“Dice”-sion–Making Under Uncertainty: When Can a Random Decision Reduce Risk?

Published Online:https://doi.org/10.1287/mnsc.2018.3108

References

  • Agranov M, Ortoleva P (2017) Stochastic choice and preferences for randomization. J. Political Econom. 125(1):40–68.CrossrefGoogle Scholar
  • An B, Tambe M, Sinha A (2016) Stackelberg security games (SSG): Basics and application overview. Abbas A, Tambe M, von Winterfeldt D, eds. Improving Homeland Security Decisions (Cambridge University Press, Cambridge, UK), 485–507.Google Scholar
  • Artzner P, Delbaen F, Eber JM, Heath D (1999) Coherent measures of risk. Math. Finance 9(3):203–228.CrossrefGoogle Scholar
  • Barks C (1953) Flip Decision, Walt Disney Comics & Stories 149, vol. 13, no. 5 (Walt Disney Company, Burbank, CA).Google Scholar
  • Bäuerle N, Müller A (2006) Stochastic orders and risk measures: Consistency and bounds. Insurance, Math., Econom. 38(1):132–148.CrossrefGoogle Scholar
  • Bellini F, Bignozzi V (2015) On elicitable risk measures. Quant. Finance 15(5):725–733.CrossrefGoogle Scholar
  • Ben-Tal A, Teboulle M (2007) An old-new concept of convex risk measures: The optimized certainty equivalent. Math. Finance 17(3):449–476.CrossrefGoogle Scholar
  • Ben-Tal A, Ghaoui LE, Nemirovski A (2009) Robust Optimization (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • Bertsimas D, Nasrabadi E, Orlin JB (2016) On the power of randomization in network interdiction. Oper. Res. Lett. 44(1):114–120.CrossrefGoogle Scholar
  • Birge JR, Louveaux F (2000) Introduction to Stochastic Programming (Springer, New York).Google Scholar
  • Bryan G, Karlan D, Nelson S (2010) Commitment devices. Ann. Rev. Econom. 2(1):671–698.CrossrefGoogle Scholar
  • Casella G, Berger RL (2002) Statistical Inference, 2nd ed. (Duxbury Thomson Learning, Pacific Grove, CA).Google Scholar
  • Cettolin E, Riedl A (2016) Revealed incomplete preferences under uncertainty: Evidence for bewley preferences. Working paper, Tilburg University, Warandelaan, Netherlands.Google Scholar
  • Chan TCY, Shen ZJM, Siddiq A (2015) Robust facility location under demand location uncertainty. Unpublished doctoral dissertation, University of Toronto, Toronto.Google Scholar
  • Cheng J, Delage E, Lisser A (2014) Distributionally robust stochastic knapsack problem. SIAM J. Optim. 24(3):1485–1506.CrossrefGoogle Scholar
  • Cheng J, Leung J, Lisser A (2016) New reformulations of distributionally robust shortest path problem. Comput. Oper. Res. 74:196–204.CrossrefGoogle Scholar
  • DeJarnette P, Dillenberger D, Gottlieb D, Ortoleva P (2018) Time lotteries. PIER Working Paper No. 15-026.Google Scholar
  • Delage E, Ye Y (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper. Res. 58(3):595–612.LinkGoogle Scholar
  • Dhaene J, Kukush A (2011) Comonotonic modification of random vector in its own probability space. Working paper, Katholieke Universiteit Leuven, Belgium.Google Scholar
  • Dominiak A, Schnedler W (2011) Attitudes towards uncertainty and randomization: An experimental study. Econom. Theory 48(2):289–312.CrossrefGoogle Scholar
  • Dwenger N, Kübler D, Weizsäcker G (2016) Flipping a coin: Evidence from laboratory and field. Technical report, University of Hohenheim, Stuttgart, Germany.Google Scholar
  • Eichberger J, Kelsey D (1996) Uncertainty aversion and preference for randomisation. J. Econom. Theory 71(1):31–43.CrossrefGoogle Scholar
  • Eichberger J, Grant S, Kelsey D (2016) Randomization and dynamic consistency. Econom. Theory 63(3):547–566.CrossrefGoogle Scholar
  • Epstein LG (1999) A definition of uncertainty aversion. Rev. Econom. Stud. 66(3):579–608.CrossrefGoogle Scholar
  • Evans-Pritchard EE (1976) Witchcraft, Oracles and Magic Among the Azande (Oxford University Press, New York).Google Scholar
  • Fishburn P (1970) Utility Theory for Decision Making, Operations Research Society of America Edition (John Wiley & Sons, New York).CrossrefGoogle Scholar
  • Föllmer H, Schied A (2011) Stochastic Finance—An Introduction in Discrete Time, 3rd ed. (Walter de Gruyter & Co., Berlin).CrossrefGoogle Scholar
  • Ghaoui LE, Oks M, Oustry F (2003) Worst-case value-at-risk and robust portfolio optimization: A conic programming approach. Oper. Res. 51(4):543–556.LinkGoogle Scholar
  • Gilboa I, Schmeidler D (1989) Maxmin expected utility with non-unique prior. J. Math. Econom. 18(2):141–153.CrossrefGoogle Scholar
  • Goh J, Sim M (2010) Distributionally robust optimization and its tractable approximations. Oper. Res. 58(4):902–917.LinkGoogle Scholar
  • Gounaris CE, Wiesemann W, Floudas CA (2013) The robust capacitated vehicle routing problem under demand uncertainty. Oper. Res. 61(3):677–693.LinkGoogle Scholar
  • Gul F, Pesendorfer W (2006) Random expected utility. Econometrica 74(1):121–146.CrossrefGoogle Scholar
  • Hey JD, Carbone E (1995) Stochastic choice with deterministic preferences: An experimental investigation. Econom. Lett. 47(2):161–167.CrossrefGoogle Scholar
  • Jiang R, Guan Y, Watson JP (2016) Risk-averse stochastic unit commitment with incomplete information. IIE Trans. 48(9):838–854.CrossrefGoogle Scholar
  • Jouini E, Schachermayer W, Touzi N (2006) Law invariant risk measures have the Fatou property. Kusuoka S, Yamazaki A, eds. Advances in Mathematical Economics (Springer, Tokyo), 49–71.CrossrefGoogle Scholar
  • Kellerer H, Mansini R, Speranza MG (2000) Selecting portfolios with fixed costs and minimum transaction lots. Ann. Oper. Res. 99(1):287–304.CrossrefGoogle Scholar
  • Keynes JM (1921) A Treatise on Probability (Macmillan & Co., London).Google Scholar
  • Kircher P, Ludwig S, Sandroni A (2013) On the difference between social and private goods. B. E. J. Theoret. Econom. 13(1):151–177.Google Scholar
  • Klibanoff P (1996) Uncertainty, decision and normal form games. Technical report, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
  • Knight FH (1921) Risk, Uncertainty and Profit (Houghton Mifflin, Boston).Google Scholar
  • Korzhyk D, Yin Z, Kiekintveld C, Conitzer V, Tambe M (2011) Stackelberg vs. Nash in security games: An extended investigation of interchangeability, equivalence, and uniqueness. J. Artif. Intell. Res. 41(2):297–327.CrossrefGoogle Scholar
  • Kusuoka S (2001) On law invariant coherent risk measures. Kusuoka S, Maruyama T, eds. Advances in Mathematical Economics, vol. 3 (Springer, Tokyo), 83–95.CrossrefGoogle Scholar
  • Lo KC (1996) Equilibrium in beliefs under uncertainty. J. Econom. Theory 71(2):443–484.CrossrefGoogle Scholar
  • Manzini P, Mariotti M (2014) Stochastic choice and consideration sets. Econometrica 82(3):1153–1176.CrossrefGoogle Scholar
  • Mastin A, Jaillet P, Chin S (2014) Randomized minmax regret for combinatorial optimization under uncertainty Elbassioni K, Makino K, eds. Algorithms and Computation. Proc. 26th Internat. Sympos., Lecture Notes in Computer Science, vol. 9472 (Springer-Verlag Berlin, Heidelberg, Germany), 491–501.Google Scholar
  • Meng F, Qi J, Zhang M, Ang J, Chu S, Sim M (2015) A robust optimization model for managing elective admission in a public hospital. Oper. Res. 63(6):1452–1467.LinkGoogle Scholar
  • Mittal S, Schulz A, Stiller S (2014) Robust appointment scheduling. Jansen K, Rolim J, Devanur N, Moore C, eds. Proc. 17th Internat. Workshop Approximation Randomized Algorithms, Leibniz International Proceedings in Informatics, vol. 28 (Schloss Dagstuhl, Wadern, Germany), 356–370.Google Scholar
  • Nash J (1951) Non-cooperative games. Ann. Math. 54(2):286–295.CrossrefGoogle Scholar
  • Postek KS, den Hertog D, Melenberg B (2016) Computationally tractable counterparts of distributionally robust constraints on risk measures. SIAM Rev. 58(4):603–650.CrossrefGoogle Scholar
  • Rosenblatt M (1952) Remarks on a multivariate transformation. Ann. Math. Statist. 23(3):470–472.CrossrefGoogle Scholar
  • Rubinstein A (2002) Irrational diversification in multiple decision problems. Eur. Econom. Rev 46(8):1369–1378.CrossrefGoogle Scholar
  • Saito K (2012) Subjective timing of randomization and ambiguity, Working paper, California Institute of Technology, Pasadena.Google Scholar
  • Saito K (2015) Preferences for flexibility and randomization under uncertainty. Amer. Econom. Rev. 105(3):1246–1271.CrossrefGoogle Scholar
  • Samuelson P (1952) Probability, utility, and the independence axiom. Econometrica 20(4):1670–678.CrossrefGoogle Scholar
  • Schmeidler D (1989) Subjective probability and expected utility without additivity. Econometrica 57(3):571–587.CrossrefGoogle Scholar
  • Shapiro A, Dentcheva D, Ruszczyński A (2009) Lectures on Stochastic Programming (SIAM, Philadelphia).CrossrefGoogle Scholar
  • Sopher B, Narramore JM (2000) Stochastic choice and consistency in decision making under risk: An experimental study. Theory Decision 48(4):323–349.CrossrefGoogle Scholar
  • Stone P (2011) A Treatise on Probability (Oxford University Press, Oxford, UK).Google Scholar
  • Strotz RH (1955–56) Myopia and inconsistency in dynamic utility maximization. Rev. Econom. Stud. 23(3):165–180.CrossrefGoogle Scholar
  • Tallec YL (2007) Robust, risk-sensitive, and data-driven control of Markov decision processes. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
  • von Neumann J, Morgenstern O (1944) Theory of Games and Economic Behavior (Princeton University Press, Princeton, NJ).Google Scholar
  • Wiesemann W, Kuhn D, Rustem B (2014a) Robust Markov decision processes. Math. Oper. Res. 38(1):153–183.LinkGoogle Scholar
  • Wiesemann W, Kuhn D, Sim M (2014b) Distributionally robust convex optimization. Oper. Res. 62(6):1358–1376.LinkGoogle Scholar
  • Yu Z (2007) Spatial energy market risk analysis using the semivariance risk measure. Internat. J. Electr. Power Energy Syst. 29(8):600–608.CrossrefGoogle Scholar
  • Zhu S, Fukushima M (2009) Worst-case conditional value-at-risk with application to robust portfolio management. Oper. Res. 57(5):1155–1168.LinkGoogle Scholar
  • Zymler S, Kuhn D, Rustem B (2013) Worst-case value at risk of nonlinear portfolios. Management Sci. 59(1):172–188.LinkGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.