454 research outputs found
Learning the optimal buffer-stock consumption rule of Carroll
This article questions the rather pessimistic conclusions of Allen et Carroll (2001) about the ability of consumer to learn the optimal buffer-stock based consumption rule. To this aim, we develop an agent based model where alternative learning schemes can be compared in terms of the consumption behaviour that they yield. We show that neither purely adaptive learning, nor social learning based on imitation can ensure satisfactory consumption behaviours. By contrast, if the agents can form adaptive expectations, based on an evolving individual mental model, their behaviour becomes much more interesting in terms of its regularity, and its ability to improve performance (which is as a clear manifestation of learning). Our results indicate that assumptions on bounded rationality, and on adaptive expectations are perfectly compatible with sound and realistic economic behaviour, which, in some cases, can even converge to the optimal solution. This framework may therefore be used to develop macroeconomic models with adaptive dynamics.Consumption decisions; Learning; Expectations; Adaptive behaviour, Computational economics
Learning the optimal buffer-stock consumption rule of Carroll
This article questions the rather pessimistic conclusions of Allen et Carroll (2001) about the ability of consumer to learn the optimal buffer-stock based consumption rule. To this aim, we develop an agent based model where alternative learning schemes can be compared in terms of the consumption behaviour that they yield. We show that neither purely adaptive learning, nor social learning based on imitation can ensure satisfactory consumption behaviours. By contrast, if the agents can form adaptive expectations, based on an evolving individual mental model, their behaviour becomes much more interesting in terms of its regularity, and its ability to improve performance (which is as a clear manifestation of learning). Our results indicate that assumptions on bounded rationality, and on adaptive expectations are perfectly compatible with sound and realistic economic behaviour, which, in some cases, can even converge to the optimal solution. This framework may therefore be used to develop macroeconomic models with adaptive dynamics.Consumption decisions; Learning; Expectations; Adaptive behaviour; Computational economics
Large Deviation Principle for Empirical Fields of Log and Riesz Gases
We study a system of N particles with logarithmic, Coulomb or Riesz pairwise
interactions, confined by an external potential. We examine a microscopic
quantity, the tagged empirical field, for which we prove a large deviation
principle at speed N. The rate function is the sum of an entropy term, the
specific relative entropy, and an energy term, the renormalized energy
introduced in previous works, coupled by the temperature. We deduce a
variational property of the sine-beta processes which arise in random matrix
theory. We also give a next-to-leading order expansion of the free energy of
the system, proving the existence of the thermodynamic limit.Comment: 80 pages, final version, to appear in Inventiones Mat
Universal Reconfiguration of Facet-Connected Modular Robots by Pivots: The O(1) Musketeers
We present the first universal reconfiguration algorithm for transforming a modular robot between any two facet-connected square-grid configurations using pivot moves. More precisely, we show that five extra "helper" modules ("musketeers") suffice to reconfigure the remaining n modules between any two given configurations. Our algorithm uses O(n^2) pivot moves, which is worst-case optimal. Previous reconfiguration algorithms either require less restrictive "sliding" moves, do not preserve facet-connectivity, or for the setting we consider, could only handle a small subset of configurations defined by a local forbidden pattern. Configurations with the forbidden pattern do have disconnected reconfiguration graphs (discrete configuration spaces), and indeed we show that they can have an exponential number of connected components. But forbidding the local pattern throughout the configuration is far from necessary, as we show that just a constant number of added modules (placed to be freely reconfigurable) suffice for universal reconfigurability. We also classify three different models of natural pivot moves that preserve facet-connectivity, and show separations between these models
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