We show that every finite N-player normal form game possesses a correlated equilibrium with a precise lower bound on the number of outcomes to which it assigns zero probability. In particular, the largest games with a unique fully supported correlated equilibrium are two-player games; moreover,...

We introduce a class of partial correlation network models with a community structure for large panels of time series. In the model, the series are partitioned into latent groups such that correlation is higher within groups than between them. We then propose an algorithm that allows one to...

We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if the sequence is a realization of a stationary and ergodic random process then the average...

We continue the development of a method for the selection of a bandwidth or a number of design parameters in density estimation. We provide explicit non-asymptotic density-free inequalities that relate the $L_1$ error of the selected estimate with that of the best possible estimate, and study in...

We derive a new inequality for uniform deviations of averages from their means. The inequality is a common generalization of previous results of Vapnik and Chervonenkis (1974) and Pollard (1986). Usingthe new inequality we obtain tight bounds for empirical loss minimization learning

We construct an uncoupled randomized strategy of repeated play such that, if every player follows such a strategy, then the joint mixed strategy profiles converge, almost surely, to a Nash equilibrium of the one-shot game. The procedure requires very little in terms of players' information about...