A Model of Evolutionay Drift

Drift appears to be crucial to study the stability properties of Nash equilibria in a component specifying different out-of-equilibrium behaviour. We propose a new microeconomic model of drift to be added to the learning process by which agents find their way to equilibrium. A key feature of the model is the sensitivity of the noisy agent to the proportion of agents in his player population playing the same strategy as his current one. We show that, 1. Perturbed Payoff-Positive and PayoffMonotone selection dynamics are capable of stabilizing pure non strict Nash equilibria in either singleton or nonsingleton component of equilibria; 2. The model is relevant to understand the role of drift in the behaviour observed in the laboratory for the Ultimatum Game and for predicting outcomes that can be experimentally tested. Hence, the selection dynamics model perturbed with the proposed drift may be seen as well as a new learning tool to understand observed behaviour.

Learning to perceive in the sensor motor approach: Piaget's theory of equilibration interpreted dynamically

Learning to perceive is faced with a classical paradox: if understanding is required for perception, how can we learn to perceive something new, something we do not yet understand? According to the sensorimotor approach, perception involves mastery of regular sensorimotor co-variations that depend on the agent and the environment, also known as the "laws" of sensorimotor contingencies (SMCs). In this sense, perception involves enacting relevant sensorimotor skills in each situation. It is important for this proposal that such skills can be learned and refined with experience and yet up to this date, the sensorimotor approach has had no explicit theory of perceptual learning. The situation is made more complex if we acknowledge the open-ended nature of human learning. In this paper we propose Piaget's theory of equilibration as a potential candidate to fulfill this role. This theory highlights the importance of intrinsic sensorimotor norms, in terms of the closure of sensorimotor schemes. It also explains how the equilibration of a sensorimotor organization faced with novelty or breakdowns proceeds by re-shaping pre-existing structures in coupling with dynamical regularities of the world. This way learning to perceive is guided by the equilibration of emerging forms of skillful coping with the world. We demonstrate the compatibility between Piaget's theory and the sensorimotor approach by providing a dynamical formalization of equilibration to give an explicit micro-genetic account of sensorimotor learning and, by extension, of how we learn to perceive. This allows us to draw important lessons in the form of general principles for open-ended sensorimotor learning, including the need for an intrinsic normative evaluation by the agent itself. We also explore implications of our micro-genetic account at the personal level.