  This paper deals with a standard stochastic game model with a continuum of
states under the duel-type setup. It newly proposes a hybrid model of game
theory and the fluctuation process, which could be applied for various
practical decision making situations. The unique theoretical stochastic game
model is targeted to analyze a two-person duel-type game in the time domain.
The parameters for strategic decisions including the moments of crossings,
prior crossings, and the optimal number of iterations to get the highest
winning chance are obtained by the compact closed joint functional. This paper
also demonstrates the usage of a new time based stochastic game model by
analyzing a conventional duel game model in the distance domain and briefly
explains how to build strategies for an atypical business case to show how this
theoretical model works.
