×

An integrated approach based on game theory and geographical information systems to solve decision problems. (English) Zbl 1411.91167

Summary: In this study, a military decision problem is handled by an integrated approach based on game theory and geographical information systems (GIS). The problem can be defined as: finding layout plan for troops who want to maximize probability of identifying enemies using particular routes to penetrate border line. The problem has been transformed to two-person zero-sum game by some assumptions and solved in four interconnected stages. First, suitable spots in the terrain for monitoring the enemies were identified. Then, visibility percentages of each of the spots were calculated by using GIS for the routes used by enemies to pass the border line. Next, by assuming the calculated visibility ratios as the probability of identifying the enemy, a two-person zero-sum payoff matrix was formed. Finally, linear mathematical model established to obtain optimal strategies with their probabilities. There are many techniques in literature to solve military decision problems but we believe that this study, by holding the peculiarity of the first study in which game theory and GIS are used together, will make a significant contribution to literature and future studies.

MSC:

91A80 Applications of game theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Davis, M. D., Game Theory: A nontechnical Introduction (1983), Basic Books Inc: Basic Books Inc New York · Zbl 1191.91001
[2] Nagy, P., GIS in the army of the 21th century, Informatics, 3, 587-600 (2004)
[3] Demers, M. N., Fundamentals of Geographic Information Systems (2009), John Wiley and Sons Inc
[4] Kelly, A., Decision Making Using Game theory: An Introduction For Managers (2003), Cambridge University Press: Cambridge University Press Cambridge
[5] Luce, D. R.; Raiffa, H., Games and Decisions: Introduction and Critical Survey (1957), John Wiley and Sons Inc: John Wiley and Sons Inc New York · Zbl 0084.15704
[6] Peters, H., Game theory: A multi-Leveled Approach (2008), Springer: Springer Berlin · Zbl 1147.91001
[7] Haywood, O. D., Military decision and game theory, J. Oper. Res. Soc. Am., 2, 365-385 (1954) · Zbl 1414.90179
[8] Berkovitz, L. D.; Dresher, M., Allocation of Two Types of Aircraft in Tactical Air War (1960), RAND Corporation: RAND Corporation California · Zbl 0096.14704
[9] Berkovitz, L. D.; Dresher, M., A Game Theory Analysis of Tactical Air War (1959), RAND Corporation: RAND Corporation California · Zbl 0121.15204
[10] Cantwell, G. L., Can Two Person Zero Sum Game Theory Improve Military Decision Making Course of Action Selection. (2003), School of Advanced Military Studies United States Army Command and General Staff College: School of Advanced Military Studies United States Army Command and General Staff College Fort Leavenworth, Kansas
[11] Brightman, H. J., Nash in Najaf: game theory and its applicability to the Iraqi conflict., Air Sp. Power J., 21, 35-41 (2007)
[12] Devine, P., War games: military strategy and economic game theory, Student Econ. Rev., 22, 23-30 (2008)
[13] Perc, M.; Szolnoki, A., Coevolutionary games - a mini review, Biosystems, 99, 109-125 (2010)
[14] Wang, Z.; Wang, L.; Szolnoki, A.; Perc, M., Evolutionary games on multilayer networks: a colloquium, Eur. Phys. J. B., 88, 1-14 (2015)
[15] Xia, C.-Y.; Miao, Q.; Wang, J.; Ding, S., Evolution of Cooperation in the traveler’s dilemma on two coupled lattices, Appl. Math. Comput., 246, 389-398 (2014) · Zbl 1338.91026
[16] Wang, Z.; Kokubo, S.; Jusup, M.; Tanimoto, J., Universal scaling for the dilemma strength in evolutionary games, Phys. Life Rev., 14, 1-30 (2015)
[17] Xia, C.-Y.; Miao, Q.; Wang, J.; Ding, S., Is the universal scaling for the dilemma strength still available in populations with heterogeneous connectivity or activities?: Comment on “universal scaling for the dilemma strength in evolutionary games” by Z. Wang et al., Phys. Life Rev., 14, 43-44 (2015)
[18] Xia, C.-Y.; Meloni, S.; Perc, M.; Moreno, Y., Dynamic instability of cooperation due to diverse activity patterns in evolutionary social dilemmas, Europhys. Lett., 109, 58002, 6-11 (2015)
[19] Xia, C. Y.; Meng, X. K.; Wang, Z., Heterogeneous coupling between interdependent lattices promotes the cooperation in the prisoner’s dilemma game, PLoS One, 10, e01295, 1-13 (2015)
[20] Swann, D., Military applications of GIS, Geographical Information Systems: Principles, Techniques, Management and Applications, 889-899 (1999), Wiley
[21] Grogan, A., Creating a Spatial Analysis Model For Generating Composite Cost Surfaces to Depict Cross Country Mobility In Natural, (Proceedings of the 2009 Fall Conference on ASPRS/MAPPS (2009), San Antonio, Texas)
[22] Baijal, R.; Arora, M. K.; Ghosh, S. K., A GIS assisted knowledge-based approach for military operations, GIS Dev., 6, 21-24 (2002)
[23] Aras, İ.; Yildiz, F., İnternet Tabanlı CBS ’ nin Sivil ve Askerî Amaçlı Acil Durum Uygulamalarında Kullanılmasında Yeni Bir Yaklaşım, Harit. Derg., 145, 38-51 (2011)
[24] Aplak, H. S.; Sogut, M. Z., Game theory approach in decisional process of energy management for industrial sector, Energy Convers. Manag., 74, 70-80 (2013)
[25] Straffin, P. D., Game Theory and Strategy (1993), The Mathematical Association of America (Inc.): The Mathematical Association of America (Inc.) Washington · Zbl 0948.91502
[26] University of Babylon, Game Theory: Solving Two Person and Zero - Sum Game, (2014). http://www.uobabylon.edu.iq/eprints/publication_2_24583_31.pdf; University of Babylon, Game Theory: Solving Two Person and Zero - Sum Game, (2014). http://www.uobabylon.edu.iq/eprints/publication_2_24583_31.pdf
[27] Abdalla, A.; Buckley, J., Monte Carlo methods in fuzzy game theory, New Math. Nat. Comput., 3, 259-269 (2007) · Zbl 1242.91008
[28] Chen, Y. W.; Larbani, M., Two-person zero-sum game approach for fuzzy multiple attribute decision making problems, Fuzzy Sets Syst., 157, 34-51 (2006) · Zbl 1117.91324
[29] F. Peldschus, Experience of the game theory application in construction management, 14 (2008) 531-545. doi:10.3846/1392-8619.2008.14.531-545.; F. Peldschus, Experience of the game theory application in construction management, 14 (2008) 531-545. doi:10.3846/1392-8619.2008.14.531-545.
[30] Arslan, S., Game Theory Approach in Telecommunications Networks (2006), Gazi University Institute of Science and Technology
[31] Hillier, F. S.; Lieberman, G. J., Introduction to Operations Research (2001), McGraw-Hill Companies: McGraw-Hill Companies New York · Zbl 0155.28202
[32] M. Vlachopoulou, G. Silleos, V. Manthou, Geographic information systems in warehouse site selection decisions, 71 (2001) 205-212.; M. Vlachopoulou, G. Silleos, V. Manthou, Geographic information systems in warehouse site selection decisions, 71 (2001) 205-212.
[33] Malpica, J. A.; Alonso, M. C.; Sanz, M. A., Dempster - Shafer theory in geographic information systems : a survey, Expert Syst. Appl., 32, 47-55 (2007)
[34] INTOSAI, Use of Geospatial Information in Auditing Disaster Management and Disaster-related Aid, 2013.; INTOSAI, Use of Geospatial Information in Auditing Disaster Management and Disaster-related Aid, 2013.
[35] Church, R. L., Geographical information systems and location science, Comput. Oper. Res., 29, 541-562 (2002) · Zbl 0995.90067
[36] Chamberlain, B. C.; Meitner, M. J., Landscape and Urban Planning A route-based visibility analysis for landscape management, Landsc. Urban Plan., 111, 13-24 (2013)
[37] Y. Kim, S. Rana, S. Wise, Exploring multiple viewshed analysis using terrain features and optimisation techniques \(, 30 (2004) 1019-1032. doi:10.1016/j.cageo.2004.07.008.; Y. Kim, S. Rana, S. Wise, Exploring multiple viewshed analysis using terrain features and optimisation techniques \), 30 (2004) 1019-1032. doi:10.1016/j.cageo.2004.07.008.
[38] Sander, H. A.; Manson, S. M., Heights and locations of artificial structures in viewshed calculation: How close is close enough?, Landsc. Urban Plan., 82, 257-270 (2007)
[39] Brabyn, L.; Mark, D. M., Using viewsheds, GIS, and a landscape classification to tag landscape photographs, Appl. Geogr., 31, 1115-1122 (2011)
[40] Blue Marble Geographics, Global Mapper Manual, (2014) 2.; Blue Marble Geographics, Global Mapper Manual, (2014) 2.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.