Academic journal article Economic Inquiry

Selling to Biased Believers: Strategies of Online Lottery Ticket Vendors

Academic journal article Economic Inquiry

Selling to Biased Believers: Strategies of Online Lottery Ticket Vendors

Article excerpt

I. INTRODUCTION

Do sellers in the marketplace take advantage of the belief biases of their consumers? Models of markets typically assume that sellers are profit maximizing, consumers are utility maximizing, and both sides of the market have accurate, unbiased beliefs. However, an increasing collection of evidence shows that the presence of cognitive and strategic heterogeneity can account for many stylized facts in the marketplace which appear puzzling when confined to the framework of classical models.

We examine the behavior of sellers in a popular online market which provides an unusual opportunity to identify seller exploitation of biased beliefs held by buyers: the Chinese collective lottery betting market. In this market, shares of ticket "portfolios" for China's national lottery are sold, commissions are charged by the sellers, and the success rates of sellers are made public. As in most state-run lotteries, success is completely random, with known probabilities that are independent of previous outcomes. These objective probabilities allow us to cleanly detect deviations from rational beliefs among buyers, and assess the corresponding responses by sellers in the market, to these demand shocks of buyers. We find evidence that sellers cater to the biased beliefs of lottery ticket buyers, by tailoring certain features of their portfolio product.

Specifically, collective lottery portfolio sellers adjust their sales strategies in response to demand fluctuations that are driven by buyers' biased beliefs about the correlation of past and future lottery outcomes. Lottery ticket buyers tend to purchase tickets with numbers which have not recently won, in accordance with previous evidence of the Gambler's Fallacy in lottery sales (Clotfelter and Cook 1993; Terrell 1994). Ticket buyers also tend to purchase tickets from those ticket sellers who have recently experienced an exogenous increase in their win rates, in accordance with previous evidence of the Hot-Hand Fallacy (Croson and Sundali 2005; Guryan and Kearney 2008). (1)

We find combined evidence that lottery portfolio sellers take advantage of buyers' belief in the Hot-Hand Fallacy in the following ways: (1) Directly following a previous win in their portfolio, sellers increase their commission rate charged to the buyers, to be collected as a percentage of the lottery winnings. Sellers are thus able to collect more commission money from the buyers conditional on winning. (2) Sellers offer portfolios of larger value (and more ticket coverage) directly following a large win in their portfolio. Using this strategy, sellers increase their chances of holding a winning ticket in the current round, as well as being able to collect more commission money conditional on winning. (3) Sellers self-invest less in their own portfolios after a large win, when their popularity among buyers in the market is high. By purchasing a lower share of their portfolios on their own, sellers are able to obtain a larger expected return without investing their personal money.

We also find some evidence consistent with lottery ticket sellers adapting to buyers' belief in the Gambler's Fallacy. First, sellers generally tend to offer lottery number portfolios which are numerically dissimilar to recent winning tickets, thus appealing to buyers with Gambler's Fallacy beliefs. Although the more numerically dissimilar the portfolio is to the previous winning ticket, the less the seller himself invests in it. Sellers who have proposed very similar numbers compared to the previous winning ticket, on the other hand, self-invest more, thus entering the lottery with higher expected returns under the pari-mutuel prize structure. This self-investment pattern is not consistent with the alternative story that sellers themselves subscribe equally to the Gambler's Fallacy compared to buyers.

Our paper is unique to the existing evidence in this area in that we are the first, to our knowledge, to study sellers' responses to consumers' probabilistic belief biases, specifically the Gambler's Fallacy and Hot-Hand Fallacy. …

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