Answer to Question #75498 in Other Economics for Elina
In the paper 'Who's who in the network, wanted key player (2006)' the author Calvo Armengol et al. shows how the position in the network changes best response outcome. I want to know What is the intuition behind using largest eigenvalues? I mean why use eigenvalue value at all why is it special and why the largest eigenvalue? Secondly, where have the made use of global substitutability in proving the existence of Nash equilibrium and uniqueness? Also, how does incorporating global substitutability help in explaining best responses?
Eigenvalues and eigenvectors feature prominently in the analysis of linear transformations. Substitutability means that products or technologies are competitive, so that a consumer will buy either one product or the other. Economically, this means that we may expect a negative cross-elasticity of demand. Source: https://www.igi-global.com/dictionary/substitutability/28673