Optimal strategies for two-person normalized matrix game with variable payoffs

Bhurjee, Ajay Kumar; Panda, Geetanjali

doi:10.1007/s12351-016-0237-x

Cited by 6 publications

(4 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Classically, a stochastic programming formulation is proposed for the special case of normal-form games with independent and normally distributed random variables in the payoff (Bhurjee and Panda, 2017). For discrete distributions, the formulation results in a mixed-integer linear programming (MILP) problem.…”

Section: Previous Workmentioning

confidence: 99%

See 1 more Smart Citation

Solving zero-sum extensive-form games with arbitrary payoff uncertainty models

Leni,

Levine,

Quigley

2019

Preprint

View full text Add to dashboard Cite

Modeling strategic conflict from a game theoretical perspective involves dealing with epistemic uncertainty. Payoff uncertainty models are typically restricted to simple probability models due to computational restrictions. Recent breakthroughs Artificial Intelligence (AI) research applied to Poker have resulted in novel approximation approaches such as counterfactual regret minimization, that can successfully deal with large-scale imperfect games. By drawing from these ideas, this work addresses the problem of arbitrary continuous payoff distributions. We propose a method, Harsanyi-Counterfactual Regret Minimization, to solve two-player zero-sum extensive-form games with arbitrary payoff distribution models. Given a game Γ, using a Harsanyi transformation we generate a new game Γ # to which we later apply Counterfactual Regret Minimization to obtain ε-Nash equilibria. We include numerical experiments showing how the method can be applied to a previously published problem.

show abstract

Section: Previous Workmentioning

confidence: 99%

“…For discrete distributions, the formulation results in a mixed-integer linear programming (MILP) problem. A similar and related problem where payoffs are modeled by closed intervals is expressed as two linear programs that are solved to find the corresponding bounds (Bhurjee and Panda, 2017).…”

Section: Previous Workmentioning

confidence: 99%

Solving zero-sum extensive-form games with arbitrary payoff uncertainty models

Leni,

Levine,

Quigley

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Li et al (2012) developed a method to solve a matrix game model with interval payoffs based on the solution of two bi-objective linear programming models using fuzzy ranking index-based auxiliary interval programming models. Bhurjee and Panda (2017) discussed the existence of the optimal strategy as well as the value of the interval matrix game models using interval analysis. Recently, Dey and Zaman (2020) developed a robust optimization method for solving two-person zero-sum and non-zero-sum game models where payoffs are at single or multiple intervals.…”

Section: Introductionmentioning

confidence: 99%

Existence of optimal strategies in a normalized interval matrix game and applications

AFREEN¹,

Bhurjee

Aziz

2022

Preprint

View full text Add to dashboard Cite

Vagueness in the real-world problem performs a significant role in determining the existence of a feasible solution to the problem. This vagueness in the model may be handled by considering the parameters of the problem as a closed interval. In this competitive world, game models with uncertain payoffs can successfully handle conflicting real-world problems. Therefore, a two-player zero-sum game model in which payoffs vary in a range is considered. Then, the existence of saddle point (pure strategy) and dominance rules are discussed for the game model, and mixed strategy is defined in the case of non-existing saddle point. Thereafter, a methodology has been developed to discuss the existence of weak and control strategies in the interval game model. Furthermore, we obtain the optimal value of the game model as a deterministic number. Finally, the developed methodology is successfully implemented to solve real-world investment problems in the stock market and obtain the optimal strategy to achieve the maximum return.

show abstract

“…Savku and Weber discussed on stochastic games for investment problems, finance problems [46,47]. Several articles have been devoted extensively on fuzzy matrix games (Bhaumik et al [5][6][7], Bhaumik and Roy [2,3], Jana and Roy [24,26,27], Osman et al [37], Roy and Mondal [43], Li [28]); and the matrix game with uncertain payoffs has been studied by several authors in different directions in the last few years (Bhurjee and Panda [8], Chandra and Aggarwal [10], Cheng et al [11], Gao et al [13,14], Li [23,29,30,32], Singh et al [48]).…”

mentioning

confidence: 99%

Solving matrix game using rough interval payoffs

Ghosh,

Bhaumik,

Weber

et al. 2024

JDG

View full text Add to dashboard Cite

In this paper, we conduct an analysis of a matrix game using rough interval payoffs, which we refer to as the rough interval matrix game (RIMG). We employ three methods to address the problem at hand: linear programming, graphical method, and algebraic method. The proposed approach offers several key advantages over existing methods, which we highlight. We introduce algorithms associated with each of the three mentioned methods to obtain optimal solutions for the RIMG. To validate the effectiveness of our proposed techniques, we present two numerical examples and apply the methodologies to solve them. In conclusion, we summarize the findings of our study and discuss potential avenues for future research based on the insights provided in this paper.

show abstract

Optimal strategies for two-person normalized matrix game with variable payoffs

Cited by 6 publications

References 17 publications

Solving zero-sum extensive-form games with arbitrary payoff uncertainty models

Solving zero-sum extensive-form games with arbitrary payoff uncertainty models

Existence of optimal strategies in a normalized interval matrix game and applications

Solving matrix game using rough interval payoffs

Contact Info

Product

Resources

About