Randomly-Furcating Stochastic Differential Games

This paper presents a class of games — designated as Randomly Furcating Stochastic Differential Game — in which random shocks in the stock dynamics and (future) stochastic changes in payoffs are present. Since future payoff are not known with certainty, the term “randomly furcating” is introduced to emphasize that a particularly useful way to analyze such a situation is to assume that payoffs change at any future time instant according to (known) probability distributions defined in terms of multiple-branching stochastic processes. New and significant mathematical results are obtained, under which it becomes possible to characterize the conditions under which previously unsolvable games can be solved. Two illustrations are provided.