On the social dimension of time and risk preferences: an experimental study.

Guth, Werner ; Levati, M. Vittoria ; Ploner, Matteo 等

I. INTRODUCTION

There is ample empirical evidence that people do not behave rationally when rationality implies maximization of one's own material rewards. To gain flexibility, economists have taken into account nonlinear evaluation of material rewards (e.g., in the familiar form of "utility of money" functions) as well as "social utilities" including other-regarding concerns, like altruism as in Andreoni and Miller (2002), inequality aversion as in Fehr and Schmidt (1999) and Bolton and Ockenfels (2000), or quasi-maximin preferences as in Charness and Rabin (2002). Undeniably, this provides a rich toolbox for "neoclassical repair," which allows aligning rational choice predictions with empirical data on decision behavior. Nonetheless, this toolbox may be a curse (a Pandora's box) rather than a blessing if, by combining the tools arbitrarily, everything can be justified as rational. Some guidance on how risk attitudes, time preferences, and other-regarding concerns are interrelated becomes, therefore, necessary when we want to make sound behavioral predictions.

To derive theoretically the interrelation of risk and time preferences over one's own and others' rewards, one could rely on models of endogenous preference formation in the tradition, for instance, of Guth and Yaari (1992). This would require knowing the habitat in which our basic behavioral disposition to cooperation in risky and dynamic endeavors has evolved. Rather than speculating on how to model this scenario, we prefer to collect first empirical evidence so as to learn the results of such possible preference evolution.

Except for a few attempts, (1) economic theory offers no idea of whether risk aversion goes hand in hand with patience and other-regarding concerns. Yet, such information may be crucial when designing social institutions or deciding on a policy. (2) Consider a cardinal utility function like

(1) [U.sub.i] = [summation over (x[member of]X)]Prob{x}[f.sub.i]([r.sup.0.sub.i](x),[r.sup.1.sub.i](x), [r.sup.0.sub.j](x),[r.sup.1.sub.j](x)),

where X is the set of random events x affecting the monetary rewards [r.sup.1.sub.i] and [r.sup.t.sub.j] of two individuals i and j in two successive periods t = 0 and t = 1. If the decision maker is not spiteful, one can assume that [f.sub.i](*) reacts positively to all its arguments. But how, and to what extent, can each argument be substituted with another? We know that discounting allows to relate [r.sup.1.sub.i](*) to [r.sup.0.sub.i](*), and other-regarding preferences allow to relate [r.sup.t.sub.i](*) to [r.sup.t.sub.j](*). But how does [r.sup.1.sub.j](*) relate to [r.sup.0.sub.i](*)? And if [U.sub.i] is concave in [r.sup.t.sub.i](*), is it also concave in [r.sup.t.sub.j](*)? Is somebody who is rather impatient when her own reward is delayed also rather impatient when others' reward is delayed? Rather than speculating about possible answers, we prefer to be guided by data. Hence, we report on an experiment designed to explore whether and how delaying outcomes, increasing their risk, and affecting in this way also others are interrelated. (3)

All previous empirical studies have explored only the private dimension of the interrelation between risk attitudes and time preferences, that is, when risks and delays affect only one's own rewards. The novelty of our study is that it relies on prospects with social consequences where risk and delay pertain not only to own payoffs (which is common) but also to others' payoffs.

Moreover, other-regarding concerns have mainly been modeled via social utilities depending on the (expected) payoffs of other individuals. To the best of our knowledge, the more subtle interrelation of other-regarding concerns with attitudes to others' risks and delays of rewards has been so far neglected. The Rawlsian philosophical idea according to which "benevolent" individuals should locate themselves in the shoes of others (see Rawls 1971) suggests other-regarding agents to have attitudes toward risks and delays faced by others similar to those they exhibit to risks and delays faced by themselves. (4) Yet, not much has been done to test this conjecture.

The research presented in this article is a follow-up to the study by Brennan et al. (forthcoming), who focus only on the relation between other-regarding concerns and risk preferences when one's own and/or another person's payoff is risky. Their major finding is that behavior is influenced by the riskiness of own payoff but not by that of the other's payoff: risk in what others get seems much less important than own risk, even for those who are other-regarding. Here, we move one step further by taking into account idiosyncratic private and social time preferences, that is, when own and/or another person's rewards are delayed.

In our experiment, each participant is asked to evaluate various allocations, each of which assigns a payoff to herself and to another participant. Payoffs can be immediate or delayed and certain or stochastic. Since each of these four possibilities applies independently to oneself as well as to the other, each participant must evaluate 16 different allocations. As elicitation procedure we use the incentive-compatible random price mechanism introduced by Becker, DeGroot, Marschak (1964). Given that the results of Brennan et al. (forthcoming) reveal a significant difference in individual valuations of risky prospects in the willingness-to-accept (but not in the willingness-to-pay) treatment, we employ only the willingness-to-accept mode. Thus, each participant is endowed with a prospect and asked to state the minimum price at which she is willing to sell it. (5)

In the following Section II, the different prospects and the experimental procedures are described in detail. The results of the experiment are reported in Section III. Section IV concludes.

II. THE EXPERIMENT

Decision Task

To address our research questions, we rely on the random price mechanism and elicit individual valuations of several prospects. Valuations are defined as certainty equivalents in the form of willingness to accept a randomly fixed amount of money to forgo a given prospect. Each prospect allocates payoffs to both the decision maker and another participant. More specifically, each member of the pair receives either a sure payoff u or a lottery ticket U, assigning [U.bar] or [bar.U] with 1/2 probability each. (6) The relation between the different payoffs is given by 0 < [U.bar] <u< [bar.U] and EU = ([U.bar] + [bar.U])/2 = u. Furthermore, both the sure and the risky payoff can be paid either immediately or after 3 mo.

We denote by [P.sup.j,[tau].sub.i,t] the prospect assigning reward i to the decision maker at time t and reward j to her passive partner at time [tau], where i, j = u, U and t, [tau] = 0, 3. Thus, we allow for 4 x 4 = 16 prospects as displayed in Table 1.

The decision maker is asked to submit a minimum selling price for each prospect, b([P.sup.j,[tau].sub.i,t]), where 0 < [b.bar] [less than or equal to] b([P.sup.j,[tau].sub.i,t]) [less than or equal to] [bar.b]. Then a random draw from a uniform distribution determines an offer p [member of] [[P.bar],[bar.p]] with 0 [less than or equal to] [p.bar] [less than or equal to] [U.bar] < [U.bar] [less than or equal to] [bar.p]. If p [greater than or equal to] b (*), the decision maker sells the prospect and collects the random price p (that is paid immediately after the experiment), while her partner receives nothing. If p < b (*), the decision maker keeps the prospect, and she as well as her partner obtain a realization of the payoffs specified by the prospect. We preserve the riskiness of the final payoff for all possible bids by imposing [p.bar] < [b.bar] < [bar.b] < [bar.p]. Thus, notwithstanding b([P.sup.j,[tau].sub.i,t]) = [b.bar] (or b([P.sup.j,[tau].sub.i,t]) = [bar.b]), the decision maker can never be sure whether she will keep the prospect or not.

A risk-neutral and time-indifferent decision maker who cares only for her own payoff should submit b([P.sup.j,[tau].sub.i,t]) = u = EU for each of the 16 prospects. However, if the decision maker cares for her partner and wants to increase the chances of keeping the prospect, she should report b([P.sup.j,[tau].sub.i,t]) > u. Comparing bids across prospects allows us to disentangle attitudes toward one's own risk and delay from attitudes toward the other's risk and delay.

Procedures

The computerized experiment was conducted at the laboratory of the Max Planck Institute in Jena, Germany, in August 2005. The experiment was programmed using the z-Tree software (Fischbacher, 2007). Participants were undergraduate students from different disciplines at the University of Jena. After being seated at a computer terminal, participants received written instructions (Appendix). Understanding of the rules was checked by a control questionnaire that subjects had to answer before the experiment started.

Thirty-two students participated in a single session, which lasted about 60 min. The experimental currency unit (ECU) was converted into Euro according to 10 ECU = 2.5 [euro]. Average earnings (including a show-up fee of 2.5 [euro]) were 9.6 [euro] when delayed and 8.0 [euro] when immediate. (7)

To collect as many as possible independent observations for all 16 prospects shown in Table 1, the strategy method was used. This means that each participant had to submit 16 reservation prices, one for each prospect, before the roles of decision makers and passive partners were assigned. (8)

The parameter values were equal to those used by Brennan et al. (forthcoming) in order to check for consistency of results as far as possible (i.e., for the top row of Table 1 with no delay of rewards at all). In particular, the lower and upper bounds, [P.bar] and [bar.p], of the uniform distribution from which the random offer prices were selected amounted to 4 and 50 ECU, respectively. (9) Participants could submit any integer value between 8 and 46 ECU. The prospect's parameters were u = 27, [U.bar] = 16, and [bar.U] = 38.

Deferred Payment

As in Anderhub et al. (2001), a problematic feature of our experiment is that some of the payments should be made in the future, that is, 3 mo after the experiment. The corresponding incentive scheme may be ineffective if subjects doubt that they will actually be paid as described in the instructions. To avoid the problem, we used written assurances, attesting that the money would be transferred into the subject's bank account 3 mo after the experiment. (10) In particular, subjects whose payment had to be postponed were required to fill in the details of their bank account, and they received a guarantee of late payment that was signed by an executive representative of the Max Planck Institute. Thus, at the end of the experiment, a subject could receive either ready money (as in the case of the prospect's sale) or a guarantee of late payment.

III. EXPERIMENTAL RESULTS

Figure 1 reports the reservation prices for each individual subject across all 16 prospects.

Decisions are, in general, scattered around the opportunistic risk-neutral prediction given by b([P.sup.j,[tau].sub.i,t]) = 27. Apart from five participants who stick to the same reservation price for all prospects, the remaining participants undertake an "active" approach to decision making, that is, they provide different valuations of the various prospects. Two patterns are recurrent: one focuses on personal risk and varies, mainly, with prospects assigning the lottery to oneself (see, e.g., Subjects 1 and 2), and the other recurrent pattern focuses on own delay and changes depending on whether one's own payment date is 0 or 3 (see, e.g., Subjects 13 and 14). Though some patterns appear more complex than those described above, they present similar features.

Aggregate Analysis

The results are summarized in Figures 2 and 3, which inform on the distribution of choices for each prospect. The 16 graphs in Figure 2 are distributed over four rows and four columns that match those of Table 1. Hence, the four distributions in, for example, the top row of the figure refer to the prospects varying only in the risk component when t = [tau] = 0.

Choices span from the minimum to the maximum of the distribution in 14 of the 16 cases. In most prospects (7 of 16), the mode is 27. The highest mean reservation price (31.16) is paid for the prospect granting sure and immediate payoffs to both the decision maker and her "passive" partner. Distributions tend to be rightward skewed when own reward is certain and immediate and leftward skewed when own reward is risky and/or delayed. The lowest mean reservation prices refer to the four prospects with delayed and uncertain payments to the decision maker. Figure 3 clearly illustrates how the distribution values shift down dramatically for prospects of the form [P.sup.j,[tau].sub.U,3]. (11) These observations already suggest that decision makers show other-regarding concerns when they can rely on a sure and prompt reward, but, in line with previous studies, uncertainty and delay in own reward induce a decrease in reservation prices.

A series of Wilcoxon signed-rank tests (two sided) comparing reservation prices for the prospect with no delay and no risk for both parties and the prospects where, ceteris paribus, one's own payoff is risky and/or delayed confirm that valuations are highly significantly different (p < 0.05 for [P.sup.u,0.sub.u,0] vs. [P.sup.u,0.sub.U,0]; p < 0.001 for [P.sup.u,0.sub.u,0] vs. either [P.sup.u,0.sub.u,3] or [P.sup.u,0.sub.U,3]). The prospect granting an uncertain and delayed reward to oneself but not to the other is also evaluated significantly differently than the prospects with neither own risk nor own delay (p < 0.01 for [P.sup.u.0.sub.U.3] vs. either [P.sup.u,0.sub.u,3] or [P.sup.u,0.sub.U.0]).

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

Next, we check whether reservation prices react also to the other's risk or delay. Wilcoxon signed-rank tests comparing [P.sup.u,0.sub.u,0] with [P.sup.U,0.sub.u,0], [P.sup.u,3.sub.u,0] and [P.sup.U,3.sub.u,0] indicate that valuations are not significantly different when the other's payoff is delayed (p = 0.373 for [P.sup.u,0.sub.u,0] vs. [P.sup.u,3.sub.u,0]). On the contrary, in line with the results of Brennan et al. (forthcoming), a weak significance is registered when introducing risk in the other's payoff (p = 0.049 for [P.sup.u,0.sub.u,0] vs. [P.sup.U,0.sub.u,0]; p = 0.053 for [P.sup.u,0.sub.u,0] vs. [P.sup.U,3.sub.u,0]). The other's situation has no impact on reservation prices when one's own payoff is both risky and delayed (p > 0.1 for all possible comparisons).

The effects of own and other's risk and those of own and other's delay on reservation prices are explored in more detail via a generalized, linear, random effects model (based on a Poisson distribution), regressing average reservation prices on the dummies OwnRisk, OwnDelay, OtherRisk, and OtherDelay. The variable OwnRisk takes value 1 for the prospects with risky payoff for the decision maker (i.e., [P.sup.i,[tau].sub.U,t] for all j, t, and [tau]) and 0 otherwise. OtherRisk equals 1 for the prospects involving risk for the other (i.e., [P.sup.U,[tau].sub.i,t] for all i, t, and [tau]) and 0 otherwise. OwnDelay is 1 when the prospects include delayed payoff for the decision maker (i.e., [P.sup.j,[tau].sub.i,3] for all i, j, and [tau]) and 0 otherwise. Finally, OtherDelay is 1 for the prospects with delay in the other's payoff (i.e., [P.sup.j,3.sub.i,t] for all i, j, and t) and 0 otherwise. Table 2 lists the estimates for the coefficients, standard errors, and z-statistics. (12)

While an increase in one's own risk and payment date tends to significantly reduce reservation prices, a risky or delayed prospect for the partner has no significant impact on behavior. These results corroborate those suggested by the nonparametric tests: decision makers do not react differently to variations in the other's reward but remain particularly attentive to risk and delay in their own payoffs.

[FIGURE 3 OMITTED]

The time preferences with respect to oneself and to the other can be better assessed via estimation of the intertemporal discount factor embedded in the evaluation of alternative prospects. In particular, the average "private" and "social" discount factors ([[delta].sub.own] and [[delta].sub.other], respectively) can be estimated from [P.sup.u,0.sub.u,3] = (P.sup.u,0.sub.u,0])[(1 + [[delta].sub.own]).sup.-t] and [P.sup.u,3.sub.u,0] = ([P.sup.u,0.sub.u,0])[(1 + [[delta].sub.other]).sup.-t], with t = 1/4. The distributions of [(1 + [[delta].sub.own]).sup.-t] and [(1 + [[delta].sub.other]).sup.-t] differ significantly. (13) The estimate for the annual [[delta].sub.own] is 128.70%, whereas that for [[delta].sub.other] is 11.71%, thereby confirming that one is much more impatient when her own reward is delayed than when the other's reward is delayed.

Individual Types

In this section, we investigate the interrelation of other-regarding concerns with attitudes toward other's risk and delay in more detail. First, we define a measure for each of the various attitudes we are interested in, thereby identifying typologies of behavior. Then we examine how types are related.

To assess individual i's concerns toward j's (j [not equal to] i) payoffs, we look at i's valuation of the prospect granting the sure reward u to both i and j at time 0. An "other-regarding" individual i should evaluate the prospect [P.sup.u,0.sub.u,0] at a price higher than u. On the other hand, if i is willing to accept less than u to sell the same prospect, she can be viewed as "spiteful" (see Dufwenberg and Guth 2000).

To measure i's attitudes toward her own risk, we use the difference in reservation prices between the prospects [P.sup.u,0.sub.u,0] and [P.sup.u,0.sub.U,0]. If this difference is positive, the subject can be considered as "risk-averse" since, ceteris paribus, she evaluates the prospect assigning her the sure payoff more than the prospect assigning her the lottery. Alternatively, if [P.sup.u,0.sub.u,0] - [P.sup.u,0.sub.U,0] is negative, subject i can be considered as "risk-seeking." Attitudes toward own delay are measured in a similar way by considering how the valuation of [P.sup.u,0.sub.u,0] compares to that of [P.sup.u,0.sub.u,3]. If [P.sup.u,0.sub.u,0] - [P.sup.u,0.sub.u,3] is positive, the subject is classified as "delay-averse"; if it is negative, she is categorized as "delay-seeking."

Finally, to assess subject i's attitudes toward risk and delay faced by her partner j, we take into account i's preferences for social allocation of risky and delayed prospects. Following Brennan et al. (forthcoming), we capture social orientation by the difference in reservation prices between the prospects [P.sup.u,0.sub.U,0] and [P.sup.U,0.sub.u,0] as far as risk is concerned and the prospects [P.sup.u,0.sub.u,3] a d [P.sup.u,3.sub.u,0] as far as time is concerned. Combining i's risk (delay) attitudes and her social risk (delay) orientation, we can define whether i is self- or other-oriented when allocating risk (delay). In particular, a risk(delay)-averse subject with a positive social risk (delay) orientation can be considered as "other-oriented" with respect to risk (delay): notwithstanding her aversion to risk (delay), she prefers the prospect including risk (delay) for herself rather than for the other. Being other-oriented when i is risk(delay)-seeking requires the corresponding measure to be negative. A brief description of the identified measures for each type is provided in Table 3, which also reports the number of observations that comply with a specific typology.

Computing these measures for each individual and combining them allow us to examine how the different attitudes interact. Table 4 displays Kendall's correlation coefficients between the various attitudes. Risk aversion and delay aversion with respect to own payoffs induce a negative correlation (-0.482 and -0.284) between other-regarding concerns and social orientations, although the correlation is not significant as to the time dimension. The opposite holds for risk-seeking behavior. Given our definition of social orientation, the observed correlation coefficients imply that people who are more other-regarding tend, on average, to be more self-oriented when allocating risky and delayed prospects.

Attitudes toward own risk and delay are always positively related with other-regarding concerns, but only risk (delay) aversion is significantly so. Furthermore, more risk-averse behavior induces, on average, more self-oriented behavior in decisions involving social redistribution of risk (the correlation coefficient between RA and Soc.Or.RA is significantly negative). The same holds for delay-averse behavior. Finally, risk attitudes and time preferences with respect to own rewards are positively correlated (Kendall's coefficient equals 0.208, p = 0.1).

How concerns toward the other's payoffs compare with social orientation to risk and delay is graphically illustrated in Figures 4 and 5, separately for risk-/delay-averse and risk-/delay-seeking subjects.

In line with the correlation analysis, risk-averse subjects tend to cluster in the upper-left quadrant, while risk-seeking subjects are more likely found in the upper-right quadrant (see Figure 4). This confirms that most individuals are concerned about what the other gets but remain self-oriented when allocating social risk. The picture does not change when considering time preferences (see Figure 5).

IV. CONCLUSIONS

In this article, we have studied the interrelation between other-regarding concerns and attitudes toward risk and delay, when risk and delay are borne not only by the actor but also by another person.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

We find evidence of other-regarding concerns when monetary payoffs are certain and immediate for both involved parties. Our results also suggest that agents react to changes in the other's status (in terms of both risk and delay) when their own reward is immediate and certain. However, they disregard the other and focus on their own condition when the latter becomes risky and/or delayed. In our view, this suggests an interesting crowding-out effect in the sense that own risky and delayed decision problems tend to crowd out concerns toward others' problems, possibly due to some cognitive and emotional overload. The regression results reveal, in fact, that only own risk and delay have significant effect on individual behavior. This may mean that the function [U.sub.i] reported in the Introduction is additively separable and takes the form

(2) [U.sub.i] = [summation over (x[member of]X)] Prob{x}[g.sub.i]([r.sup.0.sub.i](x), [r.sup.1.sub.i](x))

+ [h.sub.i](Prob{x}[g.sub.i]([r.sup.0.sub.j](x), [r.sup.1.sub.j](x))),

that is, participants mind very much risk and timing of their own reward but rely on expected total rewards when engaging in other-regarding considerations (at least, when risk and delay affect them). Again, the two evaluation functions [g.sub.i](*) and [h.sub.i](*) should depend positively on their arguments for nonspiteful decision maker i. This leaves some flexibility for neoclassical repairs and provides more specific information about how we decide when risk and timing of our own and another person's rewards are affected.

In agreement with previous research, we find that people are rather impatient when their own reward is delayed. But this strong impatience is not projected upon the other. Furthermore, in line with Anderhub et al. (2001), risk attitudes and time preferences with respect to own rewards are positively correlated: agents who are risk-averse (seeking) when their own payoffs are uncertain tend to be delay-averse (seeking) when their own payoffs are deferred. Hence, if the function g,{*) is concave in its arguments, it is usually also more reactive to [r.sup.0.sub.i](x) than to [r.sup.1.sub.i] (x).

Finally, our type analysis reveals that while exhibiting other-regarding preferences with respect to the other's expected payoff, individuals are mainly self-oriented as to social allocation of risk and delay. This is consistent with findings of Brennan et al. (forthcoming) indicating that risk in what others get is much less important than own risk, even for those who are relatively other-regarding.

ABBREVIATIONS

AIC: Akaike Information Criterion

ECU: Experimental Currency Unit

APPENDIX: TRANSLATED INSTRUCTIONS

Welcome and thanks for participating in this experiment. You receive 2.50 [euro] for having shown up on time. Please read the following instructions carefully. From now on any communication with other participants is forbidden. If you have any questions or concerns, please raise your hand. We will answer your questions individually. The unit of experimental money will be the ECU (Experimental Currency Unit), where 1 ECU = 0.25 [euro].

In this experiment you will be randomly paired with another participant, whose identity will not be revealed to you at any time. In the following, we will refer to the person whom you are paired with as "the other."

You will face 16 different prospects, each of which pays to you and to the other some positive amounts of ECU. These payments can be either certain or uncertain, and either immediate or deferred.

The certain payment gives 27 ECU for sure. The uncertain payment consists of a lottery giving either 16 ECU or 38 ECU, where both amounts are equally likely.

Four cases are possible depending on whether the payment is 1) certain for both you and the other; 2) uncertain for both you and the other; 3) certain for you and uncertain for the other; 4) uncertain for you and certain for the other.

The immediate payment will be paid out today; i.e., ECU will be converted to Euros at the end of the experiment, and the obtained amount will be paid to you and/or to the other in cash straight away. The deferred payment will be paid out later; i.e., ECU will be converted to Euros at the end of the experiment, but the obtained amount will be transferred to your and/or the other's bank account in three months. You and/or the other will receive a guarantee of late payment at the end of the experiment, after filling out a form concerning your bank account's details.

As before, four cases are possible depending on whether the payment is 1) immediate for both you and the other; 2) deferred for both you and the other; 3) immediate for you and deferred for the other; 4) deferred for you and immediate for the other.

Combining the 4 cases related to the time of the payments with the 4 cases related to their certainty yields the 4 x 4 = 16 prospects that you will face. In particular, these 16 prospects are:

1. You get 27 ECU for sure now, and the other gets the lottery now.

2. You get 27 ECU for sure later, and the other gets the lottery later.

3. You get 27 ECU for sure now, and the other gets the lottery later.

4. You get 27 ECU for sure later, and the other gets the lottery now.

5. You get the lottery now, and the other gets 27 ECU for sure now.

6. You get the lottery later, and the other gets 27 ECU for sure later.

7. You get the lottery now, and the other gets 27 ECU for sure later.

8. You get the lottery later, and the other gets 27 ECU for sure now.

9. Both you and the other get 27 ECU for sure now.

10. Both you and the other get 27 ECU for sure later.

11. You get 27 ECU for sure now, and the other gets 27 ECU for sure later.

12. You get 27 ECU for sure later, and the other gets 27 ECU for sure now.

13. Both you and the other get the lottery now.

14. Both you and the other get the lottery later.

15. You get the lottery now, and the other gets the lottery later.

16. You get the lottery later, and the other gets the lottery now.

What You Have to Do

Your task (as well as the task of each other participant) is to report the lowest amount of ECU for which you would be willing to sell each prospect. In other words, you have to state a minimum selling price for each of the 16 prospects. Each of your sixteen choices must be not smaller than 8 ECU and not greater than 46 ECU. Furthermore, it must be an integer number (i.e., 8, 9, 10, ..., 44, 45, 46).

Your Payoffs

Your payoff depends on the choices made by the two members of the group, and on three random choices made by the computer. These random choices determine an "active" player, a "relevant" prospect, and an "integer" between 4 and 50. More specifically, payoffs are determined as follows.

(I) After you and the other participant have reported the minimum selling price for each prospect, the computer will select either you or the other participant as the "active player." The minimum selling prices reported by the active player will affect the payoffs of the group, whereas the minimum selling prices reported by the other (non-active) participant do not have any effect.

(II) Once the active player has been determined, the computer will select one of the sixteen prospects faced by this player as the "relevant prospect," where all sixteen prospects are equally likely.

(III) Finally, the computer will randomly choose an "integer" between 4 and 50. You can think of this choice as drawing a ball from a bingo cage containing 47 balls numbered 4, 5, ..., 50. Any number between 4 and 50 is equally likely.

Your final payoff is computed by comparing this random integer to the minimum selling price reported by the active player (either you or the other participant) for the relevant prospect.

* If the random integer is smaller than the minimum selling price reported by the active player for the relevant prospect, the active player keeps the relevant prospect and the two members of the group obtain the payments specified by it.

* If the random integer is equal to or greater than the minimum selling price reported by the active player for the relevant prospect, the active player sells the relevant prospect and earns an amount of ECU equal to the random integer, which will be paid out to him/her in cash today. In this case, the other (non-active) player earns nothing.

If the active player does not sell the relevant prospect and this prospect consists of a lottery, the lottery will be played for real today although its outcome may be paid out in three months.

Example

Suppose that the computer chooses you as the active player, and that the prospect paying to you 27 ECU for sure now and to the other either 16 or 38 ECU later is the relevant prospect. Suppose also that you have reported a minimum selling price of 20 ECU for that particular prospect.

* If the computer chooses the integer 18, you keep the prospect (because 18 < 20). This implies that you get 27 ECU today, and the other obtains either 16 or 38 ECU in three months, where these two amounts are equally likely.

* If the computer chooses the integer 22, you sell the prospect (because 22 > 20). This implies that you get 22 ECU today, and the other participant earns nothing.

Before the experiment starts, you will have to answer some control questions to verify your understanding of the rules of the experiment.

Please remain quiet until the experiment starts and switch off your mobile phone. If you have any questions, please raise your hand now.

MATTEO PLONER, We thank Sebastian Briesemeister for writing the program for the experiment and Bettina Bartels and Frederic Bertels for their valuable assistance during the experimental session.

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Guth: Director, Max Planck Institute of Economics, Strategic Interaction Group, Kahlaische Strasse 10, D-07745 Jena, Germany. Phone 0049-3641-686620, Fax 0049-3641-686667, E-mail gueth@econ.mpg.de

Levati: Research Associate, Max Planck Institute of Economics, Strategic Interaction Group, Kahlaische Strasse 10, D-07745 Jena, Germany, and Dipartimento di Scienze Economiche, Bari University, Via C. Rosalba 53, I-70124 Bari, Italy. Phone 0049-3641686629, Fax 0049-3641-686667, E-mail levati@econ. mpg.de

Ploner: Research Fellow, LEM, Sant' Anna School of Advanced Studies, Piazza Martiri della Liberta 33, I-56127 Pisa, Italy. Phone 0039-461-882246, Fax 0039-461-882222, E-mail ploner@sssup.it

(1.) See, for example, Anderhub et al. (2001); Chesson and Viscusi (2003); Green, Myerson, and Ostaszewski (1999); and Mazur (1997).

(2.) For instance, pension funds should reduce risky options if investors in such funds, who do not mind delaying rewards, are rather risk-averse.

(3.) Smith (1982) referred to experiments, where the primary purpose is to discover empirical regularities in areas where no theory exists as heuristic.

(4.) This "replication" of attitudes may be due to false consensus effects (see Ross, Greene, and House 1977) or to a Kantian imperative suggesting how oneself and all others should cope with risk. Brennan et al. (forthcoming) discuss the issue in more details.

(5.) We are interested more in the differences among individual evaluations of the several prospects than in absolute evaluations of each prospect. Thus, we do not check whether our findings are robust with respect to the method of eliciting certainty equivalents. Samuelson and Zeckhauser (1988) and Tietz (1992) provided experimental evidence on the endowment effect.

(6.) By assigning equal probabilities to [U.bar] and [bar.U], we try to avoid the possibility of probability transformations as in cumulative prospect theory (see, e.g., Tversky and Kahneman 1992).

(7.) Note that only the immediate average earnings include zero payments to the passive partner in case the prospect is sold.

(8.) In order to avoid portfolio diversification effects, participants were paid according to one choice only.

(9.) Although there is no (normative) need of uniformity, this has been assumed because it seems the most unbiased and understandable (by the participants) distribution.

(10.) The German system did not allow us to use "deferred checks" as Anderhub et al. (2001) could do in Israel.

(11.) These prospects together with [P.sup.U,0.sub.u,3] (the mean evaluation of which is 24.97) are the only ones that are evaluated, on average, less than 27.

(12.) We estimated several models to test the interaction between the various explanatory variables. The reported model fits better the data on the basis of the Akaike Information Criterion (AIC). Although the best AIC was observed for the model omitting OtherDelay, we preferred to include this variable for completeness of information.

(13.) The p value obtained from the Wilcoxon rank-sum test with continuity correction is 0.004.

TABLE 1
The 16 Prospects Evaluated by Each Participant

 Risk

Delay No One Own

No one [p.sup.u,0.sub.u,0] [p.sup.u,0.sub.U,0]
Own [p.sup.u,0.sub.u,3] [p.sup.u,0.sub.U,3]
Other [p.sup.u,3.sub.u,0] [p.sup.u,3.sub.U,0]
Both parties [p.sup.u,3.sub.u,3] [p.sup.u,3.sub.U,3]

 Risk

Delay Other Both Parties

No one [p.sup.U,0.sub.u,0] [p.sup.U,0.sub.U,0]
Own [p.sup.U,0.sub.U,3] [p.sup.U,0.sub.U,0]
Other [p.sup.U,3.sub.U,0] [p.sup.U,0.sub.U,0]
Both parties [p.sup.U,3.sub.U,3] [p.sup.U,0.sub.U,0]

TABLE 2
Generalized Linear Mixed Effects Regression
on Reservation Prices

 Coefficient Standard z Pr([absolute
 Error value of z])

Intercept 3.485 *** 0.028 124.01 0.000
OwnRisk -0.098 *** 0.017 -5.770 0.000
OwnDelay -0.142 *** 0.017 -8.376 0.000
OtherRisk -0.020 0.017 -1.212 0.225
OtherDelay 0.002 0.017 0.144 0.885

*** 0.1% significance level.

TABLE 3
Measures of Individual Attitudes toward
Payoffs, Risks, and Delays

Attitudes Description n

Other-regarding [P.sup.u,0.sub.u,0] - u > 0 20
Spiteful [P.sup.u,0.sub.u,0] - u < 0 5
Risk-averse [P.sup.u,0.sub.u,0] - [P.sup.u,0.sub.U,0] 16
 > 0
Risk-seeking [P.sup.u,0.sub.u,0] - [P.sup.u,0.sub.U,0] 7
 < 0
Delay-averse [P.sup.u,0.sub.u,0] - [P.sup.u,0.sub.u,3] 18
 > 0
Delay-seeking [P.sup.u,0.sub.u,0] - [P.sup.u,0.sub.u,3] 2
 < 0
Risk other-oriented [P.sup.u,0.sub.U,0] - [P.sup.U,0.sub.u,0] 0
Risk self-oriented [P.sup.u,0.sub.U,0] - [P.sup.U,0.sub.u,0] 22
Delay other-oriented [P.sup.u,0.sub.u,3] - [P.sup.u,3.sub.u,0] 1
Delay self-oriented [P.sup.u,0.sub.u,3] - [P.sup.u,0.sub.u,3] 19

Notes: n denotes the number of observations. We do not report
the (neutral) cases in which the values were 0.

TABLE 4
Kendall's Correlation Coefficients between Attitudes

Attitudes OR Soc.Or.RA Soc.Or.RS Soe.Or.DA

Soc.Or.RA -0.482 ***
Soc.Or.RS -0.617 *
Soc.Or.DA -0.284
Soc.Or.DS -
RA 0.637 *** -0.735 ***
RS 0.264 0.098
DA 0.346 ** -0.599 ***
DS 1.000

Notes: Missing values are due to low number of observations.
DA = delay-averse; DS= delay-seeking; OR = other-regarding;
RA = risk-averse; RS = risk-seeking;
Soc.Or. = social orientation.

*** 1% significance levels.
** 5% significance levels.
* 10% significance levels.