Computational Statistics & Data Analysis 50 (2006) 2495 – 2507 www.elsevier.com/locate/csda Signal extraction for simulated games with a large number of players Aki Lehtinen ∗ Department of social and moral philosophy, University of Helsinki, P.O. Box 9, Helsinki 00014 Finland Available online 2 August 2005 Abstract A signal extraction problem in simulated games is studied. A modelling technique is proposed for deriving beliefs for players in simulated games. Since standard Bayesian games provide conditions for beliefs on the basis of the common prior assumption, they do not allow for non-uniform beliefs unless the game has some dynamic structure that allows for learning. The framework presented allows for deriving beliefs by characterizing the reliability of the signals, and the players’ degree of confidence in these signals. This makes it particularly suitable for games with a large number of heterogenous players. © 2005 Elsevier B.V.All rights reserved. Keywords: Signal extraction; Simulated games; Beliefs; Heterogenous players 1. Introduction In standard Bayesian incomplete information models, the players’actions are independent of the realisations of random variables because they are assumed to know the probability distributions for the relevant random variables, but not the realisations of these variables (e.g. Harsanyi, 1967–1968, 1995). These models assume that the players start with common priors and update them with Bayes’ rule as the play unfolds. Bayesian models have proven to be very useful in game theory but they are not applicable in all circumstances. For ∗ Tel.: +358 9 19129270; fax: +358 9 19129273. E-mail address: aki.lehtinen@helsinki.fi. 0167-9473/$ - see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.csda.2005.07.004