Entanglement and quantum strategies reduce congestion costs in Pigou networks

TL;DR

This paper explores how entanglement and quantum strategies can lower congestion costs in Pigou networks, revealing advantages over classical approaches in both two-player and multi-player scenarios with implications for data transfer.

Contribution

It introduces a quantum version of Pigou's network demonstrating reduced Nash equilibrium costs using entanglement, extending classical congestion analysis to quantum strategies.

Findings

Quantum entanglement lowers Nash equilibrium costs in two-player Pigou networks.

Quantum strategies reduce congestion costs in multi-player Pigou networks.

Implications for improved data transfer efficiency in quantum networks.

Abstract

Pigou's problem has many applications in real life scenarios like traffic networks, graph theory, data transfer in internet networks, etc. The two player classical Pigou's network has an unique Nash equilibrium with the Price of Stability and Price of Anarchy agreeing with each other. The situation changes for the $k-$person classical Pigou's network with $n$ being the total number of people. If we fix the behaviour of $(n-2)$ people and assume that $k-$persons take path $P_2$ where $k<(n-2)$ and the remaining take path $P_1$, the minimum cost of Nash equilibrium becomes $k$ dependent and we find a particular $k$ for which the cost is an absolute minimum. In contrast to the two person classical Pigou's network, the quantum two qubit Pigou's network with maximal entanglement gives a lower cost for the Nash equilibrium, while in contrast to $k-$person classical Pigou's network, it's quantum version gives reduced cost for the Nash equilibrium strategy. This has major implications for information transfer in both classical as well as quantum data networks. By employing entanglement and quantum strategies, one can significantly reduce congestion costs in quantum data networks.