The stability of matrix multiplicative weights dynamics in quantum games - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2023

The stability of matrix multiplicative weights dynamics in quantum games

Kyriakos Lotidis
  • Function : Author
  • PersonId : 1316255
Nicholas Bambos
  • Function : Author
  • PersonId : 1122330


In this paper, we study the equilibrium convergence and stability properties of the widely used matrix multiplicative weights (MMW) dynamics for learning in general quantum games. A key difficulty in this endeavor is that the induced quantum state dynamics decompose naturally into (i) a classical, commutative component which governs the dynamics of the system's eigenvalues in a way analogous to the evolution of mixed strategies under the classical replicator dynamics; and (ii) a non-commutative component for the system's eigenvectors. This non-commutative component has no classical counterpart and, as a result, requires the introduction of novel notions of (asymptotic) stability to account for the nonlinear geometry of the game's quantum space. In this general context, we show that (i) only pure quantum equilibria can be stable and attracting under the MMW dynamics; and (ii) as a partial converse, pure quantum states that satisfy a certain "variational stability" condition are always attracting. This allows us to fully characterize the structure of quantum Nash equilibria that are stable and attracting under the MMW dynamics, a fact with significant implications for predicting the outcome of a multi-agent quantum learning process.
Fichier principal
Vignette du fichier
Quantum_Games_CDC.pdf (578.62 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04307803 , version 1 (26-11-2023)



  • HAL Id : hal-04307803 , version 1


Kyriakos Lotidis, Panayotis Mertikopoulos, Nicholas Bambos. The stability of matrix multiplicative weights dynamics in quantum games. CDC 2023 - 62nd IEEE Conference on Decision and Control, Dec 2023, Singapore, Singapore. pp.1-8. ⟨hal-04307803⟩
45 View
24 Download


Gmail Mastodon Facebook X LinkedIn More