Q-Learning in Unstable Relationships

This study revisits Burdett, Imai and Wright's model of endogeneously unstable relationships [1]. In BIW, bilateral relationships are characterized as stable or unstable according to whether matched agents continue to search for new partners. Endogenous instability hinges on mutually reinforced beliefs about the search and acceptance behaviour of match partners in equilibrium. The model predicts multiple rational expectations (RE) equilibria in some instances and a unique RE equilibrium in others. Here, I investigate to what extent these strong equilibrium predictions are borne out when individuals are modelled as adaptive learning agents with no a priori knowledge of the environment. Attention is restricted to the version of the BIW model with just two match types and a break-up rule that precludes returning to one's previous partner once a new partner is found. Watkin's [9] Q-learning algorithm is used to simulate the adaptive learning process in the BIW environment. Consistent with the psychological concept of reinforcement, agents make subjective evaluations of behavioural alternatives based solely on direct experience and higher-valued alternatives are selected more often than lower-valued ones. Simulations of the Q-learning process point to cases in which the equilibrium conditions are not always binding; indeed, divergence from the equilibrium path is frequently observed under realistic parameter con gurations. The results suggest that adaptive learning processes like Q-learning can augment or diminish the presence of endogenous instability in actual relationships.