Network Games Made Simple

Most network games assume that the best response of a player is a linear function of the actions of her neighbors; clearly, this is a restrictive assumption. We developed a theory called sign-equivalent transformation (SET) underlying the mathematical structure behind a system of equations defining the Nash equilibrium. By applying our theory, we reveal that many network models in the existing literature, including those with nonlinear best responses, can be transformed into games with best-response potentials after appropriate restructuring of equilibrium conditions using SET. Thus, through our theory, we produce a unified framework that provides conditions for existence and uniqueness of equilibrium for most network games with both linear and nonlinear best-response functions. We also provide novel economic insights for both the existing network models and the new ones we develop in this study.