Working Paper: CEPR ID: DP17542
Authors: Yves Zenou; Junjie Zhou
Abstract: 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.
Keywords: network games; nonlinear best responses; sign equivalent transformation; variational inequalities; best-response potential
JEL Codes: C62; C72; D85; H41; Z13
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| best-response functions in network games can be transformed into sign equivalent forms (C73) | simpler analysis of equilibrium conditions (C62) |
| sign equivalent transformation set (C32) | derive best-response potential that maximizes the underlying utility function (C73) |
| best-response potential (C73) | establish a direct link between the structure of the network and equilibrium outcomes (D85) |
| conditions related to the convexity of cost functions and properties of network structure (D85) | guarantee uniqueness of Nash equilibria (C72) |
| players' actions influence one another through their connections in the network (D85) | dynamics of network games (C73) |