Network Games Made Simple

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Abstract
Most network games assume that the best-response of a player is a linear function of the actions of her neighbors; this is clearly a restrictive assumption. We develop a theory called sign-equivalent transformation (SET) underlying the mathematical structure behind a system defining the Nash equilibrium. As applications of our theory, we reveal that many network models in the existing literature, including those with non-linear best responses, can be transformed into games with best-reply potentials after appropriate reorganizations of equilibrium conditions using SET. Thus, our theory provides a unified framework connecting the existing diverse approaches in the literature. We also provide novel economic insights for both the existing network models and the ones we develop. Joint paper with Yves Zenou.

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