Team Decision Problems with Classical and Quantum Signals
Adam Brandenburger, Pierfrancesco La Mura
TL;DR
The paper investigates how teams can coordinate when direct communication is unavailable by leveraging signals in a shared environment, comparing classical and quantum resources across three decision-tree classes: Kuhn perfect recall, Kuhn imperfect recall, and Isbell trees. It introduces signal-structure concepts and two key constraints—indistinguishability and classicality—and shows that classical signals cannot improve Kuhn trees under independence, while quantum resources can improve certain imperfect-recall cases; Isbell trees admit progressive improvements from classical i.i.d. to exchangeable and to quantum signals. The authors provide constructive quantum examples and discuss no-signaling constraints, culminating in a high-frequency trading application where quantum coordination yields a higher payoff than all classical schemes. These results highlight that the physical nature of information—classical versus quantum—and memory constraints fundamentally affect coordinated decision making with practical implications for fast, information-constrained environments.
Abstract
We study team decision problems where communication is not possible, but coordination among team members can be realized via signals in a shared environment. We consider a variety of decision problems that differ in what team members know about one another's actions and knowledge. For each type of decision problem, we investigate how different assumptions on the available signals affect team performance. Specifically, we consider the cases of perfectly correlated, i.i.d., and exchangeable classical signals, as well as the case of quantum signals. We find that, whereas in perfect-recall trees (Kuhn [1950], [1953]) no type of signal improves performance, in imperfect-recall trees quantum signals may bring an improvement. Isbell [1957] proved that in non-Kuhn trees, classical i.i.d. signals may improve performance. We show that further improvement may be possible by use of classical exchangeable or quantum signals. We include an example of the effect of quantum signals in the context of high-frequency trading.