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A 2×2 game is played repeatedly by two satisficing players. The game considered includes the Prisoner's Dilemma, as well as games of coordination and common interest. Each player has anaspirationat each date, and takes an action. The action is switched at the subsequent period only if the achieved payoff falls below aspirations; the switching probability depends on the shortfall. Aspirations are periodically updated according to payoff experience, but are occasionally subject to trembles. For sufficiently slow updating of aspirations and small tremble probability, it is shown that both players must ultimately cooperate most of the time.Journal of Economic LiteratureClassification Numbers C72, D83. © 1998 Academic Press.

Interacting Hilbert space valued stochastic differential equations are studied as an extension of Funaki's model for random strings to a system of interacting strings. The martingale problem for the corresponding McKean-Vlasov equation is solved. Special results when H = L squared (G), G, a bounded domain in real numbers are obtained. Keywords: Mathematical equations/models, Differential equations.

This document considers several examples including that of a nonhomogeneous Poisson process with periodic rate function where the limiting distribution of the interevent times are obtained.

Sequential Feynman integrals are defined for classes of functions on a Hilbert space and on an abstract Weiner space. A Cameron-Martin formula is proved for analytic and sequential Feynman integrals for two classes.

A finitely additive white noise approach to nonlinear filtering is developed. It is shown that a pathwise solution of the problem is possible where the observed paths belong to the reproducing kernel Hilbert space of the Wiener process. Connections with robust filtering and recent developments are explored. (Author)

The paper presents some recently obtained results on the nonlinear filtering problem for infinite dimensional processes. The optimal filter is obtained as the unique solution of certain measure valued equations. Robustness properties - both pathwise and statistical - are given and a preliminary result shows consistency with the stochastic calculus theory. Applications to random fields and models of voltage potential in neurophysiology are briefly discussed. Keywords: Markov processes; white noise.

The finitely additive nonlinear filtering problem for the model y sub t = h sub t (X sub t) + e sub t is solved when the function h is unbounded and satisfies no growth conditions whatever. (Author)