Convexity and Complementarity in Network Formation: Implications for the Structure of Pairwise Stable Networks
AbstractThis 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.
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Bibliographic InfoPaper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 423.
Length: 30 pages
Date of creation: Nov 2009
Date of revision:
Networks; Network Formation; Game Theory; Supermodularity; Increasing Differences; Stability; Existence; Uniqueness;
Find related papers by JEL classification:
- D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-12-19 (All new papers)
- NEP-GTH-2009-12-19 (Game Theory)
- NEP-NET-2009-12-19 (Network Economics)
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