Spin Glass Mapping of the Parallel Minority Game (opens in new tab)

The parallel minority game (PMG) extends the classical minority game to many choices, with each agent restricted to two predetermined alternatives. In this condition, minimizing the population variance across all choices is a complex combinatorial optimization problem. We show that this minimization is exactly equivalent to finding the ground state of an Ising spin glass in the mean-field limit, i.e., the Sherrington-Kirkpatrick model. By enco...