Can quantum entanglement implement classical correlated equilibria?
(pp0493-0516)
Alan Deckelbaum
doi:
https://doi.org/10.26421/QIC14.5-6-7
Abstracts:
We ask whether players of a classical game can partition
a pure quantum state to implement classical correlated equilibrium
distributions. The main contribution of this work is an impossibility
result: we provide an example of a classical correlated equilibrium that
cannot be securely implemented without useful information leaking
outside the system. We study the model where players of a classical
complete information game initially share an entangled pure quantum
state. Players may perform arbitrary local operations on their
subsystems, but no direct communication (either quantum or classical) is
allowed. We explain why, for the purpose of implementing classical
correlated equilibria, it is desirable to restrict the initial state to
be pure and to restrict communication. In this framework, we define the
concept of pure quantum correlated equilibrium (PQCE) and show that in a
normal form game, any outcome distribution implementable by a PQCE can
also be implemented by a classical correlated equilibrium (CE), but that
the converse is false. We extend our analysis to extensive form games,
and compare the power of PQCE to extensive form classical correlated
equilibria (EFCE) and immediate-revelation extensive form correlated
equilibria (IR-EFCE).
Key words:
Correlated equilibria, game theory, quantum entanglement |