Strategic Interaction and Networks

CIRPEE Working Paper 10-18

44 Pages Posted: 21 May 2010

See all articles by Yann Bramoulle

Yann Bramoulle

Université Laval - Département d'Économique

Rachel Kranton

Duke University

Martin D'Amours

affiliation not provided to SSRN

Date Written: May 20, 2010

Abstract

This 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.

Keywords: Networks, potential games, lowest eigenvalue, stable equilibria, asymmetric equilibria

JEL Classification: C72, D00

Suggested Citation

Bramoulle, Yann and Kranton, Rachel and D'Amours, Martin, Strategic Interaction and Networks (May 20, 2010). CIRPEE Working Paper 10-18, Available at SSRN: https://ssrn.com/abstract=1612369 or http://dx.doi.org/10.2139/ssrn.1612369

Yann Bramoulle (Contact Author)

Université Laval - Département d'Économique ( email )

Ste-Foy, Quebec G1K 7P4 G1K 7P4
Canada

Rachel Kranton

Duke University

Social Sciences Building
Duke University
Durham, NC 27708-0204
United States
919-660-1896 (Phone)

HOME PAGE: http://econ.duke.edu/~rek8/

Martin D'Amours

affiliation not provided to SSRN ( email )

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
390
Abstract Views
2,106
Rank
139,143
PlumX Metrics