Preferences for risk in dynamic models with adjustment costs

This paper characterizes the solution to a consumption/savings decision problem in which one of the consumption goods involves transaction costs. It then analyzes how such adjustment costs affect consumersʼ risk attitudes. Previous studies have suggested that transaction costs, by resulting in infrequent but lumpy adjustments, magnify consumersʼ risk aversion with respect to moderate-stake risk and, simultaneously, stimulate the demand for large-stake wealth lotteries. This paper argues that such predictions, while naturally arising in static models, may disappear or even reverse in a dynamic setting, in which consumers can choose when to make an adjustment. Namely, it shows that such an option can eliminate the demand for large-stake lotteries, and that the consumers choosing to delay the adjustment may be more tolerant to moderate-stake risks than in the absence of adjustment costs. The paper also illustrates that both predictions crucially depend on the relationship between the time discount rate in the utility function and the interest rate.     

Information acquisition and full surplus extraction

It is well known that when agents' types are correlated, the mechanism designer can extract the entire surplus. This creates an incentive for agents to acquire information about other agents' types. Robust lotteries (are payment schemes that) support full extraction and partially robust lotteries support efficient implementation in the presence of information acquisition opportunities. Necessary and sufficient conditions for existence of robust and partially robust lotteries are derived. If an agent's information signal spans other agents' types then robust lotteries do not exist. However, if all agents report their signal realizations then robust lotteries exist in an extended type space.     

Poverty and probability: aspiration and aversion to compound lotteries in El Salvador and India

Some experimental participants are averse to compound lotteries: they prefer simple lotteries that depend on only one random event, even when the simple lotteries offer lower expected value. This paper proposes that many behavioral “investments” represent more compound risk for poorer people—who often face multiple dimensions of deprivation—than for richer people. As a result, identical aversion to compound lotteries can prevent investment among poorer people, but have no effect on richer people. The paper reports five studies: two initial studies that document that aversion to compound lotteries operates as an economic preference, two “laboratory experiments in the field” in El Salvador, and one Internet survey experiment in India. Poorer Salvadoran women who choose a compound lottery are 27 percentage points more likely to have found formal employment than those who chose a simple lottery, but lottery choice is unrelated to employment for richer women. Poorer students at the national Salvadoran university choose more compound lotteries than richer students, on average, implying that aversion to compound lotteries screened out poorer aspirants but not richer ones. Poorer and lower-caste Indian participants who choose compound lotteries are more likely than those who choose simple lotteries to have a different occupation than their parents, which is not the case for better-off participants. These findings suggest that the consequences of aversion to compound lotteries are different in the context of poverty and disadvantage.     

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.     

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.     

Beyond choice: investigating the sensitivity and validity of measures of strength of preference

Many experiments investigating different decision theories have relied heavily on pairwise choices between lotteries. These are easy to incentivise, but often yield only limited dichotomous information. This paper considers whether respondents’ judgments about their strength of preference (SoP) for one alternative over another can usefully supplement standard choice data. We report extensive evidence that such judgments show sensitivity to variations in question format and parameter values in the directions we should expect, not only within-subject but also between-sample. We illustrate how such judgments can usefully supplement standard pairwise choice data and enrich our understanding of observed behaviour.     

Noxious Facilities, Environmental Damages, and Efficient Randomized Siting

This paper considers the efficient siting of a noxious facility that causes environmental damages (for example, increased pollution) in the host community. The analysis shows that there can be multiple efficient locations without transfers, and that an efficient location need not have the smallest WTA or WTP. In general, there exist randomized outcomes that are ex ante efficient and that Pareto dominate efficient outcomes. The analysis also shows that a community’s most preferred lottery never provides full insurance. Under some conditions, lotteries with no host compensation are Pareto superior to those with compensation.     

Preference aggregation with randomized social orderings

We show that every binary and Paretian method for passing from preference profiles to lotteries over preferences is associated with a subadditive function on the set of coalitions of individuals. This function gives the power of each coalition to secure its preference for any x over any y.     

Indivisibilities, Lotteries, and Monetary Exchange

We introduce lotteries (randomized trading) into search-theoretic models of money. In a model with indivisible goods and fiat money, we show goods trade with probability 1 and money trades with probability τ, where τ<1 iff buyers have sufficient bargaining power. With divisible goods, a nonrandom quantity q trades with probability 1 and, again, money trades with probability τ where τ<1 iff buyers have sufficient bargaining power. Moreover, q never exceeds the efficient quantity (not true without lotteries). We consider several extensions designed to get commodities as well as money to trade with probability less than 1, and to illuminate the efficiency role of lotteries. Journal of Economic Literature Classification Numbers: E40, D83.     

Haggling over substitutes

Using a model of substitutable goods I determine generic conditions on tastes which guarantee that fixed prices are not optimal: the fully optimal tariff includes lotteries. That is, a profit maximising seller would employ a haggling strategy. We show that the fully optimal selling strategy in a class of cases requires a seller to not allow themselves to focus on one good but to remain haggling over more than one good. This throws new light on the selling strategies used in diverse industries. These insights are used to provide a counter-example to the no lotteries result of McAfee and McMillan (J. Econ. Theory 46 (1988) 335).     

Lotteries, Sunspots, and Incentive Constraints

We study a prototypical class of exchange economies with private information and indivisibilities. We establish an equivalence between lottery equilibria and sunspot equilibria and show that the welfare and existence theorems hold. To establish these results, we introduce the concept of the stand-in consumer economy, which is a standard, convex, finite consumer, finite good, pure exchange economy. With decreasing absolute risk aversion and no indivisibilities, we prove that no lotteries are actually used in equilibrium. We provide a simple numerical example with increasing absolute risk aversion in which lotteries are necessarily used in equilibrium. We also show how the equilibrium allocation in this example can be implemented in a sunspot equilibrium. Journal of Economic Literature Classification Numbers: D11, D50, D82.     

On the Evaluation of Options on Lotteries: An Experimental Study

We present the results of a comparative experimental study of the evaluation of simple lotteries and call/put/insurance options on these lotteries. The main findings and conclusions are:

(a) The observed bidding patterns depend on the type of asset under evaluation. In particular, subject behavior when buying or selling a basic lottery seems much more cautious than their behavior when buying or selling options on that lottery.

(b) The observed bidding patterns also depend on subject positions with respect to the underlying asset. In particular, the bids for buying lotteries and options long are statistically uncorrelated with the bids for selling the same lotteries and options short.

(c) Subjects with extreme risk attitudes are more inclined to violate basic no-arbitrage conditions (like the call-put parity) when bidding for the different lotteries.

We demonstrate that it is difficult to reconcile the experimental evidence with mainstream theories on individual decision and choice (although we find strong support for prospect theory in some parts of the data). We conclude that the evaluation of options on lotteries is context-dependent and subtler than perceived by existing theories.     

Strategic Manipulation in Voting Games When Lotteries and Ties Are Permitted

A Gibbard-Satterthwaite type theorem is established for random decision rules and rules that permit ties. The rules use full information on how individuals rank lotteries and sets of outcomes. The theorem allows restrictions on the domain of rankings. Journal of Economic Literature Classification Numbers: D7, C7.     

Funding Public Goods with Lotteries: Experimental Evidence

Why do individuals participate in charitable gambling activities? We conduct a laboratory investigation of a model that predicts risk-neutral expected utility maximizers will participate in lotteries when they recognize that lotteries are being used to finance public goods. As predicted by the model, we find that public goods provision is higher when financed by lottery proceeds than when financed by voluntary contributions. We also find support for other comparative static predictions of the model. In particular we find that ticket purchases vary with the size of the fixed prize and with the return from the public good: lotteries with large prizes are more effective, and ticket purchases drop dramatically when the public good is not valued by subjects.     

Preference for Flexibility and Dynamic Consistency

Dekel, Lipman, and Rustichini [3] characterize preferences over menus of lotteries that can be represented by the use of a unique subjective state space and a prior. We investigate what would be the appropriate version of Dynamic Consistency in such a setup. The condition we find, which we call Flexibility Consistency, is linked to a comparative theory of preference for flexibility. When the subjective state space is finite, we show that Flexibility Consistency is equivalent to a subjective version of Dynamic Consistency and that it implies that the decision maker is a subjective state space Bayesian updater. Later we characterize when a collection of signals can be interpreted as a partition of the subjective state space of the decision maker.     

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.     

Nash consistent representation of effectivity functions through lottery models

Effectivity functions for finitely many players and alternatives are considered. It is shown that every monotonic and superadditive effectivity function can be augmented with equal chance lotteries to a finite lottery model—i.e., an effectivity function that preserves the original effectivity in terms of supports of lotteries—which has a Nash consistent representation. The latter means that there exists a finite game form which represents the lottery model and which has a Nash equilibrium for any profile of utility functions satisfying the minimal requirement of respecting first order stochastic dominance among lotteries. No additional condition on the original effectivity function is needed.     

Maxmin under risk

Summary. Let be a continuous and convex weak order on the set of lotteries defined over a set Z of outcomes. Necessary and sufficient conditions are given to guarantee the existence of a set of utility functions defined on Z such that, for any lotteries p and q, The interpretation is simple: a conservative decision maker has an unclear evaluation of the different outcomes when facing lotteries. She then acts as if she were considering many expected utility evaluations and taking the worst one. Received: January 19, 2000; revised version: December 20, 2000     

Exactly what happens after the Anscombe–Aumann race?

This paper derives a representation of preferences for a choice theory with vague environments; vague in the sense that the agent does not know the precise lotteries over outcomes conditional on states. Instead, he knows only a possible set of these lotteries for each state. Thus, this paper’s main departure from the standard subjective expected utility model is to relax an assumption about the environment, rather than weakening the axiomatic structure. My model is consistent with the behavior observed in the Ellsberg experiment. It can capture the same type of behavior as the multiple priors models, but can also result in behavior that is different from both the behavior implied by standard subjective expected utility models and the behavior implied by the multiple priors models. This paper is a revised chapter of my Ph.D. dissertation at Cornell University. I am very grateful to David Easley for extensive comments and suggestions. I also thank Larry Blume, Ani Guerdjikova, Edi Karni, Ted O’Donoghue, Maureen O’Hara, Jacob Sagi, seminar participants at the University of Copenhagen, Cornell University, ESEM 2006, Fuqua—Duke University, FUR 2006, Johns Hopkins University, Purdue University, Queen’s University, the University of Warwick, the associate editor, and an anonymous referee for comments and suggestions.     

Cardinal Bayesian allocation mechanisms without transfers

In allocating goods with no use of monetary transfers, random allocation mechanisms can be designed in order to elicit information on preference intensities. I study the nontransfer allocation of two ex-ante identical objects under Bayesian incentive compatibility, with symmetric agents and independent private valuations. I find the ex-ante utilitarian-optimal mechanism, in which the probability of receiving a specified object is used as “numeraire” to purchase probability units of the other object. I characterize this mechanism as an appropriate combination of lotteries, auctions and insurance. The latter element ensures that efficient auctions are feasible. If the problem is constrained to guarantee exactly one object per agent, then the optimal mechanism uses no information other than the agents? ordinal preferences.