# Can Social Agents Efficiently Perform in Automated Negotiation?
## 3 Proposed Social Agent
### Opponent Modeling
#### 3.5.2 Issue Weight Estimation
### Performance in a Non-Stationary and Utilitarian Agent Society

In this case, we plan to study the appropriateness of the proposed agent in a dynamic agent society, where agents can change their negotiation strategy prior to engaging in a negotiation with another agent. More specifically, assuming that agents can choose based on a range of available negotiation strategies, is our proposed strategy attractive even for self-interested agents? For that, we analyze the agent society from a game-theoretic perspective. First, we formulate a game where two agents have to negotiate, and each of them can decide to play according to one of the strategies mentioned in Section 4.1.3 or the proposed social agent. Then, the agents negotiate, and by the end of the negotiation, they achieve a utility. In this game, we assume that agents are rational, and their choice is purely driven by the individual utility expected at the end of the game. Therefore, we formulate a game with two players and eight possible strategies for each agent. The payoff of each strategy combination is obtained from the average utility achieved by that pair of agents across all domains and profiles in the previous tournament. The \(9\times 9\) payoff matrix arising from the definition of this game can be observed in Table 5.

First, we carried out a pure and a mixed equilibrium analysis on the resulting game using the algorithm described in [43]. In the game, there is a single pure equilibrium consisting of one of the players using our social strategy and the other agent employing The Negotiator Reloaded strategy. A total of four mixed equilibria were found for the game, and they can be observed in Table 6. As it is observable both in Tables 5 and 6, our social agent has a significant contribution (i.e., most used strategy) to the strategy profile of at least one of the two players in the negotiation. In fact, it is the most used negotiation strategy for the two players in three out of the four mixed strategies of the game. Overall, even in a society where agents can rationally adapt their strategies for the negotiation, our social agent has a prevalence over the rest of most competitive strategies. Both game-theoretic results support the fact that our proposed agent can be an efficient choice even for self-interested agents, answering our initial research question Q3 (i.e., _Can social negotiation strategies be an efficient choice for self-interested agents in agent societies?_). ## 5 Related Work

The literature on cooperative agents is extensive, and it includes work as relevant as collaborative knowledge networks [44; 45; 46], multi-agent teams [7; 47; 48], cooperative agent planning [49; 50], coalition formation [51], etc. Despite social and cooperative negotiating agents having links with many other areas of cooperative agents, in this section, we aim to review work that is the most related to our social agent proposal. Mainly, we aim to discuss cooperative and adaptive negotiation agent proposals and highlight the differences between these agents and our proposal. [PERSON] et al. [18] proposed a multi-issue bilateral negotiation agent that is based on a bidding mechanism that proposes offers in the iso-utility curve. The agent sends up to \(k\) offers per round to its counterpart, who may accept or propose new counteroffers. The offers sent to the opponent are the most similar to the previous offers sent by the opponent. The results show that, when both agents employ this model, they are capable of reaching agreements that are very close to Pareto optimality. Our agent also employs similarity metrics when there is insufficient information to estimate the other agent's preferences correctly. However, there are several differences between our proposal and [18]. Our agent focuses on reaching social agreements, and it does not require the counterpart to be cooperative. In addition to it, our agent changes its behavior depending on available information and the opponent's moves.