We provide a new interpretation of mixed strategy equilibria that incorporates both von Neumann and Morgenstern’s classical concealment role of mixing as well as the more recent Bayesian view originating with Harsanyi. For any two-person game, G, we consider an incomplete information game, IG; in which each player’s type is the probability he assigns to the event that his mixed strategy in G is...

In this paper, we present some general results determining minimax bounds on statistical risk for density estimation based on certain information-theoretic considerations. These bounds depend only on metric entropy conditions and are used to identify the minimax rates of convergence.

In this letter, we present the general form of equations that generate a volume-preserving flow on a symplectic manifold (M, ω). It is shown that every volume-preserving flow has some 2-forms acting the rôle of the Hamiltonian functions in the Hamiltonian mechanics and the ordinary Hamilton equations are included as a special case with a 2-form 1 n−1 H ω where H is the corresponding Hamiltonian...