Abstract
In this paper, we consider undirected network design games with fair cost allocation. We introduce two concepts Potential-Optimal Price of Anarchy (POPoA) and Potential-Optimal Price of Stability (POPoS), where POPoA is the ratio between the worst cost of Nash equilibria with optimal potential and the minimum social cost, and POPoS is the ratio between the best cost of Nash equilibria with optimal potential and the minimum social cost, and show that
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The POPoA and POPoS for undirected broadcast games with n players are \(\mathrm{O}(\sqrt{\log n})\).
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The POPoA and POPoS for undirected broadcast games with |V| vertices are O(log|V|).
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There exists an undirected broadcast game with n players such that POPoA, \(\mathrm{POPoS} = \Omega(\sqrt{\log\log n})\).
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There exists an undirected broadcast game with |V| vertices such that POPoA,POPoS = Ω(log|V|).
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References
Albers, S.: On the value of coordination in network design. SIAM Journal on Computing 38, 2273–2302 (2009)
Anshelevich, E., Dasgupta, A., Kleinberg, J.M., Tardos, É., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. SIAM Journal on Computing 38(4), 1602–1623 (2008)
Anshelevich, E., Dasgupta, A., Tardos, É., Wexler, T.: Near-optimal network design with selfish agents. Theory of Computing 4(1), 77–109 (2008)
Asadpour, A., Saberi, A.: On the Inefficiency Ratio of Stable Equilibria in Congestion Games. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 545–552. Springer, Heidelberg (2009)
Bilò, V., Caragiannis, I., Fanelli, A., Monaco, G.: Improved Lower Bounds on the Price of Stability of Undirected Network Design Games. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds.) SAGT 2010. LNCS, vol. 6386, pp. 90–101. Springer, Heidelberg (2010)
Blume, L.E.: The statistical mechanics of strategic interaction. Games and Economic Behavior 5, 387–424 (1993)
Chekuri, C., Chuzhoy, J., Lewin-Eytan, L., Naor, J., Orda, A.: Non-cooperative multicast and facility location games. IEEE Journal on Selected Areas in Communications 25(6), 1193–1206 (2007)
Chen, H.L., Roughgarden, T.: Network design with weighted players. In: Proceedings of the 18th Annual ACM Symposium on Parallelism in Algorithms and Architectures, pp. 29–38 (2006)
Chen, H.-L., Roughgarden, T., Valiant, G.: Designing network protocols for good equilibria. SIAM Journal on Computing 39(5), 1799–1832 (2010)
Fabrikant, A., Papadimitriou, C.H., Talwar, K.: The complexity of pure Nash equilibria. In: Proceedings of the 36th Annual ACM Symposium on Theory of Computing, pp. 604–612 (2004)
Fiat, A., Kaplan, H., Levy, M., Olonetsky, S., Shabo, R.: On the price of stability for designing undirected networks with fair cost allocations. In: Proceedings of the 33rd Annual International Colloquium on Automata, Languages, and Programming, pp. 608–618 (2006)
Koutsoupias, E., Papadimitriou, C.H.: Worst-case equilibria. In: Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science, pp. 404–413 (1999)
Li, J.: An \(\mathrm{O}\left(\frac{\log n}{\log \log n}\right)\) upper bound on the price of stability for undirected Shapley network design games. Information Processing Letters 109(15), 876–878 (2009)
Monderer, D., Shapley, L.S.: Potential games. Games and Economic Behavior 14, 124–143 (1996)
Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65–67 (1973)
Roughgarden, T.: Potential functions and the inefficiency of equilibria. In: Proceedings of International Congress of Mathematicians (2006)
Ui, T.: Robust equilibria of potential games. Econometrica 69(5), 1373–1380 (2001)
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Kawase, Y., Makino, K. (2012). Nash Equilibria with Minimum Potential in Undirected Broadcast Games. In: Rahman, M.S., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2012. Lecture Notes in Computer Science, vol 7157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28076-4_22
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DOI: https://doi.org/10.1007/978-3-642-28076-4_22
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