Entangled and correlated photon mixed strategy for social decision making

TL;DR

This paper explores a mixed quantum-classical photon strategy for social decision making in multi-armed bandit problems, showing that combining entangled and correlated photons can enhance rewards depending on environmental dynamics.

Contribution

It introduces a novel mixed photon strategy that optimally combines entangled and correlated photons for improved social decision making.

Findings

Mixed photon strategies can outperform entangled-only strategies.

Optimal mixture depends on reward environment dynamics.

Demonstrates the application of quantum and classical photon aspects in decision making.

Abstract

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.