# Quantum Games

ThinkTank Maths’ fundamental research in quantum game theory uncovered disruptive approaches to collaboration between autonomous systems.

A very difficult challenge in current autonomous systems research is getting groups of robots, unmanned air vehicles or software agents to work together *collaboratively* without human intervention. Many such problems can be studied using the mathematics of *game theory*.

However, game theory relies on the concept of a Nash equilibrium, a set of most desirable behaviours for all players of the game. Suitable Nash equilibria may not exist. Indeed, in the well-known Prisoner’s Dilemma game, the best strategy for the players is to *avoid* collaboration. In addition, Nash equilibria can be extremely difficult to compute, making it nearly impossible to implement game theory -based collaboration in practice.

Recently, mathematicians and theoretical physicists have begun to study *quantum games*, in which the players make their moves using the kinds of quantum devices used in quantum cryptography and quantum computers. Simple known examples of such games exhibit higher levels of co-operation than their “classical” equivalents.

Given this fact, ThinkTank Maths (TTM) decided to find out what benefits near-future quantum technology could bring to autonomous system collaboration.

Through an original approach to the foundations of both quantum mechanics and game theory, TTM created a novel mathematical framework for quantum games that went far beyond the existing literature. This allowed TTM to prove that for many quantum games, easily computable equilibria always exist.

TTM’s findings also made the analysis of *large* multiplayer quantum games possible (with an arbitrary number of players and moves) — and provided new ways to tackle problems like spacecraft formation flying.

Moreover, TTM realised that quantum games as defined in the academic literature do *not*, in fact, fully exploit what is perhaps the most intriguing property of quantum systems: *entanglement*. This led to the next phase of the project, in which TTM extended this basic quantum phenomenon to complex multi-agent systems. One of the results was that agents sharing an entangled quantum resource can coordinate their actions *without communication*.