I molded my problem as the following game (it is a congestion game with varying price):$N$ players share resources $E$,$S_i$ is the strategy space of player $i$ which is in $2^E$ (where $2^E$ is the power set of resources).$P_e^i$ is the price of resource $e \in E$ considering player $i$. The price of resource $e$ is different for different users.The goal of each player is to select a strategy $S_i$ which minimize its price $\sum_{e\in S_i}P_e^i$ .My questions are:Does this game have any Nash Equilibrium (NE)? If so under which conditions? If it has any NE, what is a sample algorithm for achieving it?I searched literature but could not find any appropriate information! Any solution is appreciated!
Congestion Game with Varying Price
algorithms;optimization;game theory