On the Existence of Pure Nash Equilibria in Weighted Congestion Games
Mathematics of Operations Research
Social context in potential games
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
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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 $\mathcal{C}$ be an arbitrary set of locally bounded functions and let $\mathcal{G}(\mathcal{C})$ be the set of weighted congestion games with cost functions in $\mathcal{C}$. We show that every weighted congestion game $G\in\mathcal{G}(\mathcal{C})$ admits an exact potential if and only if $\mathcal{C}$ contains only affine functions. We also give a similar characterization for w-potentials with the difference that here $\mathcal{C}$ 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.