Abstract
Since both, decision- and game theory vitally employ optimization at their core, this chapter will provide the basic ideas, concepts and modeling aspects of optimization. It is intended to provide the mathematical basics for the further chapters. The presentation is to the point of a simple, compact and self-contained description of: (i) what is decision- and game-theory about, (ii) how do the two areas differ, and (iii) how does the practical work with these models look like when we strive for solutions. Specifically, we discuss preference relations, real and stochastic ordering relations and optimization as the most general covering framework, including single- and multi-goal optimization, with applications in being decision theory and game theory. Numeric examples accompany each section and concept. The opening of the chapter will specifically set the notation for all upcoming (mathematical) descriptions, to be consistent throughout the entire presentation (and book).
I am prepared for the worst, but hope for the best.B. Disraeli
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References
Glicksberg IL (1952) A further generalization of the kakutani fixed point theorem, with application to Nash equilibrium points. In: Proceedings of the American mathematical society, vol 3, pp 170–174. https://doi.org/10.2307/2032478
Jøsang A, Ismail R (2002) The beta reputation system. In: Proceedings of the 15th bled electronic commerce conference
Lozovanu D, Solomon D, Zelikovsky A (2005) Multiobjective games and determining Pareto-Nash equilibria. Buletinul Academiei de Stiinte a Republicii Moldova Matematica 3(49):115–122. http://D:Documentsresourcesmultiobjective_games_and_optimizationMultiobjectiveGamesandDeterminingPareto-NashEquilibria.pdf
MRC Biostatistics Unit, U.o.C. (2008) The BUGS project. https://www.mrc-bsu.cam.ac.uk/software/bugs/
Nash JF (1951) Non-cooperative games. Ann Math 54:286–295. http://www.jstor.org/stable/1969529?origin=crossref
von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, Princeton
Rass S (2009) On information-theoretic security: contemporary problems and solutions. Ph.D. thesis, Klagenfurt University, Institute of Applied Informatics
Rass S (2013) On game-theoretic network security provisioning. Springer J Netw Syst Manag 21(1):47–64. https://doi.org/10.1007/s10922-012-9229-1
Rass S, König S (2012) Turning Quantum Cryptography against itself: how to avoid indirect eavesdropping in quantum networks by passive and active adversaries. Int J Adv Syst Meas 5(1 & 2):22–33
Rass S, König S, Schauer S (2016) Decisions with uncertain consequences – a total ordering on loss-distributions. PLoS ONE 11(12):e0168583. https://doi.org/10.1371/journal.pone.0168583
Rass S, Kurowski S (2013) On Bayesian trust and risk forecasting for compound systems. In: Proceedings of the 7th international conference on IT security incident management & IT forensics (IMF). IEEE Computer Society, pp 69–82. https://doi.org/10.1109/IMF.2013.13
Rass S, Schauer S (eds) (2018) Game theory for security and risk management. Springer, Birkhäuser. http://www.worldcat.org/oclc/1019624428
Ross T, Booker JM, Parkinson WJ (2002) Fuzzy logic and probability applications: bridging the gap. ASA SIAM, Philadelphia/U.S.A
Schartner P, Rass S (2010) Quantum key distribution and Denial-of-Service: using strengthened classical cryptography as a fallback option. In: Computer symposium (ICS), 2010 international. IEEE, pp 131–136
Sion M, Wolfe P (1957) On a game without a value. Princeton University Press, pp 299–306. http://www.jstor.org/stable/j.ctt1b9x26z.20
Zhu Q, Rass S (2018) On multi-phase and multi-stage game-theoretic modeling of advanced persistent threats. IEEE Access 6:13958–13971. https://doi.org/10.1109/access.2018.2814481. https://doi.org/10.1109%2Faccess.2018.2814481
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Rass, S., Schauer, S., König, S., Zhu, Q. (2020). Mathematical Decision Making. In: Cyber-Security in Critical Infrastructures. Advanced Sciences and Technologies for Security Applications. Springer, Cham. https://doi.org/10.1007/978-3-030-46908-5_3
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DOI: https://doi.org/10.1007/978-3-030-46908-5_3
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