Two‐person games for uncertain random singular dynamic systems

Abstract

A complex system exhibiting uncertainty as well as randomness may be portrayed by an uncertain random singular difference equation. This paper investigates two-person nonzero-sum and zero-sum games based on uncertain random singular difference equations. First, an approach is proposed to translate the two-person nonzero-sum game into an equivalent game for a standard uncertain random dynamic system. The relevant recursive equations are developed to search the Nash equilibrium for the converted game. Solving the related recursive equations yields the solution to such a game. Following that, a Max-Min Theorem is provided for finding the saddle-point equilibrium of an uncertain random two-person zero-sum game. Finally, a numerical example is offered to demonstrate the validity of the findings.

Saddle-Point Equilibrium Strategy for Linear Quadratic Uncertain Stochastic Hybrid Differential Games Based on Subadditive Measures

“…Liu's pioneering work [17] in 2013 laid the foundation for exploring uncertain stochastic hybrid systems [18,19] based on subadditive measures, followed by subsequent research by Fei et al [20] in 2014, introducing uncertain stochastic hybrid optimal control and the equation of optimality via uncertain stochastic hybrid differential equations. With the help of uncertain stochastic optimal control, there has been a growing body of literature focusing on uncertain stochastic hybrid differential game systems [21][22][23][24]. Unlike the models and methods mentioned earlier, this work is the beginning of linear quadratic uncertain stochastic hybrid differential games in finite and infinite horizons.…”

Linear quadratic zero‐sum game for time‐delayed uncertain stochastic systems

“…Zero-sum games, originally introduced by Von Neumann 1 and later refined by Nash, 2 have attracted substantial attention within the research community. 3 This field has since matured into a thriving research area, yielding a wealth of theoretical insights 4,5 and offering diverse potential applications. 6,7 Linear quadratic zero-sum games (LQZSGs) represent a specific category of zero-sum games characterized by quadratic objective functions subject to linear system constraints.…”

“…Zero‐sum games, originally introduced by Von Neumann 1 and later refined by Nash, 2 have attracted substantial attention within the research community 3 . This field has since matured into a thriving research area, yielding a wealth of theoretical insights 4,5 and offering diverse potential applications 6,7 …”

Linear quadratic control for multiple time‐delayed uncertain random systems

“…Chance theory is a mathematical framework for modeling complicated systems that include both uncertainty and randomness. These systems can be found in a number of contexts, including game problems [24], portfolio selection [25], and reliability analysis [26]. Chance theory is a useful technique for dealing with uncertain random control problems [27][28][29][30].…”