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Uncertain extensive game with application to resource allocation of national security

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Abstract

Uncertain theory is a powerful tool for describing human uncertainty, especially in social economic studies. In this paper, we consider finite extensive games with payoffs being uncertain variables. We introduce three different criteria: the expected value criterion, the optimistic value criterion and the pessimistic value criterion to describe players’ behaviors in different decision-making situations. Accordingly, three types of uncertain equilibria and uncertain subgame perfect equilibria for the uncertain extensive game are proposed. Moreover, we provide theorems to prove the existence of uncertain equilibria and uncertain subgame perfect equilibria. Finally, the resource allocation problem for national security is formulated and analyzed using the uncertain extensive game. Results show that different decision criteria may lead to different subgame perfect equilibria, demonstrating the significance of introducing different uncertain subgame perfect equilibria.

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References

  • Bier V, Oliveros S, Samuelson L (2007) Choosing what to protect. J Public Econ Theory 9(4):563–587

    Article  Google Scholar 

  • Chen H, Wang X, Liu Z, Zhao R (2017) Impact of risk levels on optimal selling to heterogeneous retailers under dual uncertainties. J Ambient Intell Human Comput. doi:10.1007/s12652-017-0481-9

    Google Scholar 

  • Chen X, Gao J, Uncertain term structure model of interest rate. Soft Comput 17(4):597–604

  • Elisabeth C, Igor L, Jeffrey M (2016) A game theoretic model for resource allocation among countermeasures with multiple attributes. Eur J Oper Res 252:610–622

    Article  MathSciNet  MATH  Google Scholar 

  • Gao J (2013) Uncertain bimatrix game with applications. Fuzzy Optim Decis Mak 12(1):65–78

    Article  MathSciNet  Google Scholar 

  • Gao J, Yang X, Liu D (2017) Uncertain Shapley value of coalitional game with application to supply chain alliance. Appl Soft Comput 56:551–556

    Article  Google Scholar 

  • Guo C, Gao J (2017) Optimal dealer pricing under transaction uncertainty. J Intell Manuf 28(3):657–665

    Article  Google Scholar 

  • Harsanyi J (1995) Games with incomplete information. Am Econ Rev 85(3):291–303

    Google Scholar 

  • Ke H, Huang H, Gao X (2017) Pricing decision problem in dual-channel supply chain based on experts’ belief degrees. Soft Comput. doi:10.1007/s00500-017-2600-0

    Google Scholar 

  • Keohane N, Zeckhauser R (2003) The ecology of terror defense. J Risk Uncertain 26:201–229

    Article  MATH  Google Scholar 

  • Kuhn H (1950) Extensive games. Proc Natl Acad Sci 36:570–576

    Article  MathSciNet  MATH  Google Scholar 

  • Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin

    MATH  Google Scholar 

  • Liu B (2008) Fuzzy process, hybrid process and uncertain process. J Uncertain Syst 2(1):3–16

    MathSciNet  Google Scholar 

  • Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10

    MathSciNet  Google Scholar 

  • Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin

    Book  Google Scholar 

  • Liu Y, Chen X, Ralescu D (2015) Uncertain currency model and currency option pricing. Int J Intell Syst 30(1):40–51

    Article  Google Scholar 

  • Liu Y, Liu G (2017) Stable set of uncertain coalitional game with application to electricity suppliers problem. Soft Comput. doi:10.1007/s00500-017-2611-x

    Google Scholar 

  • Liu Y, Yao K (2017) Uncertain random logic and uncertain random entailment. J Ambient Intell Human Comput. doi:10.1007/s12652-017-0465-9

    Google Scholar 

  • Nash J (1950) Equilibrium points in n-person games. Proc Natl Acad Sci 36:48–49

    Article  MathSciNet  MATH  Google Scholar 

  • Selten R (1965) Spileltheoretische behandlung eines oligopolmodells mitnachfragetragheit. Zeitschrift furdie gesamte Staatswissenschaft 121(301–324):667–689

    Google Scholar 

  • Von Neumann J, Morgenstern D (1944) The theory of games in economic behavior. Wiley, New York

    MATH  Google Scholar 

  • Yang X, Gao J (2014) Uncertain core for coalitional game with uncertain payoffs. J Uncertain Syst 8(1):13–21

    Google Scholar 

  • Yang X, Gao J (2016) Linear-quadratic uncertain differential game with application to resource extraction problem. IEEE Trans Fuzzy Syst 24(4):819–826

    Article  MathSciNet  Google Scholar 

  • Yang X, Gao J (2017) Bayesian equilibria for uncertain bimatrix game with asymmetric information. J Intell Manuf 28(3):515–525

    Article  Google Scholar 

  • Yang X, Gao J (2013) Uncertain differential games with application to capitalism. J Uncertain Anal Appl 1:17. doi:10.1186/2195-5468-1-17

  • Zhu Y (2010) Uncertain optimal control with application to a portfolio selection model. Cybern Syst 41(7):535–547

    Article  MATH  Google Scholar 

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Correspondence to Jinwu Gao.

Additional information

This work was supported in part by National Natural Science Foundation of China under Grant 61374082, Distinguished Young Scholar Project of Renmin University of China and China Scholarship Council under Grant 201606365008.

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Wang, Y., Luo, S. & Gao, J. Uncertain extensive game with application to resource allocation of national security. J Ambient Intell Human Comput 8, 797–808 (2017). https://doi.org/10.1007/s12652-017-0538-9

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  • DOI: https://doi.org/10.1007/s12652-017-0538-9

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