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)     

What is the optimal design for lottery-linked savings programmes?

In this article, we determine the optimal design of lottery-linked savings (LLS) programmes. LLS vehicles, such as lottery bonds, are financial instruments that preserve depositors’ principal but provide randomized variable returns to these depositors through periodic lottery drawings, in lieu of the regular coupon payments traditionally received by bondholders. This type of asset is very popular in Europe. We note that the framing of LLS instruments is linked to their popularity, and we attempt to elucidate that link and thereby determine the optimal structure of payments for LLS programmes. Our goal is to frame LLS programmes in a manner that both maximizes their investors’ satisfaction and preserves their ability to serve as inexpensive sources of capital for their issuers. We demonstrate that the optimal pay-off structure is characterized by a high level of skewness, as investors are willing to accept a decrease in the small and medium prizes of the lottery in exchange for an increase in the grand prize. Thus, to attract a maximum number of depositors, the issuers of LLS programmes should prioritize the jackpot size relative to the other lottery pay-offs and insist on high skewness for the lottery pay-offs relating to the LLS assets.     

Do Subjects Separate (or Are They Sophisticated)?

In many experiments, particularly individual choice experiments, experimenters ask many questions to the subjects and use the random lottery incentive mechanism to give an incentive to the subjects. That is, the experimenter, at the end of the experiment, picks just one of the questions, plays out that question, and pays the subject on the basis of this one question. The idea is that subjects should separate the various questions and reply to each as if it were a separate question—in isolation from all the other questions in the experiment. This procedure is methodologically sound if the subjects behave in accordance with Expected Utility (EU) theory, since this theory says that the best procedure for the subjects is to separate the various questions. However, if there is any doubt as to whether the subjects obey EU theory, and particularly if the experiment is designed to test whether the behaviour of the subjects is in accordance with EU, this incentive mechanism is open to criticism. Indeed many referees use this argument against the research. The response that the subjects may not respect EU, yet still separate the various questions, is obviously open to objection and generally it is not clear whether this response is valid or not. There have been two direct tests of this separation hypothesis (by Starmer and Sugden (1991) and by Cubitt et al. (1998), which suggest that it is valid, but further evidence is required. This paper provides a further, stronger, test of this hypothesis: we confront the two stories—(1) that the subjects answer the various questions separately, and (2) that the subjects respond to the experiment as a whole—using experimental data from an experiment in which the random lottery incentive mechanism was used. Our analysis shows that it would appear that subjects do answer as if they were separating the questions. This should be considered reassuring for those experimenters who use the random lottery incentive mechanism.     

Winning probabilities in a pairwise lottery system with three alternatives

Summary. The pairwise lottery system is a multiple round voting procedure which chooses by lot a winner from a pair of alternatives to advance to the next round where in each round the odds of selection are based on each alternatives majority rule votes. We develop a framework for determining the asymptotic relative likelihood of the lottery selecting in the final round the Borda winner, Condorcet winner, and Condorcet loser for the three alternative case. We also show the procedure is equivalent to a Borda lottery when only a single round of voting is conducted. Finally, we present an alternative voting rule which yields the same winning probabilities as the pairwise lottery in the limiting case as the number of rounds of the pairwise lottery becomes large.Received: 5 June 2003, Revised: 17 June 2004, JEL Classification Numbers: D71. Correspondence to: Jac C. HeckelmanWe thank Keith Dougherty and Andrew Yates for their comments.     

AUCTION–LOTTERY HYBRID MECHANISMS: STRUCTURAL MODEL AND EMPIRICAL ANALYSIS

This article studies an auction–lottery hybrid mechanism that is widely adopted in allocating new vehicle licenses in China. We characterize individuals' entry and bidding strategies in a symmetric Bayesian Nash equilibrium, structurally estimate individuals' value distribution from a data set of a Guangzhou program, and evaluate the performance of the mechanism. Based on the estimated distribution and counterfactual analysis, our study suggests that a hybrid mechanism preserves 83% efficiency and 52% of revenue, while it improves equity by 25 times compared to a pure auction. We show that allowing auction losers to participate in the lottery can further enhance the performance.     

Lotteries, Group Size, and Public Good Provision

We analyze the effect of group size on public good provision under the Morgan (2000) lottery mechanism. For a pure public good, the lottery performs quite well as public good provision is found to increase in group size, even when the lottery prize is held constant. By contrast, for fully rival public goods, per capita provision is found to decrease in group size, even when the lottery prize is proportional to group size. Further, the per capita level of provision will approach zero when group size is sufficiently large.     

When less is more: Rationing and rent dissipation in stochastic contests

This paper shows how to maximize revenue when a contest is noisy. We consider a case where two or more contestants bid for a prize in a stochastic contest where all bidders value the prize equally. We show that, whenever a Tullock contest yields under-dissipation, the auctioneer?s revenue can be increased by optimally fixing the number of tickets. In particular, in a stochastic contest with proportional probabilities, it is possible to obtain (almost) full rent dissipation. We test this hypothesis with a laboratory experiment. The results indicate that, as predicted, revenue is significantly higher in a lottery with rationing than in a standard lottery. On the other hand, an alternative rationing mechanism that does not limit total expenditures fails to increase revenue relative to a standard lottery.     

Consuming your way to efficiency: Public goods provision through non-distortionary tax lotteries

We revisit the classical result that taxation of private consumption is distortionary and therefore precludes the efficient provision of public goods. We introduce a nonlinear consumption tax which we call a ‘tax lottery’. Under this scheme, an ad-valorem consumption tax is supplemented with a lottery in which consumers can win cash prizes. The winning probabilities in this lottery depend on all consumers' private good consumption decisions. We show that for a given ad-valorem tax, an appropriately designed lottery can implement an efficient allocation in pure-strategy Nash equilibrium. The lottery component corrects the distortion in private consumption due to the ad-valorem tax, while the resulting tax revenue is sufficient to efficiently provide the public good and pay out the lottery prize.     

Risk aversion and framing effects

We present a new experimental evidence of how framing affects decisions in the context of a lottery choice experiment for measuring risk aversion. We investigate framing effects by replicating the Holt and Laury’s (Am. Econ. Rev. 92:1644–1655, 2002) procedure for measuring risk aversion under various frames. We first examine treatments where participants are confronted with the 10 decisions to be made either simultaneously or sequentially. The second treatment variable is the order of appearance of the ten lottery pairs. Probabilities of winning are ranked either in increasing, decreasing, or in random order. Lastly, payoffs were increased by a factor of ten in additional treatments. The rate of inconsistencies was significantly higher in sequential than in simultaneous treatment, in increasing and random than in decreasing treatment. Both experience and salient incentives induce a dramatic decrease in inconsistent behaviors. On the other hand, risk aversion was significantly higher in sequential than in simultaneous treatment, in decreasing and random than in increasing treatment, in high than in low payoff condition. These findings suggest that subjects use available information which has no value for normative theories, like throwing a glance at the whole connected set of pairwise choices before making each decision in a connected set of lottery pairs.     

The effect of randomized school admissions on voter participation

There is little causal evidence on the effect of economic and policy outcomes on voting behavior. This paper uses randomized outcomes from a school choice lottery to examine if lottery outcomes affect voting behavior in a school board election. We show that losing the lottery has no significant impact on overall voting behavior; however, among white families, those with above median income and prior voting history, lottery losers were significantly more likely to vote than lottery winners. Using propensity score methods, we compare the voting of lottery participants to similar families who did not participate in the lottery. We find that losing the school choice lottery caused an increase in voter turnout among whites, while winning the lottery had no effect relative to non-participants. Overall, our empirical results lend support to models of expressive and retrospective voting, where likely voters are motivated to vote by past negative policy outcomes.     

Does peer group size influence social preferences and risk taking?

This paper examines whether the ex post relative payoffs of peers as well as the size of the peer group impact an agent's willingness to take risks. For example, persons in a flood plain may be less likely to purchase flood insurance if their neighbors also refrain from purchasing. We generalize the Fehr‐Schmidt (1999) model to allow the intensity of the social preferences to vary with the size of the peer group. Our experiment tests whether subjects are more or less likely to choose a lottery over a fixed payment when others have been assigned either the same lottery or the fixed payment. Using both between and within subject designs, we find risk‐taking behaviour is not responsive to the risks faced by others regardless of the size of peer group.     

Whose opinion counts? Implementation by sortition

Sortition is the process of selecting decision makers or senators by a lottery. We introduce sortition in implementation theory by augmenting a mechanism with a kleroterion or lottery machine p that selects the senators. An outcome is implemented after consulting only the opinions of the senators. We call the corresponding notion of implementation as “p-implementation”, and provide necessary and sufficient conditions for p-implementation. Our main result is that in “economic” environments, every Nash implementable social choice rule (SCR) is also p-implementable if p selects every quartet of players with positive probability and always selects at least three senators. We apply this result to two kleroteria: “oligarchic democracy” and “random sampling”. In economic environments, every Nash implementable SCR can be implemented by oligarchic democracy of three oligarchs. In economic environments, every Nash implementable SCR can be implemented by randomly selecting four senators.     

Unexpected windfalls,education, and mental health: evidence from lottery winners in Germany

This paper investigates the causal impact of large unexpected windfalls on individual mental health, physical health, as well as health behaviors. I use a large individual-level panel data set of lottery winners from Germany between the years 2000 and 2011 and observe lottery winners before and after winning a large lottery prize. Mental health declines immediately after winning a large lottery prize for individuals with low education and low levels of financial literacy. While these individuals report being happier after winning the lottery, evidence from commonly used SF-12 measures of mental health indicates that winners with low education experience increased role limitations due to emotional problems, are more anxious, and have less energy after their win. The impact on various measures of mental health is highly robust, statistically significant, economically significant, and persists for up to two years after the win. Unexpected windfalls have no impact on the mental health of individuals with high education or high financial literacy. Winning the lottery has no impact on individuals’ health behaviors such as smoking or alcohol consumption, and it has no impact on doctor visits, hospital stays, or illness-related work absences regardless of education level.     

Ordinal efficiency and dominated sets of assignments

Using lotteries is a common tool for allocating indivisible goods. Since obtaining preferences over lotteries is often difficult, real-life mechanisms usually rely on ordinal preferences over deterministic outcomes. Bogomolnaia and Moulin (J. Econom. Theory 19 (2002) 623) show that the outcome of an ex post efficient mechanism may be stochastically dominated. They define a random assignment to be ordinally efficient if and only if it is not stochastically dominated. In this paper we investigate the relation between ex post efficiency and ordinal efficiency. We introduce a new notion of domination defined over sets of assignments and show that a lottery induces an ordinally efficient random assignment if and only if each subset of the full support of the lottery is undominated.     

Lottery versus all-pay auction contests: A revenue dominance theorem

We allow a contest organizer to bias a contest in a discriminatory way; i.e., she can favor specific contestants by designing the contest rule in order to maximize total equilibrium effort (resp. revenue). The two predominant contest regimes are considered, all-pay auctions and lottery contests. For all-pay auctions the optimal bias is derived in closed form: It implies extreme competitive pressure among active contestants and low endogenous participation rates. Moreover, the exclusion principle advanced by Baye et al. (1993) becomes obsolete in this case. In contrast, the optimally biased lottery induces a higher number of actively participating contestants due to softer competition. Our main result regarding total revenue comparison under the optimal biases reveals that the all-pay auction revenue-dominates the lottery contest for all levels of heterogeneity among contestants. The incentive effect due to a strongly discriminating contest rule (all-pay auction) dominates the participation effect due to a weakly discriminating contest rule (lottery).     

Knock-out for descriptive utility or experimental-design error?

Using an experimental design of stating equivalent probabilities for 252 stimulus lottery pairs, Chechile and Cooke (1997) alleged to have refuted generic-utility theory which itself comprises many modern utility theories. The present paper systematically investigates the feasibility of the Chechile-Cooke experimental design using numerical methods. We examine 1,277 utility setups (involving 17 parameter sets for four probability-weighting functions and 11 parameter sets for three component utility functions) which represent ten different utility theories. Our results demonstrate that on average for more than one third of all stimulus lottery pairs no equivalent probabilities exist. That is, the Chechile-Cooke experimental design prevents subjects from stating their true probability equivalents. Therefore, they cannot claim to have refuted generic-utility theory and the members of its family.This paper was submitted to theJournal of Risk and Uncertainty on January 14, 1999. It was, however, rejected on April 16, 1999.     

Simple sequencing problems with interdependent costs

In this paper we analyze simple sequencing problems under incomplete information and interdependent costs. We prove the necessity of concave cost function for implementability of such problems. Implementability means that one can achieve aggregate cost minimization in ex-post equilibrium. We also show that simple sequencing problems are implementable if and only if the mechanism is a ‘generalized VCG mechanism.’ We then consider first best implementability, that is implementability with budget balancing transfer. We prove that for implementable n agent simple sequencing problems, with polynomial cost function of order (n−2) or less, one can achieve first best implementability. Finally, for the class of implementable simple sequencing problems with “sufficiently well behaved” cost function, this is the only first best class.     

Common fate,game harmony and contributions to public goods: experimental evidence

We experimentally study the effects of common fate on voluntary contributions to linear public goods. In each period, earnings are assigned to subjects according to the outcome of a lottery. In ‘common fate’, ‘independent fate’ and ‘rival fate’ treatments, the lottery outcomes of group members are (respectively) positively correlated, stochastically independent and negatively correlated. We observe the highest contributions and strongest reciprocity under common fate. Contrary to the game harmony hypothesis, contributions are not lower under rival fate than under independent fate. Surprisingly, under rival fate, having won the lottery in one period induces higher contributions in the next period.     

Hybrid allocation mechanisms for publicly provided goods

Motivated by efficiency and equity concerns, public resource managers have increasingly utilized hybrid allocation mechanisms that combine features of commonly used price (e.g., auction) and non-price (e.g., lottery) mechanisms. This study serves as an initial investigation of these hybrid mechanisms, exploring theoretically and experimentally how the opportunity to obtain a homogeneous good in a subsequent lottery affects Nash equilibrium bids in discriminative and uniform price auctions. The lottery imposes an opportunity cost to winning the auction, systematically reducing equilibrium auction bids. In contrast to the uniform price auction, equilibrium bids in the uniform price hybrid mechanism vary with bidder risk preferences. Experimental evidence suggests that the presence of the lottery and risk attitudes (elicited through a preceding experiment) impact auction bids in the directions predicted by theory. Finally, we find that theoretically and experimentally, the subsequent lottery does not compromise the efficiency of the auction component of the hybrid mechanisms.