Hold or roll: reaching the goal in jeopardy race games
Tóm tắt
We consider a class of dynamic tournaments in which two contestants are faced with a choice between two courses of action. The first is a riskless option (“hold”) of maintaining the resources the contestant already has accumulated in her turn and ceding the initiative to her rival. The second is the bolder option (“roll”) of taking the initiative of accumulating additional resources, and thereby moving ahead of her rival, while at the same time sustaining a risk of temporary setback. We study this tournament in the context of a jeopardy race game (JRG), extend the JRG to
$$N > 2$$
contestants, and construct its equilibrium solution. Compared to the equilibrium solution, the results of three experiments reveal a dysfunctional bias in favor of the riskless option. This bias is substantially mitigated when the contestants are required to commit in advance how long to pursue the risky course of action.
Tài liệu tham khảo
Axelrod, R. (1984). The evolution of cooperation. New York: Basic Books.
Bearden, J. N., Murphy, R. O., & Rapoport, A. (2005). A multi-attribute extension of the secretary problem: Theory and experiments. Journal of Mathematical Psychology, 49, 410–422.
Bearden, J. N., & Rapoport, A. (2005). Operations research in experimental psychology. In J. C. Smith (Ed.), Tutorials in operations research: Emerging theory, methods, and applications (pp. 213–236). Hanover, MD: INFORMS.
Bearden, J. N., Rapoport, A., & Murphy, R. O. (2006). Sequential observation and selection with rank-dependent payoffs: An experimental test of alternative decision rules. Management Science, 52, 1437–1449.
Berry, D., & Fristedt, B. (1985). Bandit problems. London: Chapman and Hall.
Biele, G., Erev, I., & Ert, E. (2009). Learning risk attitude, and hot stoves in restless Bandit problems. Journal of Mathematical Psychology, 53, 155–167.
Busemeyer, J. P., & Pleaskac, T. J. (2009). Theoretical tools for understanding and aiding dynamic decision making. Journal of Mathematical Psychology, 53, 126–138.
Camerer, C. F. (1995). Individual decision making. In J. H. Kagel & A. E. Roth (Eds.), Handbook of experimental economics (pp. 587–703). Princeton, NJ: Princeton University Press.
DeGroot, M. H. (1970). Optimal statistical decisions. New York: Wiley.
Edwards, W. (1962). Dynamic decision theory and probabilistic information processing. Human Factors, 4, 59–73.
Ferguson, T. S. (1989). Who solved the secretary problem? Statistical Science, 4, 282–296.
Hey, J. D. (1981). Are optimal search rules reasonable? And vice versa? (And does it matter, anyway?). Journal of Economic Behavior and Organization, 2, 47–70.
Hey, J. D. (1982). Search for rules of search. Journal of Economic Behavior and Organization, 3, 65–81.
Hey, J. D., & Knoll, J. A. (2007). How far ahead do people plan? Economic Letters, 96, 8–13.
Konrad, K. A. (2009). Strategy and dynamics in contests. New York: Oxford University Press.
Lejuez, C. W., et al. (2002). Evaluation of a behavior measure of risk-taking: The Balloon Analogue Risk Task (BART). Journal of Experimental Psychology: Applied, 8, 75–84.
Maner, J. K., Gailliot, M. T., Butz, D. A., & Peruche, B. M. (2007). Power, risk, and the status quo: Does power promote riskier or more conservative decision making? Personality and Social Psychology Bulletin, 33, 451–462.
Neller, T. W., & Presser, C. G. M. (2004). Optimal play of the dice game Pig. The UMAP Journal, 25, 25–47.
Neller, T. W., & Presser, C. G. M. (2005). Pigtail: A Pig Addendum. The UMAP Journal, 26, 443–458.
Rabin, M., & Vayanos, D. (2010). The gambler’s and hot-hand fallacies: Theory and applications. The Review of Economic Studies, 77, 730–778.
Rapoport, A. (1975). Research paradigms for studying dynamic decision behavior. In D. Wendt and C. Rapoport, A., Budescu, D. V. (1997). Randomization in individual choice behavior. Psychological Review, 104, 603–618.
Rapoport, A., & Tversky, A. (1966). Cost and accessibility of offers as determinants of optimal stopping. Psychonomic Science, 4, 145–146.
Rapoport, A., & Tversky, A. (1970). Choice behavior in an optimal stopping task. Organizational Behavior and Human Performance, 5, 105–120.
Rapoport, A., & Wallsten, T. S. (1972). Individual decision behavior. Annual Review of Psychology, 23, 131–176.
Scarne, J. (1945). Scarne on dice. Harrisburg, PA: Military Service Publishing Co.
Seale, D. A., & Rapoport, A. (1997). Sequential decision making with relative ranks: An experimental investigation of the secretary problem. Organizational Behavior and Human Decision Processes, 69, 221–236.
Seale, D. A., & Rapoport, A. (2000). Optimal stopping behavior with relative ranks: The secretary problem with unknown population size. Journal of Behavioral Decision Making, 13, 191–411.
Stein, W. E., Seale, D. A., & Rapoport, A. (2003). Analysis of heuristic solutions to the best choice problem. European Journal of Operational Research, 151, 140–152.
Tijms, H. (2012). Stochastic games and dynamic programming. Asian Pacific Mathematical Newsletter, 2, 6–10.
Toda, M. (1962). The design of a fungus-eater: A model of human behavior in an unsophisticated environment. Behavioral Science, 7, 164–183.
Wallsten, T. S., Pleskac, T. J., & Lejuez, C. W. (2005). Modeling behavior in clinically diagnostic sequential risk-taking task. Psychological Review, 112, 862–880.