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.     

The impact of public information on bidding in highway procurement auctions

A number of papers in the theoretical auction literature show that the release of information regarding the seller's valuation of an item can cause bidders to bid more aggressively. This widely accepted result in auction theory remains largely untested in the empirical literature. Recent theoretical work has also shown that this effect can be more pronounced in auctions with larger common cost uncertainty. We examine the impact of a policy change by the Oklahoma Department of Transportation that led to the release of the state's internal estimate of the costs to complete highway construction projects. We perform a differences-in-differences analysis comparing bidding in Texas, a state that had a uniform policy of revealing the same information all throughout the period of analysis, to bidding in Oklahoma. Our results show that, in comparison to Texas auctions, the average bid in Oklahoma fell after the change in engineers’ cost estimate (ECE) policy. This decline in bids was even larger for projects where the common uncertainty in costs is greater. Moreover, the within-auction standard deviation of bids fell after the change in ECE policy with the most significant decline observed again in projects with greater common cost uncertainty.     

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.     

A theory of subjective compound lotteries

We develop a Savage-type model of choice under uncertainty in which agents identify uncertain prospects with subjective compound lotteries. Our theory permits issue preference; that is, agents may not be indifferent among gambles that yield the same probability distribution if they depend on different issues. Hence, we establish subjective foundations for the Anscombe-Aumann framework and other models with two different types of probabilities. We define second-order risk as risk that resolves in the first stage of the compound lottery and show that uncertainty aversion implies aversion to second-order risk which implies issue preference and behavior consistent with the Ellsberg paradox.     

CROSS‐HEDGING OF EXCHANGE RATE RISKS: A NOTE*

This note studies the optimal production and hedging decisions of a competitive international firm that exports to two foreign countries. The firm faces multiple sources of exchange rate uncertainty. Cross‐hedging is plausible in that one of the two foreign countries has a currency forward market. We show that the firm's optimal forward position is an over‐hedge, a full‐hedge or an under‐hedge, depending on whether the two random exchange rates are strongly positively correlated, uncorrelated or negatively correlated, respectively.     

Bidder collusion

We analyze bidder collusion at first-price and second-price auctions. Our focus is on less than all-inclusive cartels and collusive mechanisms that do not rely on auction outcomes. We show that cartels that cannot control the bids of their members can eliminate all ring competition at second-price auctions, but not at first-price auctions. At first-price auctions, when the cartel cannot control members’ bids, cartel behavior involves multiple cartel bids. Cartels that can control bids of their members can suppress all ring competition at both second-price and first-price auctions; however, shill bidding reduces the profitability of collusion at first-price auctions.     

Large market games with demand uncertainty

We consider a market game with a continuum of consumers, where the measure of each type is stochastic. Nature selects the set of active consumers, who make bids and offers on ?−1 spot market trading posts. Existence of type-symmetric Nash equilibrium is proven. When facing price uncertainty, best responses are unique, and a Nash equilibrium to the sell-all game is typically not a Nash equilibrium to the original game. Under plausible circumstances, consumers strictly prefer to be on one side of the market.     

Procedural fairness in lotteries assigning initial roles in a dynamic setting

We extend the study of procedural fairness in three new directions. Firstly, we focus on lotteries determining the initial roles in a two-person game. One of the roles carries a potential advantage over the other. All the experimental literature has thus far focused on lotteries determining the final payoffs of a game. Secondly, we modify procedural fairness in a dynamic—i.e. over several repetitions of a game—as well as in a static—i.e. within a single game-sense. Thirdly, we analyse whether assigning individuals a minimal chance of achieving an advantaged position is enough to make them willing to accept substantially more inequality. We find that procedural fairness matters under all of these accounts. Individuals clearly respond to the degree of fairness in assigning initial roles, appraise contexts that are dynamically fair more positively than contexts that are not, and are generally more willing to accept unequal outcomes when they are granted a minimal opportunity to acquire the advantaged position. Unexpectedly, granting full equality of opportunity does not lead to the highest efficiency.     

Recursive utility and preferences for information

Summary. This paper presents an axiomatic foundation for recursive utility that captures the role of the timing of resolution of uncertainty without relying on exogenously specified objective beliefs. Two main representation results are proved. In the first one, future utility enters the recursion through the type of general aggregators considered in Skiadas (1997a), and as a result the formulation is purely ordinal and free of any probabilities. In the second representation these aggregators are conditional expectations relative to subjective beliefs. A new recursive representation incorporating disappointment aversion is also suggested. The main methodological innovation of the paper derives from the fact that the basic objects of choice are taken to be pairs of state-contingent consumption plans and information filtrations, rather than the temporal (objective) lotteries of the existing literature. It is shown that this approach has the additional benefit of being directly applicable to the continuous-time version of recursive utility developed by Duffie and Epstein (1992). Received: February 18, 1997; revised version: July 18, 1997     

Preferences for environmental quality under uncertainty

Although the expected effects of environmental policies and interventions are rarely known with certainty, stated preference surveys rarely elicit preferences over uncertain environmental outcomes. This article presents empirical results challenging the view that ignoring such uncertainty during preference elicitation is of no consequence so long as people only care about final environmental states. We show that measured preferences for final environmental states, water quality in this case, depend on whether people choose between final states or between lotteries over final states. In contrast to the typical finding for monetary lotteries, we find significant under-weighting of low probability events related to water quality.     

UNCERTAINTY AVERSION AND PORTFOLIO INERTIA

In stock markets, we often observe portfolio inertia, i.e., a situation in which some stocks are not traded or not priced for a few minutes or longer. This is neither an exceptional situation in which some stock price soars too high to be priced, nor the one where some stock price plummets too much to be traded. By introducing the concept of ‘Knightian uncertainty’, Dow and Werlang (1992) account for the existence of portfolio inertia, which has not been accounted for under the concept of ‘risk’. This paper provides a characterization of the spread between buying and selling prices based on a parameter proposed by Ozaki and Streufert (1999, 2001) that enables us to estimate the attitude towards Knightian uncertainty, and shows that an increase (a decrease) in Knightian uncertainty expands (shrinks) the interval in which an investor never changes her initial position. Furthermore, we analyse the effect of an increase in Knightian uncertainty on portfolio inertia based on Epsilon‐contaminations.     

A brain imaging study of the choice procedure

We study the behavior of subjects facing choices between certain, risky, and ambiguous lotteries. Subjects' choices are consistent with the economic theories modeling ambiguity aversion. Our results support the conjecture that subjects face choice tasks as an estimation of the value of the lotteries, and that the difficulty of the choice is an important explanatory variable (in addition to risk and ambiguity aversion).The brain imaging data suggest that such estimation is of an approximate nature when the choices involve ambiguous and risky lotteries, as the regions in the brain that are activated are typically located in parietal lobes. Thus such choices require mental faculties that are shared by all mammals, and in particular are independent of language. In contrast, choices involving partial ambiguous lotteries additionally produce an activation of the frontal region, which indicates a different, more sophisticated cognitive process.     

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.     

HETEROGENEOUS RISK ATTITUDES IN A CONTINUOUS‐TIME MODEL*

We prove that every continuous‐time model in which all consumers have time‐homogeneous and time‐additive utility functions and share a common probabilistic belief and a common discount rate can be reduced to a static model. This result allows us to extend some of the existing results of the representative consumer and risk‐sharing rules in static models to continuous‐time models. We show that the equilibrium interest rate is lower and more volatile than in the standard representative consumer economy, and that the individual consumption growth rates are more dispersed than in the absence of uncertainty.     

Expected utility theory without the completeness axiom

We study the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteries by means of a set of von Neumann-Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a well-defined sense.     

Auctions with variable supply: Uniform price versus discriminatory

We examine an auction in which the seller determines the supply after observing the bids. We compare the uniform price and the discriminatory auction in a setting of supply uncertainty, where uncertainty is caused by the interplay of two factors: the seller's private information about marginal cost and the seller's incentive to sell the profit-maximizing quantity, given the received bids. In every symmetric mixed strategy equilibrium, bidders submit higher bids in the uniform price auction than in the discriminatory auction. In the two-bidder case, this result extends to the set of rationalizable strategies. As a consequence, we find that the uniform price auction generates a higher expected revenue for the seller and a higher trade volume.     

EXPERIMENTAL AND SELF‐REPORTED MEASURES OF RISK TAKING AND DIGIT RATIO (2D:4D): EVIDENCE FROM A LARGE,SYSTEMATIC STUDY

We systematically investigate the links between the digit ratio (2D:4D)—a biomarker for prenatal testosterone exposure—and two measures of individual risk taking: (i) risk preferences (RP) over lotteries with real monetary incentives and (ii) self‐reported risk attitude (RA). We find that both the right‐hand and the left‐hand digit ratio are significantly associated with RP: Subjects with lower digit ratios tend to choose riskier lotteries. Neither digit ratio, however, is associated with self‐reported RA.     

BIDDING TO GIVE: AN EXPERIMENTAL COMPARISON OF AUCTIONS FOR CHARITY*

We experimentally compare three mechanisms used to raise money for charities: first‐price winner‐pay auctions, first‐price all‐pay auctions, and lotteries. We stay close to the characteristics of most charity auctions by using an environment with incomplete information and independent private values. Our results support theoretical predictions by showing that the all‐pay format raises substantially higher revenue than the other mechanisms.     

Market experience eliminates some anomalies—and creates new ones

We report two experiments which investigate whether experience of decision making in repeated markets purges behaviour of preference reversals. We investigate two behavioural mechanisms that may be shaping bids in repeated auctions: A tendency to adjust bids towards previously observed market prices, and a tendency to reduce bids following bad market outcomes. We find little support for the former but strong support for the latter. Also, whilst ‘just enough’ market exposure eliminates the typical preference reversal phenomenon, continued exposure fosters the mirror image anomaly. Therefore, although market experience shapes behaviour, in our experiments, it does not generally promote consistency with standard preference theory.     

MONEY CYCLES

Operating overheads are widespread and lead to concentrated bursts of activity. To transfer resources between active and idle spells, agents demand financial assets. Futures contracts and lotteries are unsuitable, as they have substantial overheads of their own. We show that money—under efficient monetary policy—is a liquid asset that leads to efficient allocations. Under all other policies, agents follow inefficient “money cycle” patterns of saving, activity, and inactivity. Agents spend their money too quickly—a hot‐potato effect of inflation. We show that inflation can stimulate inefficiently high aggregate output.