# Can Social Agents Efficiently Perform in Automated Negotiation?
## 3 Proposed Social Agent
### Opponent Modeling
#### 3.5.2 Issue Weight Estimation
To avoid overfitting of our agent to the agents selected for the experiments, we carried out manual tests using _GENIUS_ with our agent and Agent K in one of the domains: the party domain. During the tests, we observed both the outcome obtained by our agent and the evolution during the negotiation. After a few manual tests, we found a combination of hyperparameters (see Table 2) that obtained good joint utility and distances to both Nash point and the Pareto frontier. Of course, we do not claim that the configuration results in an optimal configuration of the agent, but as the reader will appreciate, these values are enough to prove the main contribution of this article: how a social agent can efficiently perform in an agent society. As only one agent and domain were employed for finding this combination of hyperparameters, we argue that there is no risk of overfitting, as there are five negotiation domains and six opponents that were not employed during this exploration. Therefore, we used the parameter values found in Table 2 for the subsequent experiments carried out to assess the performance of our social agent. ### Analyzing the Impact of the Window Size

In this first batch of experiments, we study to what extent the length of the window, employed by our agent to carry out the different behavioral analyses, impacts the social performance of our agent. The main goal of this experiment is to identify an adequate window size for properly and socially reacting to the moves of the agents in the agent society. For this first experiment, we set the value of the window size to \(=\{25,50,75\}\). The rest of the parameters of the agent were set according to the values represented in Table 2.

Each configuration of our agent faced a subset of four agents (i.e., AgentK, IAmHaggler2011, Hardheaded agent, and TheNegotiator Reloaded) in a subset of three negotiation domains (i.e., party, Amsterdam trip, and England vs. Zimbabwe domains) and negotiation profiles. The reason we carried out these experiments with just a subset of the opponents and domains is to avoid overfitting. In these experiments, each instance of our agent faced each of the four opponent agents for all three negotiation domains, using both preference profiles, and repeating each negotiation setting 10 times (a total of \(4\times 3\times 2\times 10=240\) negotiations per our social agent configuration). In addition, we measured the distance to the Nash bargaining point, the distance to the Kalai point, and the negotiation time at the end of each negotiation. The experiments were conducted using a _Genius_ simulator [42] using bilateral negotiations with a common deadline of 90 s.

Table 3 contains the results of this first experiment. As the reader may observe, a window size of 25 is capable of obtaining a lower distance to the Nash bargaining point and the Kalai point, resulting in a more social outcome than the other two configurations. More interestingly, there were no observable differences in the individual utility obtained by the proposed agent. This means that smaller window sizes also impacted the learning carried out by the agent. In fact, the larger the window sizes, the fewer updates that are carried out on the opponent model. We could not observe a notable difference between the three studied configurations in terms of speed, with negotiations taking approximately 82% of the total time. ### Performance in a Stationary Agent Society

As mentioned at the start of this section, the second experiment studies the behavior and performance of the proposed agent in a static society. The society is formed by the top-performing agents described in Section 4.1.3 and our social agent. For this analysis, we assumed that agents may face any other agent in society, including versions of themselves. Another assumption for this first experiment is that the agents face the same number of times each other in the experiment.