Research

A Mega Millions Anomaly (Job Market Paper) [pdf]

The interstate lottery game Mega Millions introduced a new product in October 2017 called Just the Jackpot. Sales of this product have been anemic. The Standard option accounts for over 90% of sales even though it is never the expected value maximizer for consumers among ticket options at any jackpot level. Several popular decision theoretic models predict Just the Jackpot should have strong appeal, while interest in the Standard option should be low. I show that consumers’ choice of product is not due to inattentiveness, liquidity constraints or lags in the adjustment of consumption to new product introduction. I argue that the data trends are due to differences in ex post outcome feedback on foregone choices depending on which option is selected, as well as minimal winner regret, something not accounted for in most models. I propose a Feedback Weighted Regret Minimax model that incorporates a feedback parameter as well as a novel winner-loser regret feature that captures the data trends significantly better. It is puzzling that lottery managers chose to introduce Just the Jackpot, as existing decision models predict negligible increases in Mega Millions participation on the extensive margin. I show that inducing players to switch from another Mega Millions option to Just the Jackpot maximizes neither lottery revenue nor lottery profits. Finally, I argue that the seemingly irrational inverse relationship between jackpot size and the Just the Jackpot sales percentage can be explained by changes in player demographics, as a larger share of players at bigger jackpots are likely unaware of the existence of the Just the Jackpot option.

Distribution-Dependent Utility of Gaming [pdf]

Submitted to the Journal of Risk and Uncertainty

There is existing evidence that decision making over risk is impacted by factors like whether or not the decision maker can self-select numbers, a type of gaming utility, a feature common in lottery games. Such preferences would violate the fundamental properties of reflexivity and FOSD, but is nevertheless within the bounds of what the current literature accounts for. This paper provides experimental evidence that the estimated financial value of such factors is non-negligible, as subjects on average are willing to forego 10% to 30% of potential winnings. A novel result is the significant variation in self-selection preferences by payoff distribution. Sales data from lottery games played in Texas are adduced to further confirm the experimental findings. In order to ascertain the dependency of the gaming utility on the payoff distribution, an additional experiment is run to control for differences in non-distributional gaming factors between the Texas lottery games. The variation persists, leading to the conclusion that a preference for self-selection of numbers is distribution-dependent for many individuals. Reasons for these apparent inconsistencies with the existing literature and decision theoretic model predictions are discussed, and a possible regret-salience motive is proposed.

Funded in part by: Dean's Research Initiative Grant

A Survey of Prize Linked Savings

with Erkut Ozbay

A survey of the existing literature on the rapidly growing Prize Linked Savings industry.

Behavioral Modifications to Prize Linked Savings (PLS)

PLS is a unique savings product that combines the principal guarantee of standard savings with the upside risk of gambling and lottos. It would therefore seem to be a substitute for both the riskless savings and the risky gambling and lottos. Assuming that substitutability increases the less differentiated two products are, making PLS more similar to gambling and lottos would increase the substitution effect from gambling and lottos to PLS. Furthermore, if gambling and lottos provide an inherent gaming or entertainment value that is independent of their payoff distribution, along with an illusion of control value, capturing these effects in PLS will only make PLS more appealing. This paper provides experimental evidence that adding gaming and illusion of control facets to PLS increases its appeal. Currently, PLS products do not systematically seek to incorporate gaming aspects; rather they focus on the uniqueness of the payoff distribution when compared to existing savings products. It would behoove proponents and providers of PLS to gamify PLS. This could be done by allowing participants to choose winning numbers, play some game to determine if they are a winner or advance into the next round of winner determination, etc.