Enlarged matrix method for stochastic decision making using orbital angular momenta

Abstract

Suitable collective decision making is crucial both in real life and in the field of computer science. Previous studies have implemented two systems using photons with superposition of orbital angular momenta (OAMs) for collective decision making: one that allows only symmetric treatments of agents and another that enables asymmetric treatments. However, these systems cannot assemble all probability matrices, i.e., only limited stochastic decision making was possible. Therefore, this study introduces a way called the enlarged matrix method to diversify stochastic decision making. The enlarged matrix method successfully extends the range of possible probability matrices, indicating the benefit of utilizing photons with superposed OAMs for various stochastic decision making. Also, this study applies decision-making systems utilizing OAM to correlated equilibria, a game theory concept that preserves benefits for all players by repressing selfish decisions. Possible equilibria for each system are described numerically and theoretically.