THE EFFECTS OF LOTTO GAME CHANGES AND LARGE JACKPOTS ON INCOME ELASTICITIES AND SALES

Using daily lottery data from Washington State by zip code from January 2011 through mid‐March 2016, we estimate that Powerball income elasticities range from ?0.16 to 0.16 as the Powerball jackpot increases from its minimum to $1.5 billion, while Mega Millions income elasticities range from ?0.08 to 0.03 as the Mega Millions jackpot increases from its minimum to $640 million. Controlling for jackpot size, each of three major game changes during this time period has a significant effect on own‐game and cross‐game sales. Despite these significant game changes, however, these lotto games are a highly regressive source of revenue for Washington State. (JEL H22, H71, L83)     

SETTING THE ODDS OF WINNING THE JACKPOT: ON THE ECONOMICS OF (RE) DESIGNING LOTTERY GAMES

In many jurisdictions, domestic lotto games have experienced a decline in sales revenue due to the introduction of new products and the absence of appealing jackpots. To reverse this trend, operators worldwide have conducted major reforms to the design of games. In this paper, we focus on Spain's largest domestic lottery game, which was redesigned in 2012 by significantly reduced the odds of winning the jackpot to produce more frequent and larger rollovers. Findings show overall negative results of such reform, as players seem to no longer react to large jackpots, and the declining trend in sales has even worsened. (JEL D12, H27, L83)     

An International Comparison and Analysis of Lotteries and the Distribution of Lottery Expenditures

Lotteries are found in nearly half of the world's countries, with annual worldwide lottery ticket sales topping $115 billion. Despite the global presence of lottery games, there has been little research conducted on any international aspect of lotteries. This paper presents the first-ever examination and comparison of lottery games from around the world. Differences in both absolute and relative lottery expenditures are presented. Estimates for the income elasticity of demand for lottery tickets provide evidence on the distributional burden of lottery expenditures. These estimates consider each country by continental location and country income level. Further analysis reveals that lower income countries could adopt Lotto games in order to increase revenues. Recognizing that the distributional impact of lottery games is one of the greatest concerns surrounding lotteries, it is shown that the introduction of Lotto games does not significantly affect the distributional burden of lottery ticket expenditures. Given the international scope of lotteries and the availability of international lottery game data, the paper concludes by discussing future research on international lottery games.     

Modelling demand for lotto using a novel method of correcting for endogeneity

Modelling lottery sales as a function of the mean, standard deviation and skewness of the probability distribution of returns potentially gives insights into how the design of a game could be modified to maximise net revenue. But use of OLS is problematic because the level of sales itself affects values of the moments (and insufficient instruments are available for IV regression). We draw on the concept of a rational expectations equilibrium, developing a new regression model which corrects for endogeneity where the causal impact of the dependent variable on the right-hand side variables is deterministic. We apply the model to data on lotto sales from Spain. Using the Spanish data, we show that results provide more reliable guidance to lottery agencies because accounting for endogeneity leads to significantly different results from OLS and these results have superior performance in out-of-sample forecasting of sales. More generally, results prove consistent with the Friedman-Savage explanation of why people buy lottery tickets and with evidence from racetrack data that ‘bettors love skewness’.     

Media exposure and individual choices: Evidence from lottery players

To what extent individual choices are influenced by media exposure? We try to provide evidence on this aspect considering how the sales of lotto tickets are determined by the size of the top prize (the jackpot) compared to the amount of attention that media devote to the game. We use data on the Italian SuperEnalotto (2003–2010) and estimate ticket sales in relation to the jackpot size and to several measures of lotto media coverage. To take into account that media attention may be affected by the amount of tickets sold we instrument media coverage with the availability of other newsworthy materials (sport events and disasters). It emerges that media attention to the game is inversely related to the availability of other news. Two-Stage-Least Squares Estimations show that, given the jackpot size, players are affected by media exposure as they spend more on lotto when media attention to the game is higher.     

THE EFFECT OF CASINO PROXIMITY ON LOTTERY SALES: EVIDENCE FROM MARYLAND

The continued expansion of the casino industry has caused increasing concern regarding the cannibalization of other industries, and in particular, state lotteries. For example, Maryland Lottery sales flattened shortly after casinos began opening in the state. Although previous papers have found that casinos and lotteries have a negative relationship with each other, no previous research has analyzed the impact of casino proximity on lottery sales or has examined the relationship between casinos and different types of lottery games. In this paper, we examine ZIP code‐level monthly lottery sales data from Maryland between July 2009 and February 2014, in order to test the impact of casino proximity on lottery sales, by type of game. Our findings indicate that aggregate lottery sales decline more in closer proximity to casinos, but that casinos affect different lottery products differently. We discuss the consumer behavior and public finance implications of the findings. (JEL H27, H4, L83)     

Technical change,technical efficiency,and input usage in Taiwanese agricultural growth

We analyse the increase in sales of Pick 3 and Pick 4 daily numbers lottery games and other Ohio Lottery games after Ohio introduced midday drawings for the Pick 3 and Pick 4 games in August 1999. The midday drawings increased Pick 3 sales by 5%, Pick 4 sales by 12%, and total lottery sales by 2% based on our analysis of a 36-month panel dataset of Ohio lottery sales by zip code. Midday drawings raise more revenue from the strongly regressive daily numbers games. However, the introduction of midday drawings does not change the negative income elasticities of demand for numbers games in an economically meaningful manner.     

Network externalities in consumer spending on lottery games: evidence from Spain

We use data from two nationally representative Spanish surveys in 2005 and 2006 to investigate spending on lottery games. Estimates from Tobit and double hurdle models of participation in lottery markets and spending on lottery tickets find that frequent participation in one game is not associated with an increased or decreased probability of participating in other games, but is associated with increased spending on other games. Consumer spending on different lottery games exhibits inter-related consumption decisions. Also, the assumptions underlying the double hurdle model, but not the Tobit model, better describe consumer spending on lottery tickets in Spain.     

OWN‐ AND CROSS‐PRICE ELASTICITIES FOR GAMES WITHIN A STATE LOTTERY PORTFOLIO

Lotto demand modeling typically focuses on a single game and evaluates whether estimated “effective price” (expected loss from buying one ticket) elasticity is consistent with net revenue maximization. However, a portfolio of several different lottery games is now usually offered to players and judging the effectiveness of agencies in generating revenue requires estimation of both cross‐price and own‐price elasticities. Here we employ data from Spain to derive elasticities. Results imply that games are under‐priced if net revenue maximization is the goal. But the cross‐price estimates suggest that the operator is successful in limiting the extent to which a large jackpot on one game cannibalizes same‐week sales of other games. The paper also analyzes the impacts from two increases in the level of entry fees introduced during the data period. These appear to have affected net revenue favorably. (JEL D12, G11, H27, H30, L83)     

Is lottery demand elasticity a reliable marketing tool? Evidence from a game innovation in greece

Demand for lotteries and especially lotto has been extensively studied in an international context, an important question being whether lottery providers correctly price their product. In Greece a lotto game has been offered since 1990 whereas a new version was introduced seven years later with a clearly more skewed payoff. The objective of this paper is to analyze whether demand estimates from the original game help explain the subsequent innovation and to assess, in that sense, the reliability of demand estimates as a marketing tool. (JEL: D12, L83)     

The economic analysis of lotteries

This paper considers policy issues arising in the design, regulation and taxation of lotteries, focusing on the market for an on-line lottery game. Demand determines who buys lottery tickets and in what quantities. The design of lotteries affects the terms on which tickets are supplied.
UK data suggest that its lottery may be priced too high to maximize lottery revenue – more revenue might be raised if the proportion of sales allocated to tax and other levies were smaller.
Having established the positive economics of lotteries, the paper then assesses their welfare implications. Pari-mutuel lotteries enjoy scale economies and, as natural monopolies, are invariably run either by government agencies or a regulated licensee. I estimate consumer surplus and identify the excess burden that arises from existing (over)taxation of lotteries. The large price elasticity of demand implies that revenue raised from the lottery is raised very inefficiently. Moreover, the demand for lottery tickets is inferior (and there is some evidence that such games are contagious and addictive). So using lotteries as a vehicle for raising revenue is extremely regressive. Finally, I consider other policy implications: induced effects on charitable giving and on other forms of gambling; the impact on the government budget; perceptions of risk; and distributional considerations.     

Fair e-lottery system proposal based on anonymous signatures

The games in which large amount of money is involved are always called into question about the existence of the possibility to manipulate the game for an immediate benefit. Lottery system is not an exception in this regard; moreover, it is a subject of rumours that the game is not as fair as it is pretended to be. After studying the advantages and drawbacks of conventional lottery systems, the authors are proposing an e-lottery system based on anonymous signatures. Even though the proposal is using electronic signatures, which imply complex calculus and the possession of digital certificates for each player, the proposed system compensates these drawbacks by increasing trust and confidence of both the players and the lottery organizer. This will lead to more players participating in the lottery, which translates to more revenue for the lottery and larger prizes for the players.     

Testing theories of behavior for extensive-form two-player two-stage games

We examine choices in two-player extensive-form games that give subjects opportunities for individualistic as well as other-regarding behavior, and where each subject makes choices in a variety of games. Following an extensive search over models, where we estimate a single parameter vector for all the games rather than different parameter vectors for each game, we find that (1) the level-n model organizes the data well, (2) other-regarding behaviors in these games appear to consist primarily of egalitarian and utilitarian behaviors, and (3) there is no significant evidence for reciprocal behavior. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Behavioral spillovers and cognitive load in multiple games: An experimental study

We present evidence from laboratory experiments of behavioral spillovers and cognitive load that spread across strategic contexts. In the experiments, subjects play two distinct games simultaneously with different opponents. We find that the strategies chosen and the efficiency of outcomes in one game depends on the other game that the subject plays, and that play is altered in predictable directions. We develop a measure of behavioral variation in a normal form game, outcome entropy, and find that prevalent strategies in games with low outcome entropy are more likely to be used in the games with high outcome entropy, but not vice versa. Taken together, these findings suggest that people do not treat strategic situations in isolation, but may instead develop heuristics that they apply across games.     

Market Games in Large Economies with a Finite Number of Types

We study market games derived from an exchange economy with a continuum of agents, each having one of finitely many possible types. The type of agent determines his initial endowment and utility function. It is shown that, unlike the well-known Shapley–Shubik theorem on market games (Shapley and Shubik in J Econ Theory 1:9–25, 1969), there might be a (fuzzy) game in which each of its sub-games has a non-empty core and, nevertheless, it is not a market game. It turns out that, in order to be a market game, a game needs also to be homogeneous. We also study investment games – which are fuzzy games obtained from an economy with a finite number of agents cooperating in one or more joint projects. It is argued that the usual definition of the core is inappropriate for such a model. We therefore introduce and analyze the new notion of comprehensive core. This solution concept seems to be more suitable for such a scenario. We finally refer to the notion of feasibility of an allocation in games with a large number of players. Some of the results in this paper appear in a previous draft distributed by the name “Cooperative investment games or Population games”. An anonymous referee of Economic Theory is acknowledged for his/her comments     

Analogy-based expectation equilibrium

In complex situations, agents use simplified representations to learn how their environment may react. I assume that agents bundle nodes at which other agents must move into analogy classes, and agents only try to learn the average behavior in every class. Specifically, I propose a new solution concept for multi-stage games with perfect information: at every node players choose best-responses to their analogy-based expectations, and expectations correctly represent the average behavior in every class. The solution concept is shown to differ from existing concepts, and it is applied to a variety of games, in particular the centipede game, and ultimatum/bargaining games. The approach explains in a new way why players may Pass for a large number of periods in the centipede game, and why the responder need not be stuck to his reservation value in ultimatum games. Some possible avenues for endogenizing the analogy grouping are also suggested.     

ADOLESCENT VIDEO GAME PLAYING AND FIGHTING OVER THE LONG‐TERM

I present new evidence of the link between video game play and fighting. The General Learning Model predicts that increased aggression from playing violent video games. These predictions are tested using a large longitudinal data set tracking adolescents over time. Consistent with previous research, there is a positive raw correlation between video game playing as an adolescent and aggressive outcomes, in this case fights, even more than a decade later. However, multivariate and instrumental variables estimators do not find a causal relationship. Some implications are: support policy for further interventions is undermined, future research should be more careful about identification threats, and similar methodological approaches can be applied to the effects of other new communication technologies. (JEL D18, L86, O35)     

Cournot and Bertrand Games

The author describes a series of matrix choice games illustrating monopoly, shared monopoly, Cournot, Bertrand, and Stackelberg behavior given either perfect complements or perfect substitutes. The games are created by using a spreadsheet to fill out a profit table given the choices of two players. One player selects the column, the other the row, and the table gives the profit of the row chooser. Because each player has a table, each thinks of him- or herself as the row chooser and the other as the column chooser. The games may be applied to international trade through the traditional Boeing v. Airbus story or, more currently, through foreign sales corporations. Addition of Bertrand competition allows discussion of price wars, and addition of perfect complements allows discussion of the proposed Microsoft breakup.     

Jackpot promotion model for Taiwan Lotto

Lotto was inaugurated in January 2002, and immediately became a popular activity in Taiwan; as the big craze following its initial introduction has subsided, the growth of Lotto game sales has slowed. To maintain lottery sales’ momentum, operators have conducted numerous jackpot promotions; this study examines the effectiveness of various jackpot promotional strategies. The analytical results can provide a valuable reference for operators and governmental authorities regarding ways of increasing lottery earnings. The empirical findings of this investigation include the following: (1) the effective price elasticity of Lotto is ?0.382; Taipei Fubon Bank can increase the revenue gained from Lotto by increasing the effective price; (2) operators can significantly increase lottery sales by declaring the jackpot as an unconditional added fixed or variable bonus.     

Games of Status

A status game is a cooperative game in which the outcomes are rank orderings of the players. They are a good model for certain situations in which players care about how their "status" compares with that of other players.
We present several formal models within this class. Included are authoritarian status games (where coalitions may assign positions in the rank ordering to nonmembers) and oligarchic status games (where they are unableto do so). We consider the issues of a value concept for authoritarian games and that of core existence for oligarchic games. We then add a transferable resource to the models, obtaining "games of wealth and status."
Finally, we consider an interesting variant, called a "secession game," where coalitions have the right to secede from the grand coalition and form their own smaller "subsocieties," each with its own hierarchy.