Guiding Agents of Quantum Games to Equilibrium using Matrix Exponential Fixed-Point Iteration
MEFPIA searches quantum-game equilibria faster, with lower error than matrix multiplicative-weights updates on tested instances.
The paper studies equilibrium search in extended Gutoski-Watrous quantum games where each player's strategy is a local density matrix. Tensor-contraction expressions for payoffs and gradients avoid constructing the full joint density matrix. The proposed Matrix Exponential Fixed-Point Iteration with Annealing (MEFPIA) is compared with Matrix Multiplicative Weights Update. On the tested instances both methods approach similar strategy profiles and payoffs, while MEFPIA reaches lower relative error in fewer iterations.
- Player strategies are local density matrices in extended Gutoski-Watrous games
- Tensor contractions avoid building the full joint density matrix
- MEFPIA reports lower relative error in fewer iterations than MMWU
From the original article
1 min read at arxiv.orgIn recent years, quantum game theory has gained significant attention as a framework for studying decision-making in multi-agent systems using quantum principles. However, computing equilibrium strategies is challenging because the dimension of the joint Hilbert space grows as the product of the players' local dimensions.
By Alireza Habibi · arxiv.org
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