Loss Aversion and Reference-Dependent Preferences in Multi-Attribute Negotiations
HENNER GIMPEL
Institute of Information Systems and Management, University of Karlsruhe, Englerstr 14, 76131 Karlsruhe, Germany
(E-mail: gimpel@iism.uni-karlsruhe.de)
Abstract
Negotiation analysis and game theoretic bargaining models usually assume parties to have exogenous preferences from the beginning of a negotiation on and independent of the history of offers made. On the contrary, this paper argues that preferences might be based on attribute-wise reference points changing during the negotiation process. Aversion against losses relative to the reference point determines negoti- atorsdecisions in the negotiation and after its termination. The emergence and implications of reference points in a negotiation context are motivated, exemplified, and modeled formally. Furthermore, data from an internet experiment on endogenous preferences in bilateral multi-attribute negotiations is presented.
The data supports the behavioral model.
Key words: behavioral biases, experimental economics, loss aversion, negotiation analysis, prospect theory, quasi-endowment effect
1. Introduction
In a negotiation, two individuals are interested in reaching one of several possible agreements, but their preferences over these agreements are not completely identical.
In multi-attribute negotiations, studied here, parties usually have the possibility to simultaneously negotiate over several attributes and to search for integrative potential. Negotiators play a non-constant-sum game.
Empirically, negotiators oftentimes fail to reach mutually beneficial agreements in integrative multi-attribute negotiations and – even if they reach an agreement at all – it is oftentimes non-Pareto optimal (Pruitt 1981; Raiffa 1982; Vetschera 2004; Block et al. 2006). It appears that there is a serious behavioral bias preventing Pareto- optimal solutions, namely the quasi-endowment effect leading to endogenous pref- erences changing over the course of the negotiation process. The two questions at hand are:
1. Do preferences change during a negotiation upon receiving an offer?
2. If so, how do negotiators update their preferences?
These two questions are examined in the following. To this end, the remainder of the paper is structured as follows: at first, Section 2 surveys related work. The notion
of a quasi-endowment effect in negotiations is then outlined in Section 3. Section 4 illustrates how negotiators might update their preferences during a negotiation and then formalizes this process in a theoretical model. Section 5 reports on an internet experiment testing for endogenous preferences, and finally, Section 6 concludes.
2. Related Work
Literature on negotiation analysis brought up several explanations for empirically observed negotiator behavior. The lack of Pareto-optimal outcomes, for example, is frequently attributed to cognitive biases like the fixed pie illusion, the illusion of conflict, reactive devaluations, fairness perceptions, and the self-enhancement bias.
See Bazerman et al. (2000) for an overview. The offer-dependent preference con- struction outlined in the following sections is not in conflict with these established behavioral patterns and biases but introduces a new perspective on negotiator decision making. All of these effects might interact with each other.
Reference-dependent evaluation of offers is related to anchoring which is a common mistake in negotiations (Bazerman and Neale 1992, Chapter 4). However, studies on anchors in negotiations regard the initial positions of bargainers, i.e. their opening offers, as anchors. How negotiators adapt anchors and reference points gradually during the process of negotiating is not resolved up to know.
2.1. Prospect theory
Furthermore, the influence of reference-dependent evaluation on multi-attribute decision making is well-known since Tversky and Kahneman (1991) extended the concept of reference points from risky choices to riskless multi-attribute choices.
The authors cover the effect of reference-dependence in great detail without addressing the origin of reference points in a multi-attribute decision space. Ko¨szegi and Rabin (2006) highlight the lack of explanations for the origin of reference points by stating that ‘predictions of reference-dependent theories also depend crucially on the understudied issue of what the reference point is.The present paper takes up the established reference point concept and studies its emergence in bilateral negotia- tions.
Curhan, Neale and Ross (2004) study preferences changing during a negotiation with a focus on dissonance and self-perception theory. The basic idea of endoge- nously constructed preferences is related to the present study. Yet the authors do not address endowment effects and loss aversion and therefore have a different perspective on a related phenomenon.
2.2. Game theory
Besides the negotiation analytic approaches outlined above, game theory deals with bilateral bargaining. Game theoretic models of negotiations with reference-depen- dent preferences are build by Shalev (2002), Compte and Jehiel (2003), Li (2004), and
Hyndman (2005). Their players utility depends on a reference point that either changes as a function of offers received as advocated in the following sections or from one negotiation to the next one. All these papers, however, focus on single- attribute negotiations and their equilibrium results do not straightforwardly apply to multi-attribute negotiations.
Finally, and again for the single-attribute case, Kristensen and Ga¨rling (2000) find experimental evidence on subjects evaluating offers relative to adaptive reference points. These single-attribute studies strengthen the assumption that related effects might emerge in multi-attribute negotiations as well. This is outlined and tested in the remainder of the paper.
3. Quasi-Endowment Effect in Negotiations
Integrative bargaining is oftentimes regarded as joint problem solving and jointly exploring the space of potential agreements; search techniques like logrolling and trade-off heuristics for finding mutually beneficial agreements are proposed (Tajima and Fraser 2001; Faratin, Sierra and Jennings 2002). However, many practical heuristics and advices how to negotiate have the limitation of assuming preferences to be exogenously given and fix during the negotiation process. This may not be the case in many real life negotiations.
The value of a good to an individual increases when the good becomes part of the individuals endowment (e.g. Kahneman, Knetsch and Thaler 1990). This effect – termedendowment effect– grows stronger with duration of ownership and prevails after termination of ownership (Strahilevitz and Loewenstein 1998). During a negotiation process, parties constantly gain virtual possession on single attributes and afterwards feel entitled to the specific value on this attribute. In a study on auctions, Heyman, Orhun, and Ariely (2004) term a related phenomenon of the attachment to an un-owned item quasi-endowment effect. The quasi-endowment influences the reference point and negotiators then value the counterpartys pro- posals relative to this reference point. The reference point is adjusted attribute-wise during the negotiation process. A proposal which is seen as a loss relative to the current reference point on one or more attributes, is devalued: preferences are endogenously changing and depend on the history of the specific negotiation. Each single offer proposed to the counterparty might change the counterpartys prefer- ences and therefore might destroy potential agreements. Searching the agreement space extensively becomes prohibitive.
The status-quo is oftentimes assumed to be the reference point. However, Ko¨szegi and Rabin (2006) argue that instead an expected future state rather than the current state might serve as reference point. This supports the idea of a quasi-endowment effect in auctions and negotiations. Even if a negotiator does not yet own an item, the expectation to potentially own it in the future might influence the negotiators ref- erence point. It is reasonable to expect that offers during a negotiation influence the expectation in the negotiations outcome.
Block et al. (2006), among others, analyze data gathered with the Inspire nego- tiation support system: in a pre-negotiation phase preferences are elicited, then the negotiation is conducted, and – if an inefficient agreement is reached – Pareto- improvements are presented to the negotiators by the Inspire system. 58% of the agreements in their data set are inefficient with respect to the preferences elicited in the first phase. However, only 23.4% of negotiators are willing to accept the pro- posed Pareto-improvements. At first sight this seems puzzling and irrational; but if preferences are endogenous and change during the negotiation, the systems proposal in the post-settlement phase may be unacceptable with respect to the ex-post pref- erences. This might explain the low acceptance rate. Other explanations are outlined and tested empirically by Block et al.
Vetschera (2004) analyzes utility functions, offers made, and final agreements in a related set of Inspire negotiations. He reports that in about 25% of the cases, negotiators violated consistency in the sense that their observed behavior did not fit the ex-ante elicited utility functions. Negotiators inconsistency could possibly be tracked back to a changed preference structure by the time the seemingly inconsis- tent behavior is observed. Again, endogenous preference changes are not the only possible explanation for the behavior. Nuisance in the specific utility elicitation technique employed in the first phase of negotiation support might, for example, serve as a reason for the observed inconsistencies as well. Other reasons are presented by Vetschera.
The aim of the study is not to test whether behavior recorded by Inspire can really be tracked to endogenous preferences but rather to test for the endogeneity in a specifically tailored internet experiment. To this end, endogenous reference-depen- dent preferences and the process of attribute-wise updating reference points is exemplified and modeled in the following before the experiment is outlined there- after.
4. Endogenous Preferences
The introduction presents two questions: do negotiatorspreferences change, and if so, how do they change. This section hypothesizes on the answer to the second question, i.e. the specific process of how preferences change. Whether this hypo- thetical process is in congruence with what really happens in a negotiation, is then analyzed in Section 5.
4.1. Graphical example
Figure 1 displays a bilateral two-attribute alternating-offer negotiation in a sequence of Edgeworth-boxes. The two negotiators are labeled S (she) and H (he) and the two attributes are namedAandB. The attributes are normalized to the unit interval and both parties prefer more to less on both attributes. The share of negotiator S is measured from the lower left corner of the box. Accordingly, negotiator Hs share is
measured from the upper right corner. For the sake of simplicity, only negotiator S has a shifting reference point in this example.
Figure 1a shows the initial condition at time t= 0; time is indicated by super- scripts. Three of negotiator S’s indifference curves are displayed and the associated utility levels are indicated at the top of the figure; u0S;3>u0S;2>u0S;1 holds in this example. Furthermore, S has a reference pointr0Swhich might initially be at zero on both attributes and S makes an offer o0S at t= 0. Here, S is quite greedy and demands the best possible outcome for herself.
reference point S indifference curve S offer from S offer from H a)
c)
e)
b)
d)
Figure 1. Bilateral negotiation in an Edgeworth box.
Att= 1 (1b), H makes a counteroffer anywhere in the interior of the Edgeworth box. It is namedo1H.
Att= 2 (1c), it is Ss term again and the quasi-endowment effect applies the first time: S sees what she is offered, namelyo1H, and feels entitled to this level ofAandB.
Not, that it would already be hers – after all the negotiation is still going on – but she now feels a quasi-endowment and might assume that she never has to accept less on any attribute. Ss reference point shifts to rS2 which is identical witho1H here. Fur- thermore, S makes the new offero2S.
Three things about shifting the reference point are noteworthy here: First, rS2 equals o1H in this example. This is not necessarily the case and the reference point could be anywhere between r0S and o1H as in the model presented in Section 4.2.
Second, it is not only that S expects to get a utility of at leastu0S;1. S expects to get at least as much on A, asr2Sis in this attribute and at least as much on B, asr2Sgives.
Third, this process of shifting the reference point will go over the entire negotiation and there will be a history of quasi-endowment effect (cf. Strahilevitz and Loe- wenstein 1998).
Att= 3 (1d), H rejectso2Sand counters witho3H. Subsequently this is rejected by S att= 4 (1e). The negotiation goes on, but the interesting point is reached here, so the description ends.
The rejection ofo3His somewhat puzzling. With respect to Ss preferences att= 0, given by the dotted indifference curves,o3H gives utility u0S;3 which is strictly more thanu0S;2. So H offers S a higher utility att= 3, than S asked for att= 2. However, Ss preferences fromt= 0 might no longer be the current preferences if S evaluates o3H with respect to rS2. On attribute B,o3H is much better for S, then the reference point; on the other hand, it is a little worth on A. Every potential agreement worse thanrS2 on any attribute is shaded in Figure 1e.
If S would be concerned with (ex-ante) utility only, she would accept o3H, as the huge increase in B over-compensates the small loss in A. But if she cares about reference points and attribute-wise losses or gains, she (irrationally?) rejectso3H. The decision not to accept any offer worse than the reference point on any attribute is an extreme case in this example. In the following model, different attributes are still traded-off against each other. Nevertheless, trade-offs and indifference curves change depending on the reference point.
4.2. Theoretical model
Two aspects have to be modeled for analyzing attribute-wise reference points: On the one hand, the emergence of reference points and, on the other hand, the implications of reference points for subsequent choices in a negotiation.
Consider a bilateral alternating-offers negotiation among negotiators S and H.
One of them, without loss of generality S, starts with an initial offer at timet= 0.
Afterwards, they take turns in making offers; S does so at timet= 2, 4, 6, ... and H at timet= 1, 3, 5, ... until one of them accepts the other ones offer. The following presentation focuses on S but can be applied to H analogously.
4.2.1. Agreement space
Let X be the agreement space, i.e. the set of all possible agreements that can be reached by negotiators S and H. Furthermore, let each pointx2Xbe characterized according to (potentially) several attributes. Thus, x is a vector x = (x1,x2,...,xn) withn‡1 attributes and valuesxk‡0"k 2{1,2,...,n}. Finally, assume that for each single attribute negotiator S prefers higher values to lower values given that all other attributes are unchanged.
The assumptions of non-negative values and Ss preference for higher instead of lower values can always be fulfilled by rescaling and changing the orientation of an attribute. The only assumption that really limits applicability is that Ss preferences have to be monotonic in each single attribute, at least in the range included in the agreement space.
4.2.2. Emergence of reference points
Negotiator S evaluates each potential agreement x2X with respect to a time- dependent reference pointrt= (rt1,rt2,...,rtn)2X. The reference point is influenced by the quasi-endowment effect; it is updated each time S receives an offer. The initial reference point at the beginning of the negotiation is assumed to be the origin of the agreement space:
rk0¼0 8k2 f1;. . .;ng
Subsequently, at each timet= 2, 4, 6,... and for each attributek= 1,...,nSs new reference is given by
rkt ¼ rkt2þfkðot1k rt2k Þ ifot1k rkt2;
rkt2 otherwise
whereot-1kis the last offer made by H andfk(Æ) is a strictly increasing function such thatfk(0) = 0 andfk(a)£a"a‡0. The formalization of the reference point update is in analogy to the single-attribute model by Compte and Jehiel (2003).
The intuition of the above formula is as follows: Each time S receives an offer that grants more on attributekthan she already assumed as entitlement (ot-1k‡rt-2k), she updates her reference point on that attribute. The update is a shift in the direction of the current offer (fk(Æ)‡0) without going beyond the offer (fk(a)£a). The specific functional form offk(Æ) likely depends on personal characteristics of the negotiator as well as on the specific attributek.
Note that the standard model of exogenously given and fix preferences is a special case of the model outlined here with fk(a) = 0 " a‡0,k2{1,...,n}. The partial adaptation to a new offer is in line with the finding that reference point adaptation is not all or nothing but a slowly progressing process (Strahilevitz and Loewenstein 1998). Furthermore, the attribute-wise update functionfk(Æ) takes into account that the endowment effect is rather strong for consumption goods and virtually non- existent for resale goods and money (e.g. Kahneman, Knetsch and Thaler 1990).
Finally, the fact that the update functions might differ across negotiators integrates
the fact that, for example, experience influences the strength of the endowment effect (e.g. List 2003).
4.2.3. Loss aversion
A reference structure is a family of indexed preference orderingsrt wherexrt y stands for agreementxbeing strictly preferred toyevaluated from reference pointrt with x, y, rt2X (Tversky and Kahneman 1991). Following standard textbook assumptions, the relationrt is assumed to be asymmetric and negatively transitive;
with these assumptions, indifferencert and an utility representation urtðxÞfollow from strict preference as for non-indexed preference orderings (Kreps 1990, Chapter 2).
The following definition of loss aversion is exemplified by Figure 2. Pointsxandy are the ones to be compared and pointsrt-2and rtare reference points at different times. A reference structure satisfies loss aversion if " x, y, rt-2, rt2X, k, l2{1,2,...,n}, and k„ l with xk‡ rtk>rt-2k=yk, yl>xl, and rtl=rl
t-2 the fol- lowing condition holds:xrt2 y)xrty(Tversky and Kahneman 1991). Note that
‡, >, and = refer to the numerical values on single attributes whereasand~are relations of multi-attribute agreements.
As mentioned before, Figure 2 exemplifies the definition. Assume that at time t)2 the negotiator was indifferent when evaluatingxandyfrom reference pointrt-2, i.e.xrt2y. Both points lie on the same indifference curve labeledurt2. At timet, the reference point is updated as described above. Seen fromrt, the advantageyhas on attributeland the disadvantageyhas on attributekdo no longer cancel out. Losses loom larger than gains and, thus, xrt y. Thus, the negotiators preference over different possible agreements changes as the reference point changes.
Several studies support the existence of loss aversion in multi-attribute choice, e.g.
the evidence presented by Tversky and Kahneman (1991).
4.2.4. Implications for negotiations Under the assumptions that
1. a negotiator evaluates points in a multi-attribute agreement space relative to a reference point,
Figure 2. Implications of reference points for multi-attribute preferences.
2. the reference point changes depending on offers received as outlined above, and 3. the negotiator is loss averse on single attributes as outlined above,
one can predict the change in the negotiators preferences during a negotiation. On each attribute, the reference point moves towards the counterpartys offers. Thus, differences in an attribute on which the counterparty frequently offers high values tend to be evaluated as losses rather than gains. Hence, such attributes become more important in trading off different attributes during the negotiation and in subsequent choices. The interesting question now is, whether such patterns can be found in empirical data on negotiations.
5. Experiment
The notion of endogenous reference-dependent preferences is tested in an internet experiment on multi-attribute negotiations. The main challenge for testing on endogenous preferences is, that subjectspreferences are neither directly observable, nor can they be elicited reliably, at least not multiple times from the same subject.
Hence, within-subject comparisons of preferences at different times are not possible and a between-subject comparison is applied. Obviously, a between-subject com- parison is complicated as well, as preferences naturally differ across subjects.
However, with a randomized assignment to treatments a between-subject design appears appropriate.
5.1. Experiment Setup
The basic idea of the experiment is to confront subjects in different treatments with different negotiation strategies and to measure their ex-post preferences. As the assignment of subjects to treatments is randomized, there should be no systematic differences in the subjects ex-post preferences between treatments except if the preferences are influenced by the negotiation process itself. Thus, systematic differ- ences between treatments support the hypothesis that preferences are endogenously formed in a negotiation.
The operationalization is as follows: subjects negotiate bilaterally with a software agent on a tenancy contract. The monthly rent, the availability of an elevator, and the existence of a balcony are negotiable attributes in the tenancy contract. All other attributes like the size of the apartment, the available furniture, the location, etc. are non-negotiable and fixed in the subjectsinstructions. After negotiating, the subjects willingness to accept a change in a single attribute of the negotiated agreement is elicited and compared between treatments.
The experiment took place in April 2005 at the University of Karlsruhe, Ger- many. The procedure was as follows: subjects were recruited in an undergraduate class on business administration; the lecturer briefly promoted participation and sheets of paper with the login data were handed out. Subjects then logged in from home over the internet via a web browser. A subjects session starts with two pages of
instructions followed by a questionnaire to ensure understanding of the instructions.
Then the subject negotiates over a tenancy contract. The strategies will be described afterwards. The entire procedure is explained to subjects in the experiments instructions. The full instructions, the questionnaire to check for understanding, and screenshots from the system (all in German) are available upon request.
5.1.1. Alternating-offers
During the negotiation, offers for contracts are exchanged between the two parties.
A software agent representing the landlord starts with an initial offer and subse- quently the parties alternate in deciding on the acceptability of an offer and pro- posing a counteroffer after rejecting an offer. If a maximum of six offers per party is reached, i.e. overall twelve offers, without any of the offers being accepted, an arbitrator steps in and proposes an agreement which is binding for the two parties.
The subject can, however, improve its contract by accepting a second landlords proposal which always is strictly better than the arbitrators proposal.
5.1.2. Measurement of ex-post preferences
After the negotiation terminates, a second landlord steps in and offers an alternative contract. This second landlord serves for giving subjects in different treatments the same final contract and, thus, to allow for a blocked analysis of the data. Each subject accepted the second landlords offer, as it is by design strictly better than any agreement the subject could have with the first landlord. From this contract, the subjects willingness to accept a worsening in either the attribute elevator (attribute A) or the attribute balcony (attribute B) is elicited by asking the subject to solve two indifference equations for the respective monthly rent, i.e. the monthly rent is taken as numeraire.
The agreement space in the experiment is X= {x= (A,B,R)|A,B2{yes,no}, R2[0,999]}. The final contract of each subject i, i.e. the contract with the second landlord, is (yes,yes,Ri), whereRidiffers across subjects. The indifference equations to solve are (yes,yes,Ri)~(yes,no,Ri,B)~(no,yes,Ri,A).Riis given via the offer of the second landlord and the subject entersRi,AandRi,B. From this, one can calculate a subjects willingness to accept (WTA) a worsening in either attribute AorB. They are defined as follows:
WTAi;A¼RiRi;A and WTAi;B¼RiRi;B
These WTA values are analyzed in the following.
Finally, a subjects session ends with retrieving some demographic data, thanking the subject, and asking for general comments on the experiment.
5.1.3. Incentives
A week after recruitment, 50 euros were awarded to one of the participants in a lottery held in the lecture. Each participant had the same chance of winning the lottery which was not related to the subjectsspecific choices during the experiment.
Therefore, the lottery served as an incentive for participation but was not a salient reward as oftentimes used in experimental economics.
A critical point in analyzing the data gathered in the experiment is whether the subjects were sufficiently motivated to participate and sincerely considered the choices presented to them. As the financial reward was non-salient, this might be questioned. However, casual observations indicate that subjects were motivated.
Immediately accepting the first landlords first offer would have been the fastest way to secure participation in the lottery. However, none of the subjects chose this least- effort-way and just one subject accepted the landlords second offer. All other sub- jects eagerly negotiated. Overall, 47 students logged in at the experimental system;
this is about 90% of the students addressed in the lecture. In four cases, the session was abandoned by the respective subject and one observation was discarded as the subject used the web browsers forward and backward functionality. In the instructions, subjects were explicitly asked not to use these functions as it allows them to retract to a previous offer by the agent for accepting it after seeing the agents next offer. Overall, there are 42 valid observations and the subjects intrinsic moti- vation for participating sincerely appears to be rather good.
5.1.4. Treatments
The experiment embraces four treatments, i.e. four classes of strategies. Strategies in treatment 1 (T1) have in common that each single offer grants an elevator to the subject, i.e.A=yesatt= 1,3,.... In treatment 2 (T2), no offer grants an elevator to the respective subject, i.e.A=noat t= 1,3,.... The values of the other attributes are randomized with a slight tendency to making concessions as the negotiation progresses. Treatments 3 and 4 (T3 andT4) utilize the strategies employed inT1 and T2 with the difference that attributes AandB are reversed, i.e.T3 always offers a balcony to the subject while randomizing the values of the remaining two attributes andT4 never offers a balcony. The software agents simply present the sequence of predefined offers and do not accept any subjects offer unless it dominates either a previous offer by the agent or the next offer to be made.
5.2. Theoretical predictions
The model presented in Section 4 is based on attribute-specific and strictly increasing update functionsfk(Æ). To determine the exact location of a subjects reference point depending on the agents offers, one needs to know the specific functional form of fk(Æ) for every attribute. However, the relative location of different reference points to each other is independent from the specific functions. Thus, the relative location of hypothesized reference points for different subjects can be calculated without assuming specific update functions.
Figure 3 displays these relative locations with respect to the attributesAandB.
The axes do not have any marks in between 0 and 1, as this would depend on the functional form of the respectivefk(Æ). The third attribute, i.e. the monthly rent, is omitted here, as it is not used as treatment variable. Solid circles represent possible
reference points in T1, triangles in T2, squares in T3, and diamonds stand for possible reference points inT4. One clearly sees thatT3 andT4 are derived fromT1 and T2, respectively by exchanging attributes A and B. For data analysis the treatments will be grouped accordingly. For each single treatment, there are different possible reference points, as the duration of a negotiation is determined by the subject. In all treatments, the reference point starts at the origin and gradually moves towards the upper right corner when the subject receives an offer by the agent.
The numbers close to the potential reference points indicate how many subjects are expected to end at this specific point. This information takes the observed duration of each subjects negotiation in account.
Figure 3 suggests that the reference points of subjects inT1 andT2 are about the same with respect to attributeB but very different on attributeA. Attribute A is termedreference attribute forT1 andT2. Subjects in T1 are expected to feel more entitled to getting an apartment with an elevator than subjects inT2. The measure WTAA captures how strongly subjects perceive a change from an apartment with balcony and elevator (the upper right corner of Figure 3) to an apartment with balcony but without elevator (the upper left corner of Figure 3). For subjects inT1, the loss of an elevator presumably looms larger than for subject inT2. With respect to attributeB, no difference betweenT1 andT2 is expected. AttributeBis termed non-reference attributeforT1 andT2. For treatmentsT3 andT4 the reasoning works analogously by exchanging attributesAandB. Thus, observations fromT1 andT3 can be grouped together as well as observations fromT2 andT4. The differentiation between attributes is then concerning the reference attribute (AinT1 andT2,BinT3 andT4) and the non-reference attribute (Bin T1 andT2,Ain T3 andT4).
Attribute A (Elevator)
Attribute B (Balcony)
0 (no) 1 (yes)
0 (no)1 (yes)
T1 T2
T3
T4 11
12 3
10
1 7
7
Figure 3. Hypothesized reference points for different subjects in the four treatments.
Overall, the predictions from the behavioral model introduced in Section 4.2 are:
WTATRef1;T3>WTATRef2;T4 and WTATNRef1;T3 ¼WTATNRef2;T4
where the subscript Ref indicates the reference attribute and NRef the non-reference attribute.
On the contrary, a neoclassical model without reference points and loss aversion predicts that the willingness to accept should be independent of the treatment. More formally, this means that the two equations
WTAT1;T3
Ref ¼WTAT2;T4
Ref and WTAT1;T3
NRef¼WTAT2;T4 NRef should hold.
5.3. Data Analysis
Table1 displays the values for the subjectswillingness to accept which follow from the two indifference equations solved by every subject (cf. Section 5.1). Each line gives the data from two subjects in different treatments: either one subject inT1 and the other one inT2 or a pair fromT3 andT4. Column 1 shows the treatments as well as the monthly rentRi that a subject has in its final contract. The subjectsidenti- fication numbers are given in column 2. The data is grouped by treatments andRi, as these factors are likely to introduce variance in the elicited WTA values. The pair- wise display of two specific subjects in one line is for layout reasons. Data from subject 13, for example, are in one line with subject 49s data; it could as well have been in the same line with the observations from either subject 63 or 64: the grouping by treatments andRiis relevant, the lines are not.
Overall, there are 13 subjects in T1, 14 inT2, 7 inT3, and 8 inT4. In treatment T1, for example, there are three subjects (numbered 13, 69, and 98) that had a contract for an apartment with both an elevator and a balcony and a rent of 161 euros when they were asked to specify equally desirable rent contracts for apart- ments that either do not have an elevator (columns 3 and 4) or no balcony (columns 5 and 6). Subject 13, for example, chose a monthly rent of 150 euros for an apart- ment without elevator but with balcony. Accordingly, WTAAis 11 for this subject;
the value is given in column 3 ofTable1. Remember thatAis the reference attribute in T1. Ranks of the observations are given in parentheses besides the respective values.
5.3.1. Non-reference attribute
For the non-reference attribute, the predictions of the neoclassical and the behav- ioral model coincide: there shouldnt be a treatment effect. The mean as well as the median value of WTAs – given at the lower end of columns 5 and 6 – support this hypothesis as they are approximately equal. To test for significance, a two-sided rank-based exact permutation test is employed which accounts for (1) the special grouping of observations by treatments andRi, (2) outliers, (3) the non-normality of
the data, and (4) the relatively small sample size that renders approximate parametric methods inappropriate. The test is explained in the Appendix. The null hypothesis that there is no treatment effect for the non-reference attribute cannot be rejected (p- value >0.5). Thus, for the non-reference attribute, a significant difference between treatments is not found.
5.3.2. Reference attribute
For the reference attribute, the neoclassical model predicts no treatment effect whereas the behavioral model predicts greater values, and hence a greater rank sum, forT1 and T3 than forT2 and T4. The null hypothesis tested in a one-sided rank- based exact permutation test (as described in the Appendix) is that the rank sum in
Table1. WTA values elicited in the experiment.
1 2 3 4 5 6
Treatment (final Ri)
Subject numbers
WTAT1,T3Ref
(Rank)
WTAT2,T4Ref
(Rank)
WTAT1,T3NRef
(Rank)
WTAT2,T4NRef
(Rank)
T1/T2 (161) 13/49 11 (6) 6 (3) 11 (3.5) 31 (6)
69/63 10 (5) 0 (1.5) 30 (5) 6 (1)
98/64 8 (4) 0 (1.5) 11 (3.5) 10 (2)
T1/T2 (176) 53/74 8 (3) 6 (2) 10 (1) 16 (2.5)
/80 0 (1) 16 (2.5)
T1/T2 (193) 75/54 13 (5) 8 (3) 7 (2) 13 (5)
81/65 13 (5) 0 (1) 10 (4) 8 (3)
88/83 13 (5) 5 (2) 3 (1) 23 (6)
T1/T2 (215) 14/12 15 (5.5) 0 (1) 25 (5.5) 5 (2.5)
66/16 10 (4) 15 (5.5) 5 (2.5) 5 (2.5)
99/84 5 (2.5) 5 (2.5) 5 (2.5) 25 (5.5)
T1/T2 (232) 67/58 12 (3) 10 (2) 0 (1) 17 (5)
76/52 20 (5) 14 (4) 2 (2) 12 (4)
96/61 30 (6) 0 (1) 20 (6) 10 (3)
T3/T4 (161) 78/68 6 (3) 0 (1) 1 (1) 5 (2)
/77 5 (2) 10 (3)
T3/T4 (215) 10/11 30 (6) 5 (3.5) 15 (5) 10 (2.5)
59/60 5 (3.5) 0 (1.5) 5 (1) 10 (2.5)
70/95 10 (5) 0 (1.5) 15 (5) 15 (5)
T3/T4 (232) 71/62 49 (4) 0 (1) 30 (3) 8 (1)
87/73 67 (6) 17 (3) 102 (6) 52 (5)
90/94 52 (5) 4 (2) 32 (4) 12 (2)
Mean WTA 19.4 4.6 17.0 14.5
Median WTA 12.5 4.5 10.5 11.5
Rank sum (91.5) (46.5) (64.5) (73.5)
T1 andT3 is less or equal to the rank sum inT2 andT4. This null hypothesis can be rejected (p-value < 0.001) and, thus, there is a significant difference between treat- ments as predicted by the behavioral model. The difference is statistically significant and, more importantly, it is of economic relevance: if the feature of an apartment – i.e. the elevator or the balcony – is included in every single of up to six offers, then on average the WTA value is more than four times as high as if the feature is not included in any single offer.
Overall, the behavioral model based on loss-aversion and attribute-wise reference points is in line with the data, whereas the neoclassical model of exogenously given and invariable preferences cannot account for the observed differences.
6. Conclusion and Outlook
Negotiators oftentimes do not enter a negotiation process with a fixed valuation of alternatives and invariable trade-offs between attributes. On the contrary, prefer- ences are endogenously adapted and depend on the history of offers in the a nego- tiation process. The behavioral foundations for this endogenous preference construction – namely reference points, loss aversion, and the quasi-endowment effect – were outlined in the paper along with a model how they apply in negotia- tions. Furthermore, data gathered in an internet experiment with students negoti- ating about tenancy contracts supports the supposition of endogenous preferences in negotiations.
The two questions posed in the introduction can be answered based on the pre- vious sections:
1. Yes, there are negotiations in which preferences do change, for example the ones in the reported experiment (cf. Section 5).
2. A model on how negotiators update attribute-wise reference points and thereby change their preferences was presented (cf. Section 4). The experimental data is in congruence with the models predictions whereas it does not support predic- tions by neoclassical models.
The answers just stated have obvious limitations. It cannot be claimed that endogenous preferences occur in any negotiation but just that they might occur in some. Furthermore, the presented model fits the data but, nevertheless, it might not be the only model to do so. Furthermore, the experimental results should be inter- preted with care, as the experiment has several limitations. Among these is the lack of salient rewards. Furthermore, standard criticisms of the student subject pool apply; see Harrison and List (2004) for a general discussion of the matter and e.g.
Bellemare, Kro¨ger and van Soest (2005) for recent evidence on how biased a student subject pool might be.
For negotiation support systems (NSS), the implications are as follows: (1) Sys- tems might warn their users to avoid the sketched bias, (2) they should re-elicit users preferences at the end of a negotiation if a proposed improvement should be
acceptable, and (3) if the changed preference structure is temporary and the (true) ex- ante preferences recur, the system should propose improved agreements with con- siderable delay after the end of the negotiation. Furthermore, a NSS could assist its user in the offer generation process and might recommend offers specifically fostering or specifically counteracting the formation of quasi-endowment by the counterparty.
To the best of the authors knowledge there is no NSS to date that explicitly ad- dresses these points. Some do, however, allow to adjust the utility function when a negotiator finds the initial function inappropriate. Inspire, for example, has this feature.
Future work will include experiments on negotiations dealing with durable con- sumer goods and experiments with both parties being played by humans. These experiments will, contrary to the one presented above, be based on salient rewards.
Appendix Details on the permutation test
The statistical test employed in Section 5.3 is a rank-based exact permutation test (Good 2000). For the non-reference attribute, i.e. for columns 5 and 6 ofTable 1, it works as follows: The ranking is done for eachcellof the table individually: ranks are given to observations from paired treatments (T1 compared toT2 orT3 com- pared toT4) and from subjects that have the same monthly rentRias basis for the indifference equations (cf. Section 5.1). For WTANRefthere are six such cells with six observations each and two cells with three observations each. The permutation test creates all permutations of observations for WTANRefunder the condition that each observation has to be assigned to its original cell and the number of observations per treatment is not changed. This specific structure assures that, for example, data from T1 are not directly compared to T4 and that data from subjects with different contracts are not directly compared. The purpose is to reduce external variability.
Under this side constraints, the observations are assumed to be independent and exchangeable and hence the test is unbiased, i.e. it is more likely to reject a false hypothesis than a true one.
The basic idea of the test is that the assignment of a subject to a cell is randomly determined by the experiment software. Within each cell the observed WTA values are compared to all possible other arrangements of these values. Overall, there are
N¼ 6
3
6
3 1
2
¼576106 arrangements. The rank sum of column 5 serves as test statistic. For each permutation, the test statistic is computed and all possible values of the statistic taken together give a permutation distribution ranging from 40 to 94 with mean and median at 67. Transferred to the test statistic the null hypothesis of no treatment effect is equivalent to an equal rank sum for columns 5 and 6. Given the permutation distribution, the observed rank sum of 64.5 does not constitute an extremely low or high value (two-sided test, p-value¼395;858;896
N >0:5). For the reference attribute, the test works analogous. The null hypothesis tested is that the rank sum inT1 andT3 is less or equal to the rank sum inT2 andT4. The rank sum
of column 3 serves as test statistic. The derived permutation distribution function for this test statistic ranges from 38.5 to 95.5 with mean and median again at 67. The slight difference to the distribution function for the non-reference attribute comes from different ties in the data. Given this distribution, the observed rank sum of 91.5 can be identified as an extremely high value and, thus, the null hypothesis can be rejected (one-sided test,p-value =820N <0:001).
See Sheskin (2004, Test 12a) for a short and Good (2000, especially Chapters 1–3, 9–11, and 14) for an extensive and excellent overview on permutation tests.
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