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Adversarial risk analysis under partial information. (English) Zbl 1443.91117

Summary: Adversarial risk analysis provides one-sided decision support to decision makers faced with risks due to the actions of other parties who act in their own interest. It is therefore relevant for the management of security risks, because the likely actions of the adversary can, to some extent, be forecast by formulating and solving decision models which explicitly capture the adversary’s objectives, actions, and beliefs. Yet, while the development of these decision models sets adversarial risk analysis apart from other approaches, the exact specification of the adversary’s decision model can pose challenges. In response to this recognition, and with the aim of facilitating the use of adversarial risk analysis when the parameters of the decision model are not completely known, we develop methods for characterizing the adversary’s likely actions based on concepts of partial information, stochastic dominance and decision rules. Furthermore, we consider situations in which information about the beliefs and preferences of all parties may be incomplete. We illustrate our contributions with a realistic case study of military planning in which the Defender seeks to protect a supply company from the Attacker who uses unmanned aerial vehicles for surveillance and the acquisition of artillery targets.

MSC:

91B06 Decision theory
91A80 Applications of game theory

References:

[1] Antos, D.; Pfeffer, A., Representing Bayesian games without a common prior, Proceedings of the ninth international conference on autonomous agents and multiagent systems: volume 1-volume 1, 1457-1458 (2010), International Foundation for Autonomous Agents and Multiagent Systems
[2] Banks, D. L.; Aliaga, J. M.R.; Ríos Insua, D., Adversarial risk analysis (2015), CRC: CRC Boca Raton, FL
[3] Bawa, V. S., Optimal rules for ordering uncertain prospects, Journal of Financial Economics, 2, 1, 95-121 (1975)
[4] Bier, V.; Oliveros, S.; Samuelson, L., Choosing what to protect: Strategic defensive allocation against an unknown attacker, Journal of Public Economic Theory, 9, 4, 563-587 (2007)
[5] Börgers, T., Weak dominance and approximate common knowledge, Journal of Economic Theory, 64, 1, 265-276 (1994) · Zbl 0822.90141
[6] Brown, G.; Carlyle, M.; Salmerón, J.; Wood, K., Defending critical infrastructure, Interfaces, 36, 6, 530-544 (2006)
[7] Cox, A. L.JR, Game theory and risk analysis, Risk Analysis, 29, 8, 1062-1068 (2009)
[8] of Finland, N. L. S. (2007). Topographic map raster 1:50 000. https://tiedostopalvelu.maanmittauslaitos.fi/tp/kartta?lang=en. Accessed: 2017-6-16.
[9] Fishburn, P. C., Non-cooperative stochastic dominance games, International Journal of Game Theory, 7, 1, 51-61 (1978) · Zbl 0372.90133
[10] Fishburn, P. C., Stochastic dominance and moments of distributions, Mathematics of Operations Research, 5, 1, 94-100 (1980) · Zbl 0434.90014
[11] Hadar, J.; Russell, W. R., Rules for ordering uncertain prospects, The American Economic Review, 59, 1, 25-34 (1969)
[12] Hämäläinen, R. P., Behavioural issues in environmental modelling-the missing perspective, Environmental Modelling & Software, 73, 244-253 (2015)
[13] Harsanyi, J. C., Games with incomplete information played by Bayesian players, I-III part i. the basic model, Management Science, 14, 3, 159-182 (1967) · Zbl 0207.51102
[14] Ríos Insua, D.; Ruggeri, F., Robust Bayesian analysis, vol. 152 (2012), Springer Science & Business Media: Springer Science & Business Media New York
[15] Kangaspunta, J.; Liesiö, J.; Salo, A., Cost-efficiency analysis of weapon system portfolios, European Journal of Operational Research, 223, 1, 264-275 (2012) · Zbl 1253.90146
[16] Keeney, R.; von Winterfeldt, D., A value model for evaluating homeland security decisions, Risk Analysis, 31, 9, 1470-1487 (2011)
[17] Kim, C., Stochastic dominance, Pareto optimality, and equilibrium asset pricing, The Review of Economic Studies, 65, 2, 341-356 (1998) · Zbl 0908.90034
[18] Lappi, E., Sandis military operation analysis tool, Proceedings of the second nordic military analysis symposium, Stockholm, Sweden, November 17-18 (2008)
[19] Levy, H., Stochastic dominance and expected utility: Survey and analysis, Management Science, 38, 4, 555-593 (1992) · Zbl 0764.90004
[20] Liesiö, J.; Mild, P.; Salo, A., Robust portfolio modeling with incomplete cost information and project interdependencies, European Journal of Operational Research, 190, 3, 679-695 (2008) · Zbl 1161.91398
[21] Liesiö, J.; Salo, A., Scenario-based portfolio selection of investment projects with incomplete probability and utility information, European Journal of Operational Research, 217, 1, 162-172 (2012) · Zbl 1244.91111
[22] McLay, L.; Rothschild, C.; Guikema, S., Robust adversarial risk analysis: A level-k approach, Decision Analysis, 9, 1, 41-54 (2012) · Zbl 1398.91193
[23] Nikoofal, M. E.; Zhuang, J., On the value of exposure and secrecy of defense system: First-mover advantage vs. robustness, European Journal of Operational Research, 246, 1, 320-330 (2015) · Zbl 1346.91032
[24] Ortega, J.; Rios, D.; Cano, J., Bi-agent influence diagrams from an adversarial risk analysis perspective, European Journal of Operational Research, 273, 3, 1085-1096 (2019)
[25] Ozdaglar, A.; Menache, I., Network games: theory, models, and dynamics (2011), Morgan & Claypool Publishers · Zbl 1304.91008
[26] Perea, A.; Peters, H.; Schulteis, T.; Vermeulen, D., Stochastic dominance equilibria in two-person noncooperative games, International Journal of Game Theory, 34, 4, 457-473 (2006) · Zbl 1154.91314
[27] Rass, S.; König, S.; Schauer, S., Defending against advanced persistent threats using game-theory, PLoS One, 12, 1, e0168675 (2017)
[28] Rios, J.; Ríos Insua, D., Adversarial risk analysis for counterterrorism modeling, Risk Analysis, 32, 5, 894-915 (2012)
[29] Ríos Insua, D.; Rios, J.; Banks, D., Adversarial risk analysis, Journal of the American Statistical Association, 104, 486, 841-854 (2009) · Zbl 1390.91117
[30] Roponen, J.; Salo, A., Adversarial risk analysis for enhancing combat simulation models, Journal of Military Studies, 6, 2, 82-103 (2015)
[31] Rothschild, C.; McLay, L.; Guikema, S., Adversarial risk analysis with incomplete information: A level-k approach, Risk Analysis: An International Journal, 32, 7, 1219-1231 (2012)
[32] Sevillano, J. C.; Ríos Insua, D.; Rios, J., Adversarial risk analysis: The somali pirates case, Decision Analysis, 9, 2, 86-95 (2012) · Zbl 1398.91202
[33] Shachter, R. D., Evaluating influence diagrams, Operations research, 34, 6, 871-882 (1986)
[34] Shaked, M.; Shanthikumar, J. G., Stochastic orders (2007), Springer Science & Business Media: Springer Science & Business Media New York · Zbl 1111.62016
[35] Tatman, J. A.; Shachter, R. D., Dynamic programming and influence diagrams, IEEE Transactions on Systems, Man, and Cybernetics, 20, 2, 365-379 (1990) · Zbl 0715.90094
[36] Wang, S.; Banks, D., Network routing for insurgency: An adversarial risk analysis framework, Naval Research Logistics (NRL), 58, 6, 595-607 (2011) · Zbl 1267.91024
[37] Washburn, A. R.; Kress, M., Combat modeling, vol. 139 (2009), Springer: Springer New York · Zbl 1184.91010
[38] Xu, J.; Zhuang, J., Modeling costly learning and counter-learning in a defender-attacker game with private defender information, Annals of Operations Research, 236, 1, 271-289 (2016) · Zbl 1345.91064
[39] Zhuang, J.; Bier, V. M., Balancing terrorism and natural disasters defensive strategy with endogenous attacker effort, Operations Research, 55, 5, 976-991 (2007) · Zbl 1167.91331
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