Bramoullé, Yann, Rachel Kranton, and Martin D'Amours
March 2014 AER
https://www.aeaweb.org/articles.php?doi=10.1257/aer.104.3.898
March 2014 AER
https://www.aeaweb.org/articles.php?doi=10.1257/aer.104.3.898
In this paper the authors investigate a way to generalize the use of network pattern in a large class of games. They find a striking result that a global characteristic of a network, the lowest eigenvalue, determines the equilibria of the game (where agents have linear best replies, like a public good game) on it. This is because the lowest eigenvalue captures the cumulative effects of agents’ actions on others. In this regard, direct substitute effect transmitted by links causes ups and downs of actions (For example, one providing more public goods makes his neighbor free ride and his neighbor’s neighbor providing more). When the lowest eigenvalue is large in magnitude, the ups and downs lead in several directions and there can be multiple equilibria. When it’s small, on the other hand, the network dampens the ups and downs to converge to a unique equilibrium.
As any n-player simultaneous-move game can be described as a network game by a matrix indicating interactions among the players, this paper provides a new way to study multiple equilibria in games and largely broadens the area of games on networks. Based on this work, not only lab experiment but also field data can be applied in order to dig more in network effects in social and economic life, like diffusion of information and micro-finance.
As any n-player simultaneous-move game can be described as a network game by a matrix indicating interactions among the players, this paper provides a new way to study multiple equilibria in games and largely broadens the area of games on networks. Based on this work, not only lab experiment but also field data can be applied in order to dig more in network effects in social and economic life, like diffusion of information and micro-finance.