Markov chains theory for the prediction of emotional interactions

A model for producing emotional interactions between an agent and a human user, or between two synthetic agents, is proposed, based on probabilistic finite state automata. The emotional state of the agent changes according to a probabilistic transition function (defining the personality of the agent) that depends on the previous state and on the input received from the interacting partner. Moreover, the history of the ongoing interaction can modify these transition probabilities, therefore changing the attitude of the agent toward the interlocutor. This leads to an adaptation process that makes the resulting interaction flexible and life-like. In an interaction scenario where two synthetic agents interact so that the state of one agent is the input for the other one and vice versa, the resulting emotional interactions can be analyzed in a quantitative way by resorting to the ergodic properties of Markov chains. In particular, the stationary distribution allows us to determine specific properties of the interaction between the agents. For instance, the frequency of each emotional state and the mean time for going from one state to another one can be computed. Such information can be used to check how many time steps, on average, are required for an agent to enter a critical state (e.g. an assigned goal state), or to get the frequency of a critical state. This analysis process is valuable, for instance, for guiding the design of efficient emotional agents, that are capable of producing successful emotional interaction with an artificial or natural partner.