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. In contrast to $k$ person classical Pigou’s network, its quantum version with the quantum miracle move strategy $M$ has reduced cost for the Nash equilibrium. 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.

庇古的问题在现实生活中有许多应用，例如交通网络，图论，互联网网络中的数据传输等。两个参与者的经典庇古网络具有唯一的纳什均衡，其稳定价格和无政府状态价格彼此一致。情况因$ķ$ 人与经典庇古的网络 $ñ$是总人数。如果我们修复行为$（ñ-\mathrm{2个}）$ 人们并假设 $ķ$ 人走道路 $P_{\mathrm{2个}}$ 在哪里 $ķ<（ñ-\mathrm{2个}）$ 剩下的走的路 $P_{\mathrm{1个}}$，纳什均衡的最低成本变为 $ķ$ 依赖，我们发现一个特殊的 $ķ$成本是绝对最低的。与两人经典的庇古网络相反，具有最大纠缠度的量子二量子比特庇古网络为纳什均衡提供了较低的成本。与之相反$ķ$ 人经典的庇古网络，其量子版本与量子奇迹移动策略 $\mathrm{中号}$降低了纳什均衡的成本。这对于经典数据网络和量子数据网络中的信息传输都具有重大意义。通过采用纠缠和量子策略，可以显着降低量子数据网络中的拥塞成本。