scholarly journals Computation of Nash equilibria in three-personmatrix game

2009 ◽  
Vol 50 ◽  
Author(s):  
Sigutė Vakarinienė ◽  
Daina Sudžiūtė
Keyword(s):  
Nash Equilibrium ◽  
Optimization Model ◽  
Nash Equilibria ◽  
Equilibrium Points ◽  
Linear Optimization ◽  
Matrix Game ◽  
Binary Variables ◽  
Linear Optimization Model

The method for finding Nash equilibrium in three-person matrix game is introduced in this paper. Linear optimization model with binary variables for computation of equilibrium points in three-person matrix game is proposed.

scholarly journals Linear model for coputation of equilibrium point in bimatrix game

2021 ◽  
Vol 47 ◽  
Author(s):  
Sigutė Vakrinienė ◽  
Daina Sudžiūtė
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Linear Model ◽  
Optimization Model ◽  
Equilibrium Points ◽  
Linear Optimization ◽  
Bimatrix Game ◽  
Binary Variables ◽  
Linear Optimization Model

The methods for finding Nash equilibrium in bimatrix game are introduced in this paper.  Linear optimization model with binary variables for coputation of all equilibrium points in nongenerate bimatrix game is proposed.

Approximating Nash Equilibrium Using Genetic Algorithm

2013 ◽  
Vol 734-737 ◽  
pp. 3098-3101
Author(s):  
Chang Bing Li ◽  
Hui Ying Cao
Keyword(s):  
Genetic Algorithm ◽  
Nash Equilibrium ◽  
Optimization Model ◽  
Linear Optimization ◽  
Evolutionary Search ◽  
Linear Optimization Model ◽  
Non Linear ◽  
Person Game

The problem of detecting the Nash equilibrium of a non cooperative n-person game is solved by introducing a non-linear optimization model that enables evolutionary search operators to converge towards Nash Equilibrium of a game.

Nash Equilibrium Points for Generalized Matrix Game Model with Interval Payoffs

2021 ◽  
pp. 2150021
Author(s):  
Ajay Kumar Bhurjee ◽  
Vinay Yadav
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Linear Optimization ◽  
Sufficient Conditions ◽  
Matrix Game ◽  
Game Model ◽  
Data Sets ◽  
Nash Equilibrium Point ◽  
Generalized Matrix

Game theory-based models are widely used to solve multiple competitive problems such as oligopolistic competitions, marketing of new products, promotion of existing products competitions, and election presage. The payoffs of these competitive models have been conventionally considered as deterministic. However, these payoffs have ambiguity due to the uncertainty in the data sets. Interval analysis-based approaches are found to be efficient to tackle such uncertainty in data sets. In these approaches, the payoffs of the game model lie in some closed interval, which are estimated by previous information. The present paper considers a multiple player game model in which payoffs are uncertain and varies in a closed intervals. The necessary and sufficient conditions are explained to discuss the existence of Nash equilibrium point of such game models. Moreover, Nash equilibrium point of the model is obtained by solving a crisp bi-linear optimization problem. The developed methodology is further applied for obtaining the possible optimal strategy to win the parliament election presage problem.

scholarly journals An Algorithmic Procedure for Finding Nash Equilibrium

2020 ◽  
Vol 40 (1) ◽  
pp. 71-85
Author(s):  
HK Das ◽  
T Saha
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Payoff Matrix ◽  
Matrix Game ◽  
Perfect Equilibrium ◽  
Repeated Use ◽  
Definition Of ◽  
Zero Sum ◽  
Mathematical Construction ◽  
Algorithmic Procedure

This paper proposes a heuristic algorithm for the computation of Nash equilibrium of a bi-matrix game, which extends the idea of a single payoff matrix of two-person zero-sum game problems. As for auxiliary but making the comparison, we also introduce here the well-known definition of Nash equilibrium and a mathematical construction via a set-valued map for finding the Nash equilibrium and illustrates them. An important feature of our algorithm is that it finds a perfect equilibrium when at the start of all actions are played. Furthermore, we can find all Nash equilibria of repeated use of this algorithm. It is found from our illustrative examples and extensive experiment on the current phenomenon that some games have a single Nash equilibrium, some possess no Nash equilibrium, and others had many Nash equilibria. These suggest that our proposed algorithm is capable of solving all types of problems. Finally, we explore the economic behaviour of game theory and its social implications to draw a conclusion stating the privilege of our algorithm. GANIT J. Bangladesh Math. Soc.Vol. 40 (2020) 71-85

scholarly journals A scenario-based optimization model for planning and redesigning the sale and after-sales services closed-loop supply chain

2020 ◽  
Author(s):  
Nazanin Esmaeili ◽  
Ebrahim Teimoury ◽  
Fahimeh Pourmohammadi
Keyword(s):  
Supply Chain ◽  
Customer Satisfaction ◽  
Optimization Model ◽  
Linear Optimization ◽  
Spare Parts ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Warranty Period ◽  
Linear Optimization Model ◽  
Mixed Integer Linear Optimization

In today's competitive world, the quality of after-sales services plays a significant role in customer satisfaction and customer retention. Some after-sales activities require spare parts and owing to the importance of customer satisfaction, the needed spare parts must be supplied until the end of the warranty period. In this study, a mixed-integer linear optimization model is presented to redesign and plan the sale and after-sales services supply chain that addresses the challenges of supplying spare parts after the production is stopped due to demand reduction. Three different options are considered for supplying spare parts, including production/procurement of extra parts while the product is being produced, remanufacturing, and procurement of parts just in time they are needed. Considering the challenges of supplying spare parts for after-sales services based on the product's life cycle is one contribution of this paper. Also, this paper addresses the uncertainties associated with different parameters through Mulvey's scenario-based optimization approach. Applicability of the model is investigated using a numerical example from the literature. The results indicate that the production/procurement of extra parts and remanufacturing are preferred to the third option. Moreover, remanufacturing is recommended when the remanufacturing cost is less than 23% of the production cost.

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