Co-evolutionary stability in the alternating-offer negotiation

Co-evolution has been proved by experiments to be a promising technique to achieve the automatic acquisition of the optimal strategies in automated negotiations. However, little theoretical work can be found currently to verify its validity. In this paper, we will use evolutionary game theory and replicator dynamics as theoretical foundation and study the co-evolutionary stability of the sub-game perfect equilibrium in alternating-offer protocol, which is widely used in the e-commerce negotiations. We first propose a reasonable assumption, then prove the sub-game perfect equilibrium can repel any rare mutations occurred on its equilibrium and non-equilibrium paths, and finally draw a conclusion that the sub-game perfect strategy is co-evolutionary stable. In the end of this paper, we design an experiment with co-evolutionary genetic algorithm and validate the conclusion.