# Can Social Agents Efficiently Perform in Automated Negotiation?
## 3 Proposed Social Agent
### Opponent Modeling
#### 3.5.2 Issue Weight Estimation
Can a social agent obtain a high utility in heterogeneous environments? * Q2. Can a social agent achieve socially efficient agreements in heterogeneous environments? * Q3. Can social negotiation strategies be an efficient choice for self-interested agents in agent societies? To answer these questions, we designed three types of experiments. The first experiment serves to analyze the impact of the length of the window of bids on the performance of our social agent. The second experiment aims to analyze the behavior and performance of our social agent in a static society of agents. By a static society of agents, we mean a society where multiple types of agents exist, but they do not change their strategies. With this experiment, we aim to find if our social agent can achieve socially efficient agreements in heterogeneous environments. Lastly, we carry out a theoretical analysis using game theory to find out about the prospective use of our social strategy in a society where agents can decide their negotiation strategies. This experiment aims to find if a social strategy such as the one proposed in this article may be efficient even for self-interested agents. The structure of this section is organized as follows. First, we describe the experimental settings common to all our experiments. Then, we describe and analyze the experiments carried out to identify an appropriate window size for the proposed agents. After that, we provide the empirical results for the experiment carried out to determine the behavior and

Figure 5: The issue weight update for various levels of \(\beta\). performance of our agent in a static agent society. Finally, we describe the insights arising from the theoretical analysis carried out in a dynamic setting. ### General Experimental Setting

In this subsection, we describe the settings and design decisions common to all the experiments carried out to assess the performance of our social agent. To be more specific, we describe the metrics employed to evaluate the performance of the agents as well as the agents that form the agent society in which our agent interacts. #### 4.1.1 Quality Metrics

As mentioned throughout the article, the goal of the proposed agent is to be social and reaching an agreement that is as fair as feasible for both agents. For that reason, most of the metrics employed to assess the performance of the agent aim to measure the fairness/quality of the agreement from both agents' perspectives. Next, we describe each of the metrics that we use in our experimental setting:

* Individual utility: This is the utility received by the agent at the end of the negotiation. When the negotiation ends with no agreement, then the agent gets an individual utility of 0.0. Otherwise, the utility obtained by the agent is that of the individual utility reported by the agreement. * Nash bargaining point distance: The Nash bargaining point is the Pareto optimal point that maximizes the product of both agents' utilities. Traditionally, as the product of the two utilities penalizes scenarios where one of the agents gets a very high utility while the other agent gets a low utility, the Nash bargaining point is considered as an indicator of the fairness of the resulting agreement. Thus, in practice, the closer an agreement is to the Nash bargaining point, the fairer it should be for both involved parties. * Kalai point distance: The Kalai point also seeks to find an outcome that is fair for both parties. However, differently from the Nash bargaining point, the Kalai point considers the initial reservation utilities of the agents (i.e., the status quo solution) when computing the fairness of the agreement. In essence, both parties should gain in the same proportion from their status-quo point. Thus, the Kalai point is the Pareto optimal solution that maximizes the ratio of the gains of both agents. In practice, the closer an agreement is to the Kalai point, the fairer it should be for both involved parties.