Linear programming and game theory

Author(s):  
Roberto Lucchetti
2013 ◽  
Vol 59 (No. 1) ◽  
pp. 1-7 ◽  
Author(s):  
S. Cabrera García ◽  
J.E. Imbert Tamayo ◽  
J. Carbonell-Olivares ◽  
Y. Pacheco Cabrera

This paper deals with the application of Game Theory with Perfect Information to an agricultural economics problem. The goal of this analysis is demonstrating the possibility of obtaining an equilibrium point, as proposed by Nash, in the case of an agricultural company that is considered together with its three sub-units in developing a game with perfect information. Production results in terms of several crops will be considered in this game, together with the necessary parameters to implement different linear programming problems. In the game with perfect information with the hierarchical structure established between the four considered players (a management center and three production units), a Nash equilibrium point is reached, since once the strategies of the rest of the players are known, if any of them would use a strategy different to the one proposed, their earnings would be less than the ones obtained by using the proposed strategies. When the four linear programming problems are solved, a particular case of equilibrium point is reached.


Author(s):  
A. M. Alli ◽  
David L. May

This article develops strategic decision tables to be used by management in bidding based on optimal duration costs. In addition, a process is proposed to find the optimal economic duration of the project using crashing techniques, the simplex method of linear programming, and game theory.  Standardized software packages for Decision Support Systems (DSS) are used in facilitating the calculations.


Author(s):  
Christogonus Ifeanyichukwu Ugoh ◽  
Chinwendu Alice Uzuke ◽  
Obiora-Ilouno Happiness Onyebuchi ◽  
Obi-Okpala Chinelo Ijeoma ◽  
Orji gabriel Oyo ◽  
...  

The aim of this paper is to obtain the optimal strategies of two competitive players using Game Theorem and to make future predictions of games using Markov Chains involving the EPL. All the teams that have participated since 2005/2006 EPL season to EPL 2019/2020 season were considered and the method of proportion of wins was used to select five best teams. Linear programming was employed to select the optimal strategies, while the predictions for seasons 2020/2021 to 2023/2024 are obtained by Markov chain method. The results obtained revealed that Man U is the optimal strategy for Player A, and that Player A has to choose Man U to maximize his profit, meanwhile, Chelsea is the optimal strategy for Player B and he has to choose Chelsea to minimize his loss. The findings of the results also revealed that for Man U or Chelsea to win their home games, it will depend on their current home winning against the team they are playing with.


Author(s):  
William P. Fox

This chapter discusses the use of mathematical modeling with technology in risk assessment in the broad area of operations research. The authors provide modeling as a process and illustrate suggested steps in the process. This chapter reviews some of the main modeling texts and provide a brief discussion of their processes. Many illustrative examples are provided to show the breadth of mathematical modeling. These examples cover such topics as discrete dynamical systems, game theory, multi-attribute decision making, data envelopment analysis with linear programming, and integer programming. The authors discuss the important of sensitivity analysis, as applicable. Several scenarios are used as illustrative examples of the process.


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