Abstract
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 C contains only affine functions. We also give a similar characterization for weighted 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.
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Harks, T., Klimm, M., Möhring, R.H. (2009). Characterizing the Existence of Potential Functions in Weighted Congestion Games. In: Mavronicolas, M., Papadopoulou, V.G. (eds) Algorithmic Game Theory. SAGT 2009. Lecture Notes in Computer Science, vol 5814. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04645-2_10
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DOI: https://doi.org/10.1007/978-3-642-04645-2_10
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