# Multi-Issue Negotiation Protocol with Pre-Domain Narrowing
## 3 Related Works  
In large-scale multi-issue negotiation, the negotiation domain size increases exponentially as the number of issues and options increases. To solve this problem, some negotiation protocols have been studied. Some existing negotiation protocols for multiple interdependent issue negotiations introduce the effect of heuristic methods that aim to find suboptimal agreements. We briefly cover this section's most relevant related works and provide a comparison table in Table 1.  
[PERSON] et al. [14] proposed methods based on the linear combinations of simple functions, called tactics, that manipulate the utility of contracts. These methods were divided into tradeoffs and issue manipulation mechanisms [15]. They later presented a tradeoff strategy, where multiple negotiation decision variables were traded off against one another to develop a heuristic computational model for this strategy and showed that it could increase social welfare for the considered system [16]. Their algorithm used the notion of fuzzy similarity to approximate the preference structures of other agents and used hill-climbing to explore the space of possible tradeoffs for the most acceptable. [PERSON] et al. [17] proposed negotiation protocols focusing on nonlinear utility functions and described a simulated annealing-based approach that achieved near-optimal social welfare for negotiations. [PERSON] et al. [8] proposed a protocol that repeatedly narrows the negotiation domain space. Each agent performs a rough search of the negotiation domain space, identifying the range wherein its utility is expected to be high and submits this to the mediator. The mediator presents a range within the negotiation domain space that is an intersection of the ranges submitted by each agent. By repeating these operations multiple times, the scope of negotiation is gradually narrowed, until a single consensus is ultimately decided upon. When using this protocol, there is a possibility that no intersection exists when agents submit extremely narrow ranges, and that narrowing fails. Moreover, if agents submit ranges that are too extensive, it is then difficult to efficiently narrow the domain. [PERSON] et al. [9] proposed a meditation protocol that employs a genetic algorithm for negotiations based on utility that changes over time. In this protocol, the mediator prepares multiple alternatives of agreement and presents them to the agents. Each agent reorders \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Our Work** & \begin{tabular}{c} **[PERSON]** \\ **1998 [14]** \\ **etc.** \\ \end{tabular} & \begin{tabular}{c} **[PERSON]** \\ **2007 [8]** \\ \end{tabular} & \begin{tabular}{c} **[PERSON]** \\ **2013 [9]** \\ \end{tabular} & \
\begin{tabular}{c} **[PERSON]** \\ **2014 [10]** \\ \end{tabular} \\ \hline Bi/Multi-lateral & Bilateral & Bilateral & Multilateral & Multilateral & Multilateral \\ Utility Function &
\begin{tabular}{c} Weighted- \\ sum \\ \end{tabular} & Linear & Constraint & Constraint & Constraint \\
**Mediator in main** & & & & & \\
**negotiation phase** & **No** & Yes & Yes & Yes & Yes \\
**Privacy** & **Yes** & No & No & No & No \\ Primary Approach of & & & & & \\ improving efficiency & Pre-domain & Meta & Multi & Genetic & Issue \\  & narrowing & heuristics & narrowing & algorithm & clustering \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison matrix for selected relevant related studies. these alternatives in descending order of their utilities and submits them to the mediator. Based on the submitted orders, the mediator uses a genetic algorithm to search for Pareto-dominated bids. The Pareto optimal solution is obtained by repeating this operation. [PERSON] et al. [10] proposed a method of searching for the final offer by simulated annealing, where the negotiation domain space is first partitioned using clustering. In a utility space where a dependent relationship exists among issues, an agent submits a group of issues with a strong dependent relationship to the mediator.