Quantum routing games

TL;DR

This paper explores how quantum strategies in distributed routing games can resolve Braess' paradox by reducing equilibrium costs to optimal levels, demonstrating the potential of quantum resources in network optimization.

Contribution

It introduces a quantum extension to non-atomic routing games, showing that quantum strategies can eliminate Braess' paradox and achieve optimal network flow.

Findings

Quantum strategies lower equilibrium costs to optimal levels.

Quantum resources resolve Braess' paradox in routing networks.

Classical equilibrium has higher costs than quantum-enhanced equilibrium.

Abstract

We discuss the connection between a class of distributed quantum games, with remotely located players, to the counter intuitive Braess' paradox of traffic flow that is an important design consideration in generic networks where the addition of a zero cost edge decreases the efficiency of the network. A quantization scheme applicable to non-atomic routing games is applied to the canonical example of the network used in Braess' Paradox. The quantum players are modeled by simulating repeated game play. The players are allowed to sample their local payoff function and update their strategies based on a selfish routing condition in order to minimize their own cost, leading to the Wardrop equilibrium flow. The equilibrium flow in the classical network has a higher cost than the optimal flow. If the players have access to quantum resources, we find that the cost at equilibrium can be reduced to the optimal cost, resolving the paradox.