Strategic Interaction and Networks
AbstractThis paper brings a general network analysis to a wide class of economic games. A network, or interaction matrix, tells who directly interacts with whom. A major challenge is determining how network structure shapes overall outcomes. We have a striking result. Equilibrium conditions depend on a single number: the lowest eigenvalue of a network matrix. Combining tools from potential games, optimization, and spectral graph theory, we study games with linear best replies and characterize the Nash and stable equilibria for any graph and for any impact of players’ actions. When the graph is sufficiently absorptive (as measured by this eigenvalue), there is a unique equilibrium. When it is less absorptive, stable equilibria always involve extreme play where some agents take no actions at all. This paper is the first to show the importance of this measure to social and economic outcomes, and we relate it to different network link patterns.
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Bibliographic InfoPaper provided by CIRPEE in its series Cahiers de recherche with number 1018.
Date of creation: 2010
Date of revision:
Networks; potential games; lowest eigenvalue; stable equilibria; asymmetric equilibria;
Find related papers by JEL classification:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D00 - Microeconomics - - General - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-05-29 (All new papers)
- NEP-GTH-2010-05-29 (Game Theory)
- NEP-NET-2010-05-29 (Network Economics)
- NEP-URE-2010-05-29 (Urban & Real Estate Economics)
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