Quantum Nonlocality and Game Theory
https://phys.org/news/2013-07-link-quantum-physics-game-theory.html
https://www.nature.com/articles/ncomms3057
This paper in Nature Communications from a few years ago established an interesting connection between Bell’s inequality in quantum mechanics and Bayesian games. Bell’s inequality establishes quantum mechanics as a nonlocal theory, which means that objects in our universe can be affected by events that are not in the immediate vicinity of that object. Although this sounds incredibly unintuitive, multiple measurements and experiments have confirmed that nature is inherently nonlocal.
In their paper, Brunner and Linden analyze Bayesian games. In our class, most games we discussed were ones in which players had complete information. Bayesian games are examples of games where players have incomplete knowledge of other players. Each game has an advisor that sends incomplete information to the players. They showed that in these games, the payoff of different strategies corresponds to Bell’s Inequality. However, if the advisor is allowed to use quantum technologies to relay information to the players, such as a pair of quantum entangled particles, the ‘quantum’ strategies adopted by the players outperformed the ‘classical’ strategies built from information from a normal advisor. That is to say, quantum strategies outperformed classical strategies in Bayesian games, as predicted by Bell’s Inequality. Quantum nonlocality allows for this type of ‘quantum supremacy’.
This work bridges two different fields but also has important implications in quantum information processing. Auctions, which we covered extensively in class, can be modelled as Bayesian games. Therefore, this work shows important applications of quantum technologies in game theory and auction performance. With new quantum computers being built every year with higher and higher qubit coherence, it is only a matter of time before quantum technologies can be implemented in game-theoretic problems. Understanding quantum strategies in Bayesian games is an important step in this process.