  This paper investigates the powers and limitations of quantum entanglement in
the context of cooperative games of incomplete information. We give several
examples of such nonlocal games where strategies that make use of entanglement
outperform all possible classical strategies. One implication of these examples
is that entanglement can profoundly affect the soundness property of two-prover
interactive proof systems. We then establish limits on the probability with
which strategies making use of entanglement can win restricted types of
nonlocal games. These upper bounds may be regarded as generalizations of
Tsirelson-type inequalities, which place bounds on the extent to which quantum
information can allow for the violation of Bell inequalities. We also
investigate the amount of entanglement required by optimal and nearly optimal
quantum strategies for some games.
