Mapping Game Theory to Quantum Systems: Nash Equilibria via Neutral Atom Computing

TL;DR

This paper proposes a quantum computing approach using Rydberg atom arrays to find Nash equilibria by mapping game theory problems onto physical ground states, potentially solving complex NP-Hard problems.

Contribution

It introduces a novel mapping of Nash equilibria to quantum ground states via maximum independent sets on unit-disk graphs, leveraging neutral atom computing.

Findings

Simulations demonstrate the effectiveness of the quantum approach.

The method offers a new avenue for solving NP-Hard game theory problems.

Potential for applying quantum systems to complex optimization tasks.

Abstract

Nash equilibria are crucial for understanding game behavior and systems in economics, physics, biology, and computer science. A significant application arises from the connection between Nash equilibria and optimization problems . However, finding Nash equilibria is challenging due to its NP-Hard complexity, specifically within the PPAD class. By exploiting the correspondence between Maximum Independent Sets (MIS) and Nash equilibria on unit-disk graphs, we map these problems onto the ground state configurations of Rydberg atom arrays. Simulations show the effectiveness of this quantum method, highlighting its potential for solving complex problems in game theory.