Two-player nonzero-sum and zero-sum games subject to stochastic noncausal systems

This paper studies two-player nonzero-sum and zero-sum games within the context of stochastic noncausal systems (SNSs). These SNSs are transformed into subsystems consisting of forward and backward stochastic difference equations through an equivalent conversion. Subsequently, recurrence equations are introduced to convert stochastic two-player nonzero-sum games into deterministic difference equation solving problems. These recurrence equations are then utilised to derive the relevant equations needed to deduce the saddle-point equilibrium solutions for two-player zero-sum games embedded within linear and nonlinear SNSs. The resolution of these equations yields analytical expressions that encapsulate the saddle-point equilibrium solutions for such types of two-player zero-sum games. To illustrate these findings, an illustrative example is provided.