Theoretical properties of the MiCRO negotiation strategy

Recently, we have introduced a new algorithm for automated negotiation, called MiCRO, which, despite its simplicity, outperforms many state-of-the-art negotiation strategies (de Jonge, in: Raedt (ed) Proceedings of the thirty-first international joint conference on artificial intelligence, ijcai.org, Vienna, Austria, 2022). Furthermore, we claimed that under certain conditions which typically hold in the Automated Negotiating Agents Competition (ANAC), it is a game-theoretically optimal strategy. The goal of this paper is to formally prove those claims. Specifically, we define ‘negotiation’ as an extensive-form game and define the class of consistent strategies for this game, which consists of those strategies that satisfy a number of rationality criteria. We then prove that under the above mentioned conditions MiCRO is a best response against itself among all consistent negotiation strategies. Furthermore, we define the notion of a balanced negotiation domain, which is a domain in which two MiCRO agents would always come to an optimal agreement. Finally, we show that many of the domains used in ANAC indeed happen to be (approximately) balanced. The importance of this work is that if we know under which conditions MiCRO is theoretically optimal, then we can use this to test to what extent other negotiation algorithms are able to achieve similar results to MiCRO when applied under those same conditions. Furthermore, it would help researchers to design more challenging test cases for automated negotiation in which MiCRO is not optimal.