Quantum Strategic Game Theory
Shengyu Zhang

TL;DR
This paper extends classical game theory to the quantum setting, exploring how quantum strategies can significantly increase players' payoffs and introducing correlation complexity as a new measure of quantum advantage.
Contribution
It introduces a quantum extension of Nash and correlated equilibria, analyzes payoff improvements, and proposes correlation complexity as a novel measure with implications in physics and computational complexity.
Findings
Quantum strategies can dramatically increase payoffs in certain games.
Some correlated equilibria can be generated with minimal quantum resources but require more classical communication.
Correlation complexity relates to Bell's inequality and has implications in physics and complexity theory.
Abstract
We propose a simple yet rich model to extend the notions of Nash equilibria and correlated equilibria of strategic games to the quantum setting, in which we then study the relations between classical and quantum equilibria. Unlike the previous work that focus on qualitative questions on specific games of small sizes, we address the following fundamental and quantitative question for general games: How much "advantage" can playing quantum strategies provide, if any? Two measures of the advantage are studied, summarized as follows. 1. A natural measure is the increase of payoff. We consider natural mappings between classical and quantum states, and study how well those mappings preserve the equilibrium properties. Among other results, we exhibit correlated equilibrium whose quantum superposition counterpart is far from being a quantum correlated…
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Taxonomy
TopicsQuantum Mechanics and Applications · Quantum Computing Algorithms and Architecture · Game Theory and Applications
