Weitere Kapitel dieses Buchs durch Wischen aufrufen
One of the main criticisms to game theory concerns the assumption of full rationality. Logit dynamics is a decentralized algorithm in which a level of irrationality (a.k.a. “noise”) is introduced in players’ behavior. In this context, the solution concept of interest becomes the logit equilibrium, as opposed to Nash equilibria. Logit equilibria are distributions over strategy profiles that possess several nice properties, including existence and uniqueness. However, there are games in which their computation may take exponential time. We therefore look at an approximate version of logit equilibria, called metastable distributions, introduced by Auletta et al. . These are distributions which remain stable (i.e., players do not go too far from it) for a large number of steps (rather than forever, as for logit equilibria). The hope is that these distributions exist and can be reached quickly by logit dynamics.
We identify a class of potential games, that we name asymptotically well-behaved, for which the behavior of the logit dynamics is not chaotic as the number of players increases, so to guarantee meaningful asymptotic results. We prove that any such game admits distributions which are metastable no matter the level of noise present in the system, and the starting profile of the dynamics. These distributions can be quickly reached if the rationality level is not too big when compared to the inverse of the maximum difference in potential. Our proofs build on results which may be of independent interest, including some spectral characterizations of the transition matrix defined by logit dynamics for generic games and the relationship among convergence measures for Markov chains.
Bitte loggen Sie sich ein, um Zugang zu diesem Inhalt zu erhalten
Sie möchten Zugang zu diesem Inhalt erhalten? Dann informieren Sie sich jetzt über unsere Produkte:
The extent to which the number of \(+1\) must be larger than the number of \(-1\) can depend on n, but it can be bounded by a single function F on the number of players.
Auletta, V., Ferraioli, D., Pasquale, F., Penna, P., Persiano, G.: Convergence to equilibrium of logit dynamics for strategic games. In: SPAA, pp. 197–206 (2011)
Auletta, V., Ferraioli, D., Pasquale, F., Persiano, G.: Mixing time and stationary expected social welfare of logit dynamics. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds.) SAGT 2010. LNCS, vol. 6386, pp. 54–65. Springer, Heidelberg (2010) CrossRef
Auletta, V., Ferraioli, D., Pasquale, F., Persiano, G.: Metastability of logit dynamics for coordination games. In: SODA, pp. 1006–1024 (2012)
Fabrikant, A., Papadimitriou, C.H., Talwar, K.: The complexity of pure nash equilibria. In: STOC, pp. 604–612 (2004)
Ferraioli, D., Goldberg, P.W., Ventre, C.: Decentralized dynamics for finite opinion games. In: Serna, M. (ed.) SAGT 2012. LNCS, vol. 7615, pp. 144–155. Springer, Heidelberg (2012) CrossRef
Ferraioli, D., Ventre, C.: Metastability of potential games. CoRR, abs/1211.2696 (2012)
Levin, D., Yuval, P., Wilmer, E.L.: Markov Chains and Mixing Times. American Mathematical Society, Providence (2008) CrossRef
Lipton, R.J., Markakis, E., Mehta, A.: Playing large games using simple strategies. In: ACM EC, pp. 36–41 (2003)
Montanari, A., Saberi, A.: Convergence to equilibrium in local interaction games. In: FOCS (2009)
Young, H.P.: The economy as a complex evolving system. In: The Diffusion of Innovations in Social Networks, vol. III (2003)
Schiller, R.J.: Irrational Exuberance. Wiley, New York (2000)
- Metastability of Asymptotically Well-Behaved Potential Games
- Springer Berlin Heidelberg
Neuer Inhalt/© ITandMEDIA