Team Decision Problems with Classical and Quantum Signals

TL;DR

This paper explores how classical and quantum signals can enhance team decision-making in environments without direct communication, revealing potential improvements especially with quantum signals in complex scenarios.

Contribution

It introduces the potential of quantum signals to improve team performance in decision problems with imperfect recall, extending previous classical signal results.

Findings

Quantum signals can improve performance in imperfect-recall trees.

Classical i.i.d. signals may enhance decision outcomes in non-Kuhn trees.

Quantum signals offer further advantages over classical signals in certain decision contexts.

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.