# Can Social Agents Efficiently Perform in Automated Negotiation?
## 3 Proposed Social Agent
### Opponent Modeling
#### 3.5.2 Issue Weight Estimation
The game-theoretic analysis carried out in Section 4.4 helps us to answer what would happen if the agent society started from other different agent distributions in the society. To carry out an experiment with this type of setting, we run a _GENIUS_ tournament between all of the agents described in Section 4.1.3 and our agent. Each agent faces each other agent (including itself) 10 times in every single domain and for every possible profile \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Value** \\ \hline \(t_{exp}\) & Ratio of time spent using the Strict Exploration strategy & 0.33 \\ \hline \(a_{exp}\) & Ratio of offers explored that is necessary to change to Nash optimizer & 0.05 \\ \hline \(t_{sim}\) & Ratio threshold to jump from the Exploratory to the Similarity TFT strategy & 0.9 \\ \hline \(t_{eager}\) & Ratio threshold to jump to the Eager strategy & 0.999 \\ \hline \(z\) & Percentile employed to apply the top median mechanism & 80 \\ \hline \(c_{max}\) & Maximum concession step at each update & 0.03 \\ \hline \(\alpha\) and \(\beta\) & Time-dependent decay for the issue weight update mechanism & 5 and 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: General configuration for our social agent during the experiments. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Window Size** & **Nash Distance** & **Kalai Distance** & **Ind. Utility** & **\% Time** \\ \hline
25 & 0.050 & 0.045 & 0.80 & 0.82 \\ \hline
50 & 0.057 & 0.052 & 0.80 & 0.82 \\ \hline
75 & 0.056 & 0.052 & 0.80 & 0.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average distance to the Nash bargaining point, to the Kalai point, average individual utility, and ratio of negotiation time consumed for three window sizes. in that domain. This means that each pair of agents faces in \(10\times 6\times 2=120\) negotiations. In order to analyze the behavior and performance of each agent, we record the utility achieved at the end of the negotiation, the distance to the Nash bargaining and Kalai point, and the time taken to finish the negotiation. The parameters of our social agent are set at the ones described in Table 2 and the appropriate negotiation window size highlighted in the previous experiment (i.e., 25 bids). First, we focus on analyzing the overall performance of our social agent in this tournament. The overall results of this experiment can be found in Table 4. The table shows the average individual utility, distance to the Nash bargaining point, distance to the Kalai point, and negotiation time in the negotiations carried out by each of the agents in the society. As it can be observed, our social agent obtains the best average utility, distance to the Nash bargaining point, and distance to the Kalai point. These overall results point to various insights. First, the distance to the Nash and Kalai points corroborates that our agent is indeed a social agent. It is, in fact, the most social agent among the agents in this society, including [PERSON], which was awarded as the most social agent in the ANAC 2012 competition. The reader should be reminded that both the Nash bargaining and the Kalai point are considered fair outcomes in negotiation settings. Therefore, the closer that the agreements are to these points, the fairer outcome that is achieved. A social agent should aim to be fair, as it tends to maximize the utility of both parties at the same time. Hence, our agent outperforms the current state of the art in terms of social agents. These results corroborate our second research question Q2 (i.e., _Can a social agent achieve socially efficient agreements in heterogeneous environments?_). Second, one can also observe that our agent is capable of obtaining competitive results concerning the individual utility of the agent. Our social agent obtains the best average utility for the agents included in the experiment. This includes winning agents from the ANAC competition such as Agent K, CUHK Agent, and HardHeaded.