  We introduce a new class of games called the networked common goods game
(NCGG), which generalizes the well-known common goods game. We focus on a
fairly general subclass of the game where each agent's utility functions are
the same across all goods the agent is entitled to and satisfy certain natural
properties (diminishing return and smoothness). We give a comprehensive set of
technical results listed as follows.
  * We show the optimization problem faced by a single agent can be solved
efficiently in this subclass. The discrete version of the problem is however
NP-hard but admits an fully polynomial time approximation scheme (FPTAS).
  * We show uniqueness results of pure strategy Nash equilibrium of NCGG, and
that the equilibrium is fully characterized by the structure of the network and
independent of the choices and combinations of agent utility functions.
  * We show NCGG is a potential game, and give an implementation of best/better
response Nash dynamics that lead to fast convergence to an
$\epsilon$-approximate pure strategy Nash equilibrium.
  * Lastly, we show the price of anarchy of NCGG can be as large as
$\Omega(n^{1-\epsilon})$ (for any $\epsilon>0$), which means selfish behavior
in NCGG can lead to extremely inefficient social outcomes.
