.1007/978-1-4615-1569-2 · doi:10.1007/978-1-4615-1569-2 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.