Convexity and complementarity in network formation. Implications for the structure of pairwise stable networks

Hellmann T (2009) Working Papers. Institute of Mathematical Economics; 423.
Bielefeld: Universität Bielefeld.

Diskussionspapier | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
This paper studies the properties of convexity (concavity) and strategic complements (substitutes) in network formation and the implications for the structure of pairwise stable networks. First, different definitions of convexity (concavity) in own links from the literature are put into the context of diminishing marginal utility of own links. Second, it is shown that there always exists a pairwise stable network as long as the utility function of each player satisfies convexity in own links and strategic complements. For network societies with a profile of utility functions satisfying concavity in own links and strategic complements, a local uniqueness property of pairwise stable networks is derived. The results do neither require any specification on the utility function nor any other additional assumptions such as homogeneity.
Stichworte
Existence; Stability; Uniqueness; Supermodularity; Increasing differences; Networks; Game theory; Network formation
Erscheinungsjahr
2009
Band
423
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2316427

Zitieren

Hellmann T. Convexity and complementarity in network formation. Implications for the structure of pairwise stable networks. Working Papers. Institute of Mathematical Economics. Vol 423. Bielefeld: Universität Bielefeld; 2009.
Hellmann, T. (2009). Convexity and complementarity in network formation. Implications for the structure of pairwise stable networks (Working Papers. Institute of Mathematical Economics, 423). Bielefeld: Universität Bielefeld.
Hellmann, T. (2009). Convexity and complementarity in network formation. Implications for the structure of pairwise stable networks. Working Papers. Institute of Mathematical Economics, 423, Bielefeld: Universität Bielefeld.
Hellmann, T., 2009. Convexity and complementarity in network formation. Implications for the structure of pairwise stable networks, Working Papers. Institute of Mathematical Economics, no.423, Bielefeld: Universität Bielefeld.
T. Hellmann, Convexity and complementarity in network formation. Implications for the structure of pairwise stable networks, Working Papers. Institute of Mathematical Economics, vol. 423, Bielefeld: Universität Bielefeld, 2009.
Hellmann, T.: Convexity and complementarity in network formation. Implications for the structure of pairwise stable networks. Working Papers. Institute of Mathematical Economics, 423. Universität Bielefeld, Bielefeld (2009).
Hellmann, Tim. Convexity and complementarity in network formation. Implications for the structure of pairwise stable networks. Bielefeld: Universität Bielefeld, 2009. Working Papers. Institute of Mathematical Economics. 423.
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2019-09-06T08:57:54Z
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