Loss Aversion and Reference-Dependent Preferences in Multi-Attribute Negotiations

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 negotiators’ decisions 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.

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 of Table 1, it works as follows: The ranking is done for each cell of the table individually: ranks are given to observations from paired treatments (T1 compared to T2 or T3 compared to T4) and from subjects that have the same monthly rent R _i as basis for the indifference equations (cf. Section 5.1). For WTA_NRef there are six such cells with six observations each and two cells with three observations each. The permutation test creates all permutations of observations for WTA_NRef under 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$N =\left(\begin{array}{l}6\\ 3\end{array}\right)^{6}\ast \left(\begin{array}{l}3\\ 1\end{array}\right)^{2}=576\ast 10^{6}$ 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-value $=\frac{395,858,896}{N}> 0.5$).

For the reference attribute, the test works analogous. The null hypothesis tested is that the rank sum in T1 and T3 is less or equal to the rank sum in T2 and T4. 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 =$\frac{820}{N}< 0.001$).

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.