  We study the problem of achieving decentralized coordination by a group of
strategic decision makers choosing to engage or not in a task in a stochastic
setting. First, we define a class of symmetric utility games that encompass a
broad class of coordination games, including the popular framework known as
\textit{global games}. With the goal of studying the extent to which agents
engaging in a stochastic coordination game indeed coordinate, we propose a new
probabilistic measure of coordination efficiency. Then, we provide an universal
information theoretic upper bound on the coordination efficiency as a function
of the amount of noise in the observation channels. Finally, we revisit a large
class of global games, and we illustrate that their Nash equilibrium policies
may be less coordination efficient then certainty equivalent policies, despite
of them providing better expected utility. This counter-intuitive result,
establishes the existence of a nontrivial trade-offs between coordination
efficiency and expected utility in coordination games.
