Saddle point equilibrium model for uncertain discrete systems

Sun, Yun; Yan, Hongyan; Zhu, Yuanguo

doi:10.1007/s00500-020-05206-x

Cited by 7 publications

(21 citation statements)

References 30 publications

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“…Then, a Max‐Min Theorem is derived for finding the saddle‐point equilibrium of an uncertain random zero‐sum game problem. These findings extend the results in [16] and enlarge the scope of the game with indeterminacy.…”

Section: Introductionsupporting

confidence: 89%

“…Remark Researchers [16] examined the bang‐bang game with an uncertain difference equation describing its dynamic system. We studied the bang‐bang game whose dynamic system is characterized by an uncertain random singular difference equation.…”

Section: Two‐person Zero‐sum Gamementioning

confidence: 99%

“…The above analysis motivated this work to make the following contributions: (i)In an uncertain random singular dynamic system, uncertainty and randomness coexist. It is significantly different from the proceeding works about the dynamic systems with uncertainty [16, 30] or randomness [14, 20]. Therefore, it is more suitable for complex situations where uncertainty and randomness occur simultaneously. (ii)A two‐person nonzero‐sum game for uncertain random singular dynamic systems is studied.…”

Section: Introductionmentioning

confidence: 99%

“…Probability theory focuses on frequency analysis, whereas uncertainty theory concerns with belief degree analysis (see Figure 1). Based on uncertainty theory, references [16] and [23], respectively, adopted uncertain difference equations and uncertain differential equations to characterize uncertain dynamic systems. Uncertain variables or uncertain processes are expressions of uncertainty.…”

Section: Introductionmentioning

confidence: 99%

“…There are various kinds of two-person games with indeterminacy. Two-person stochastic games (zero-sum game [13] and nonzero-sum game [14]) and two-person uncertain games (zero-sum game [16] and nonzero-sum game [17]) are different kinds of games with [22] indeterminacy. A two-person stochastic game is a game concerned with randomness, while a two-person uncertain game is a game concentrated upon uncertainty.…”

Section: Introductionmentioning

confidence: 99%

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Two‐person games for uncertain random singular dynamic systems

Chen

Zhu

Park

2022

IET Control Theory & Appl

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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.

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Section: Introductionsupporting

confidence: 89%

Section: Two‐person Zero‐sum Gamementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Two‐person games for uncertain random singular dynamic systems

Chen

Zhu

Park

2022

IET Control Theory & Appl

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

Chen,

Yuan,

Yuan

et al. 2024

Optim Control Appl Methods

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SummaryThis study focuses on the analysis of a linear quadratic zero‐sum game (LQZSG) for time‐delayed uncertain stochastic systems. To begin, we introduce a general time‐delayed zero‐sum game. Employing an algebraic transformation method, we transform the time‐delayed zero‐sum game into an equivalent uncertain random zero‐sum game without time delay. Subsequently, we present equilibrium equations that streamline the transformation of the uncertain random zero‐sum game into problems solvable as deterministic difference equations. We then investigate the LQZSG involving a linear time‐delayed uncertain stochastic system with a quadratic objective function. Within this framework, we provide a unified framework for solving this type of game and obtaining the analytic expression for the saddle‐point equilibrium of the LQZSG. Additionally, we present a numerical example and a counter‐terrorism economic game to illustrate the applicability of our findings.

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