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:

  1. Does this game have any Nash Equilibrium (NE)? If so under which conditions?
  2. 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!


1 Answer 1


I think the answer is yes, there is a Nash equilibrium, and it can be attained just by letting each person in turn change his selection to the best possible alternative.

For more information, read this paper:

Weighted congestion games with separable preferences

by: Igal Milchtaich



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.