  Collective decision making is important for maximizing total benefits while
preserving equality among individuals in the competitive multi-armed bandit
(CMAB) problem, wherein multiple players try to gain higher rewards from
multiple slot machines. The CMAB problem represents an essential aspect of
applications such as resource management in social infrastructure. In a
previous study, we theoretically and experimentally demonstrated that entangled
photons can physically resolve the difficulty of the CMAB problem. This
decision-making strategy completely avoids decision conflicts while ensuring
equality. However, decision conflicts can sometimes be beneficial if they yield
greater rewards than non-conflicting decisions, indicating that greedy actions
may provide positive effects depending on the given environment. In this study,
we demonstrate a mixed strategy of entangled- and correlated-photon-based
decision-making so that total rewards can be enhanced when compared to the
entangled-photon-only decision strategy. We show that an optimal mixture of
entangled- and correlated-photon-based strategies exists depending on the
dynamics of the reward environment as well as the difficulty of the given
problem. This study paves the way for utilizing both quantum and classical
aspects of photons in a mixed manner for decision making and provides yet
another example of the supremacy of mixed strategies known in game theory,
especially in evolutionary game theory.
