When to Quit Gambling, if You Must!

TL;DR

This paper models the optimal stopping problem in casino gambling under cumulative prospect theory, accounting for time inconsistency and randomization, and predicts gambler behaviors under various conditions.

Contribution

It introduces a computational approach to solve CPT-based gambling models, deriving optimal randomized Markovian stopping rules and analyzing behavioral predictions.

Findings

Gamblers may enter casinos even with a single allowed play.

Longer gambling depends on gain or loss status.

Naive gamblers tend to never stop when facing losses.

Abstract

We develop an approach to solve Barberis (2012)'s casino gambling model in which a gambler whose preferences are specified by the cumulative prospect theory (CPT) must decide when to stop gambling by a prescribed deadline. We assume that the gambler can assist their decision using an independent randomization, and explain why it is a reasonable assumption. The problem is inherently time-inconsistent due to the probability weighting in CPT, and we study both precommitted and naive stopping strategies. We turn the original problem into a computationally tractable mathematical program, based on which we derive an optimal precommitted rule which is randomized and Markovian. The analytical treatment enables us to make several predictions regarding a gambler's behavior, including that with randomization they may enter the casino even when allowed to play only once, that whether they will play longer once they are granted more bets depends on whether they are in a gain or at a loss, and that it is prevalent that a naivite never stops loss.