Technical Note - Path-Dependent and Randomized Strategies in Barberis' Casino Gambling Model

We consider the dynamic casino gambling model initially proposed by Barberis (2012) and study the optimal stopping strategy of a precommitting gambler with cumulative prospect theory (CPT) preferences. We illustrate how the strategies computed in Barberis (2012) [Barberis N (2012) A model of casino gambling. Management Sci. 58(1): 35–51.] can be strictly improved by reviewing the betting history or by tossing an independent coin, and we explain that the improvement generated by using randomized strategies results from the lack of quasi-convexity of CPT preferences. Moreover, we show that any path-dependent strategy is equivalent to a randomization of path-independent strategies.

[1]  J. Quiggin.  A theory of anticipated utility , 1982 .

[2]  P. Wakker.  Separating marginal utility and probabilistic risk aversion , 1994 .

[3]  A. Tversky,et al.  Prospect theory: an analysis of decision under risk — Source link , 2007 .

[4]  D. Prelec.  The Probability Weighting Function , 1998 .

[5]  P. Blavatskyy.  Violations of betweenness or random errors , 2006 .

[6]  Vicky Henderson,et al.  Randomized Strategies and Prospect Theory in a Dynamic Context , 2017, J. Econ. Theory.

[7]  Nicholas Barberis,et al.  A Model of Casino Gambling , 2009, Manag. Sci..

[8]  Georg Weizsacker,et al.  Flipping a Coin: Theory and Evidence , 2012, SSRN Electronic Journal.

[9]  Colin Camerer,et al.  Violations of the betweenness axiom and nonlinearity in probability , 1994 .

[10]  A. Tversky,et al.  Advances in prospect theory: Cumulative representation of uncertainty , 1992 .

[11]  X. Zhou,et al.  Optimal Exit Time from Casino Gambling: Strategies of Pre-Committed and Naive Gamblers , 2019 .

[12]  Mark J. Machina,et al.  Stochastic Choice Functions Generated from Deterministic Preferences over Lotteries , 1985 .

[13]  Pietro Ortoleva,et al.  Stochastic Choice and Preferences for Randomization , 2015, Journal of Political Economy.

[14]  M. Yaari.  The Dual Theory of Choice under Risk , 1987 .

[15]  R. Thaler,et al.  Gambling with the house money and trying to break even: the effects of prior outcomes on risky choice , 1990 .

[16]  Pietro Ortoleva,et al.  Stochastic Choice and Hedging , 2013 .

[17]  P. Strack,et al.  Until the Bitter End: On Prospect Theory in a Dynamic Context , 2012 .