Quantum entanglement helps to beat multiplayer games

In game theory, multiplayer games involve three or more individuals. In these games, individuals adapt strategies based on self-interest that often result in less than optimal results for everybody overall, as in the tragedy of commons. Minority games are an intriguing subset of these games, where the individual agents must all compete for a finite resource.

A recent paper published in Chaos explores a toy model for a minority game with four users connected to the same communication network, competing for spectral resources in two different scenarios. In both cases, each individual aims to be the only one of the four players to connect to the network, and is allowed to evolve strategy over time before reaching an equilibrium in its success rate.

In the classical approach, the equilibrium for an individual’s success rate is 1/8, expected as the chance for the other three individuals to choose not to transmit is 1/2 to the third power, equaling 1/8. On the contrary, if each individual’s decision-making process is connected to a quantum entangled state, then overall efficiency can increase to 1/4 — the optimal equilibrium for a four-player system.

The quantum approach would first briefly stabilize at 1/8 before evolving further to 1/4, but only if the players are willing to expend more energy to increase the success rate. This revelation gives future researchers something to consider when designing systems where resource-sharing is relevant, such as in communication networks.

Source: “Evolutionary quantum minority game: A wireless network application,” by O. G. Zabaleta and C. M. Arizmendi, Chaos: An Interdisciplinary Journal of Nonlinear Science (2018). The article can be accessed at https://doi.org/10.1063/1.5027739 .