Geodesic
Choice of mixed strategy in matrix game with nature by Hurwitz criterion
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 14 (2022) no. 2, pp. 64-75 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article solves the problem of choosing an optimal, by the Hurwitz criterion, mixed strategy for arbitrary matrix game against nature. We reduce the problem to solving $n$ linear programming problems (where $n$ is the number of scenarios). As far as we know, this is a new result. It can be used to make decisions in uncertain environments, if the game situation is repeated many times, or physical mixture of pure strategies is realizable.
Keywords: uncertainty, decision making, game against nature, Hurwitz criterion, mixed strategy, linear programming. 
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     author = {Stepan Yu. Ponomarev and Alexandr B. Khutoretskii},
     title = {Choice of mixed strategy in matrix game with nature by {Hurwitz} criterion},
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Stepan Yu. Ponomarev; Alexandr B. Khutoretskii. Choice of mixed strategy in matrix game with nature by Hurwitz criterion. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 14 (2022) no. 2, pp. 64-75. http://geodesic.mathdoc.fr/item/MGTA_2022_14_2_a3/

[1] Aibazova S. Kh., “Optimizatsiya logisticheskikh izderzhek v biznese s ispolzovaniem sinteticheskogo kriteriya Gurvitsa dlya smeshannykh strategii”, Ekonomicheskie nauki, 113 (2014), 130–136

[2] Vilenskii P. L., Livshits V. N., Smolyak S. A., Otsenka effektivnosti investitsionnykh proektov: teoriya i praktika, Delo, M., 2008

[3] Kibalov E. B., Kin A. A., “Uchet faktora neopredelennosti pri otsenke effektivnosti krupnomasshtabnykh regionalno-transportnykh proektov”, Region: ekonomika i sotsiologiya, 2014, no. 2(82), 81–94

[4] Labsker L. G., Teoriya kriteriev optimalnosti i ekonomicheskie resheniya, KNORUS, M., 2012

[5] Smolyak S. A., Otsenka effektivnosti investitsionnykh proektov v usloviyakh riska i neopredelennosti (teoriya ozhidaemogo effekta), Nauka, M., 2002

[6] Gärdenfors P., “Manipulation of social choice functions”, Journal of Economic Theory, 13 (1976), 217–228 | DOI | MR | Zbl

[7] Groenewald M. E., Pretorius P. D., “Comparison of decision-making under uncertainty investment strategies with the money market”, Journal of Financial Studies and Research, 2011 (2011), 16 pp.

[8] Gaspars-Wieloch H., “On a decision rule for mixed strategy searching under uncertainty on the basis of the coefficient of optimism”, Procedia – Social and Behavioral Sciences, 110:2 (2014), 223–931

[9] Jaffray J.-Y., Jeleva M., “Information processing under imprecise risk with the Hurwicz criterion”, Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications, Action M Agency, Prague, 2007, 233–242

[10] Kannai Y., Peleg B., “A note on the extension of an order on set to the power set”, Journal of Economic Theory, 32 (1984), 172–175 | DOI | MR | Zbl

[11] Milnor J. W., “Games against Nature”, Decision Processes, Wiley, New York, 1954, 49–60 | MR

[12] Rzepecki L., Jaśkowski P., “Application of game theory against nature in supporting bid pricing in construction”, Symmetry, 13:1 (2021) | DOI

[13] Smirnova L. V., “Nash–Hurwitz equilibrium for non-cooperative games”, Game Theory and Application, v. 4, Nova Science Pub. Inc., UK, 1999, 130–141 | MR