How Well Agents Represent Their Principals’ Preferences: The Effect of Information Processing, Value Orientation, and Goals

Abstract

There is an implicit assumption that the agents who negotiate on behalf of principals prepare for the negotiations. This study focuses on the negotiation preparation phase during which the agents are given information in both text and graphical forms, which unambiguously expresses their principal’s preferences. The analysis of data obtained from the online bilateral negotiation experiments shows that the majority of the agents make both ordinal and cardinal errors in the reconstruction of the principal’s preferences. It shows that the agents’ intrinsic motivation contributes to the errors and has a negative effect on their preparation. To determine how different types of motivation contribute to the agents’ inaccuracy, a hierarchical framework of the epistemic, social, and identity motivation is proposed. The framework is analyzed with a structural equation model (SEM) and the resulting model shows relations among the motivation types and between motivation and accuracy. The results show that the rational motivation system has a significant direct effect on social motivation (accommodating, competing, and collaborating intentions) and identity motivation (learning and substantive goals). The experiential motivational system has no significant effect on social motivation but it affects two goals of identity motivation (substantive and relational). The model also shows that only identity motivation has a direct effect on the accuracy of the preferences formulated by the agents in comparison with their principal’s preferences.

Appendix. Similarity of Two Preference Systems

The principal’s and the agents’ preference systems are both represented with a vector of natural numbers. The similarity of these two systems can be measured on ordinal and cardinal scales. Ordinal comparisons can be done with Hamming distance because it counts the number of differences made in pairwise comparisons and is easy to interpret (Hamming 1950).

Let $S_{P} = \left\{ {w_{ij}^{P}, i = 1, \ldots, m_{j}, j = 1, \ldots,n} \right\}$ and $S_{A} = \left\{ {w_{ij}^{A}, i = 1, \ldots, m_{j}, j = 1, \ldots,n} \right\}$ denote the preference systems of respectively the principal and the agent, where $w_{ij}$ is the score of the $i$ th option of the $j$ th negotiation issue, $m_{j}$ is the number of options in issue $j$, and $n$ is the number of issues. Without loss of generalization, we assume that the score of the best option for an issue is equal to the score (rating) of this issue, i.e. $\max_{i} \left( {w_{ij}^{P} } \right) = w_{j}^{P}$ and $\max_{i} \left( {w_{ij}^{A} } \right) = w_{j}^{A}$.

Hamming distance measures the similarity of $S_{P}$ and $S_{A}$; it is the number of times the agent made an ordinal error in comparing two issues or two options of an issue. If an issue (option) is more important for the principal than another issue (option) but it is less or equally important for the agent, then 1 is added to the distance. If it is also more important for the agent, then 0 is added. Let $r_{jj^{\prime}}$ define the agent’s error in scoring issues j and $j^{\prime}$. The values $r_{{jj^{\prime}}}$ are obtained from:

$$ r_{{jj^{\prime}}} = \left\{ {{ }\begin{array}{*{20}l} {1{\text{ if sign}}\left( {w_{j}^{P} - { }w_{{j^{\prime}}}^{P} } \right) \ne {\text{sign}}\left( {w_{j}^{A} - { }w_{{j^{\prime}}}^{A} } \right){ }} \hfill \\ {0{\text{ otherwise}}} \hfill \\ \end{array} } \right. $$

(1)

where: $j=1, \ldots, n-1; j^{\prime} = j + 1, \ldots ,n$, and sign(x) is a function that extracts the sign of w.

Error for comparison for options $i$ and $i^{\prime}$ of $j$ th issue is $r_{{jj^{\prime}}}^{j}$ and its values are obtained from:

$$ r_{{ii^{\prime}}}^{j} = \left\{ {{ }\begin{array}{*{20}l} {1{\text{ if sign}}\left( {w_{ij}^{P} - { }w_{{i^{\prime}j}}^{P} } \right) \ne {\text{sign}}\left( {w_{ij}^{A} - { }w_{{i^{\prime}j}}^{A} } \right){ }} \hfill \\ {0{\text{ otherwise}}} \hfill \\ \end{array} } \right. $$

(2)

for each $j = 1,{ } \ldots ,{ }n;i = 1, \ldots ,m_{j} - 1$ and $i^{\prime} = i + 1, \ldots ,m_{j}$.

Hamming distance between S_P and S_A is

$$ D_{H} \left( {S_{P} ,S_{A} } \right) = \sum\nolimits_{j = 1}^{n - 1} {\sum\nolimits_{{j^{\prime} = j + 1}}^{n} {r_{{jj^{\prime}}} } } + \sum\nolimits_{j = 1}^{n} {\sum\nolimits_{i = 1}^{{m_{j} - 1}} {\sum\nolimits_{{i^{\prime} = i + 1}}^{{m_{j} }} {r_{{ii^{\prime}}}^{j} .} } } $$

(3)

Agents who make no pairwise comparison errors are ordinal-accurate, i.e., D_H(S_P, S_A) = 0.

The second measure of accuracy is cardinal and we use block (Manhattan) distance $L_{1}$. The cardinal distance between two preference systems S_P and S_A is the sum of the absolute differences of the principal’s and the agent’s scores, that is:

$$ L_{1} \left( {S_{P} ,S_{A} } \right) = \sum\nolimits_{j = 1}^{n} {\sum\nolimits_{i = 1}^{{m_{j} }} {\left| {w_{ij}^{P} - w_{ij}^{A} } \right|} } . $$

(4)

The agent is cardinal-accurate if L₁(S_P, S_A) = 0, for inaccurate agents L₁(S_P, S_A) > 0.