**October 20, 2020**. Read More

# Analyzing on the Decomposition based Pricing Procedure for Solving Two Person Zero Sum Game Problems through Computer Algebra

10.5120/ijca2016912578 |

H K Das and Sajal Chakroborty. Analyzing on the Decomposition based Pricing Procedure for Solving Two Person Zero Sum Game Problems through Computer Algebra. *International Journal of Computer Applications* 156(12):37-47, December 2016. BibTeX

@article{10.5120/ijca2016912578, author = {H. K. Das and Sajal Chakroborty}, title = {Analyzing on the Decomposition based Pricing Procedure for Solving Two Person Zero Sum Game Problems through Computer Algebra}, journal = {International Journal of Computer Applications}, issue_date = {December 2016}, volume = {156}, number = {12}, month = {Dec}, year = {2016}, issn = {0975-8887}, pages = {37-47}, numpages = {11}, url = {http://www.ijcaonline.org/archives/volume156/number12/26763-2016912578}, doi = {10.5120/ijca2016912578}, publisher = {Foundation of Computer Science (FCS), NY, USA}, address = {New York, USA} }

### Abstract

Objective of this paper is to analyze on the decomposition based pricing (DBP) method for solving two person zero sum game problems. Decomposition based algorithms have been developed which is able to solve two person zero sum game problems with single payoff elements using the linear programming (LP). To develop this procedure, idea of DBP method have used. Its computer oriented program has also introduced by using a mathematical programming language (AMPL). A real life oriented problem has introduced to show the efficiency of our algorithm and its program. The ability of our program has shown in saving labor and time for solving game problems by analyzing a number of numerical examples.

### References

- Davis M., 1983. Game Theory: An Introduction, Basic Books, Ney York.
- Dantzig, G.B. and P. Wolfe, 1961. The Decomposition Algorithm for Linear Programming, Econometrica, 29 (4).
- Das H. K., T. Saha and M. Babul Hasan, 2012. Numerical Experiments By Improving a Numerical Methods For Solving Game Problems Through Computer Algebra, International Journal of Decision Sciences, 3(1), 23-52.
- Das H.K. and M. Babul Hasan, 2011. An Algorithm and Its Computer Technique for Solving Game Problems Using LP method, Int. J. of Basic & Applied Sciences”, 11(3), 90-99.
- Dantzig, G.B., 1963. Linear Programming and Extensions, Princeton University Press, Princeton, U.S.A.
- Fourer, R., D.M. Gay and B.W. Kernighan, 2003. A Modeling Language for Mathematical Programming, Second edition, Thomson Publication.
- Winston, W.L., 1994. Linear Programming: Applications and Algorithm, Duxbury press, Belmont, California, U.S.A..
- Eugene Don. Theory and Problems of Mathmatica, McGRAW-HILL, Schaum’s Outline Series, New York, San Francisco Washington, D.C.
- Nisan N., Roughgarden T., Tardos E., Vazirari V.V., “ Algorithmic Game Theory”, Cambridge University Press, 2007.
- Von Neumann J., and O. Morgenstern, “Theory of Games and Economic Behavior”, second edition, Princeton University Press, Princeton, N.J., 1947.
- Von Neumann J., 1928. Zur Theorie der Gesselschaftsspiele, Mathematische Annalen 100.
- Mamer, J. W. & R. D. McBride, 2000. A Decomposition-based Pricing Procedure for Large- Scale Linear Programs: An application to the linear multi-commodity Flow Problem, 46(5), 693-709.
- Dantzig, G. B., & P. Wolfe, 1961. The Decomposition Algorithm for Linear Programming, Econometrica, 29(4), 767-778.
- Libbecke, M. E. & J. Desrosiers, 2005. Selected topics in column generation, Operations research, 53(6), 1007-1023.
- Das H.K. and M. Babul Hasan, 2011. An Algorithm and Its Computer Technique for Solving Game Problems Using LP method, Int. J. of Basic & Applied Sciences”, 11(3), 90-99.
- Arshaful Islam, M. Babul Hasan and H.K. Das, 2014. A new Decomposition-Based Pricing Technique for Solving Large-Scale Mixed IP with a Computer Technique, GANIT, Bangladesh Mathematical Society, 34, 5-20.
- H. K. Das and M. Babul Hasan, 2013. An Improved Decomposition Approach and Its Computer Technique for Solving Primal Dual LP & LFP Problems, GANIT, J. Bangladesh Math. Society, 33, 65-75.

### Keywords

Game, Pure and Mixed strategy, DBP, LP, Computer Algebra.