Generating efficient automata for negotiations – an exploration with evolutionary algorithms

The rapid growth of a global electronic market place, together with the establishment of standard negotiation protocols, currently leads to the development of multi-agent architectures in which artificial agents can negotiate on behalf of their users (Maes et al., 1999). Most of today's (prototype) systems for automated negotiations, like Kasbah or Tete-a-Tete, use simple and static negotiation rules. Ideally, however, negotiating agents should be able to deal successfully with a variety of opponents (with different tactics and different preferences). Furthermore, they should be able to adapt their strategies to deal with changing opponents. Such flexible and powerful bargaining agents can be obtained by representing the agents' bargaining strategies as finite automata. A finite automaton representation allows an agent to behave differently against different opponents. We demonstrate that highly effective bargaining automata are generated by an evolutionary algorithm (EA). Our application domain is rather complex compared to the simple games considered in previous works [e.g., the iterated prisoner's dilemma (IPD) (Miller, 1996) or Nash's demand game (Ashlock, 1997)]. We focus on so-called multi-issue negotiations. In multi-issue negotiations not only the price of a product is important, but other aspects are also taken into account (for instance the quality of the product, the delivery time, etc.). Obviously, the complexity of such multi-issue negotiations increases rapidly when the number of issues becomes large. We show how successful strategies (represented as finite automata) can be generated for this class of complex bargaining problems. We follow Miller's (1996) approach by encoding the automata as linear strings. We show that very efficient strategies can be generated by evolving these strings using a GA (when the strings are binary coded). We also propose a hybrid EA model, based upon evolutionary programming (EP) and evolution strategies (ES), which performs well in case of real codings. We validate our approach in a series of experiments by testing the performance of the evolving automata in a competition with a variety of fixed opponents. A similar approach has been used in the past to generate robust strategies for the IPD (Axelrod, 1987). Current work focusses on the development of automata that perform well against co-evolving opponents.