(from <a href="http://arxiv.org/pdf/1210.1173v1.pdf" rel="nofollow">http://arxiv.org/pdf/1210.1173v1.pdf</a>)<p><i>However, in certain cases
the players may adapt their strategy depending on a
piece of advice. The latter is delivered to all players
by an advisor. This opens the possibility for the
players to adopt correlated strategies, which can
outperform independent strategies. There are various
forms that advice can take. For example in the case of
correlated classical advice, the advice is represented
by a classical variable, l, with prior r(l). Each player
can then choose a strategy depending on his type and
on l.</i><p>...<p><i>For Bayesian games, the possibility of having access to nonlocal correlations, for instance using entanglement, has important implications. First let us
imagine that the players can share quantum advice,
that is, the advisor is able to produce entangled particles and to send them to the players, who then perform local measurements on their particles. Since the
statistics of such measurements can in general not be
reproduced by any classical local model, the players
now have access to strategies which would be impossible in the case of a classical advisor. Thus, players
sharing quantum advice can outperform any classical
players.</i><p>So, if some players have information that other players don't, they can outperform the others? Astonishing :-|