Characterizing the Existence of Potential Functions in Weighted Congestion Games
Since the pioneering paper of Rosenthal a lot of work has been done in order to determine classes of games that admit a potential. First, we study the existence of potential functions for weighted congestion games. Let C be the set of weighted congestion games with cost functions in G(C) contains only affine functions. We also give a similar characterization for w-potentials with the difference that here C consists either of affine functions or of certain exponential functions. We finally extend our characterizations to weighted congestion games with facility-dependent demands and elastic demands, respectively.
potential functions weighted congestion games pure nash equilibria