Welfare and Convergence Speed in the Ramsey Model under two Classes of Gorman Preferences

Using a one-sector, discrete-time Ramsey model, we analyze and compare the implications for welfare, capital accumulation, and speed of convergence to the steady state of two classes of utility functions that represent Gorman preferences, namely homothetic and Stone\u2013Geary preferences. For identical economies, we show that the preference structure does not affect only the capital dynamics and social welfare but also the speed of convergence to the steady-state equilibrium

A joint scheduling and content caching scheme for energy harvesting access points with multicast

© 2017 IEEE. In this work, we investigate a system where users are served by an access point that is equipped with energy harvesting and caching mechanism. Focusing on the design of an efficient content delivery scheduling, we propose a joint scheduling and caching scheme. The scheduling problem is formulated as a Markov decision process and solved by an on-line learning algorithm. To deal with large state space, we apply the linear approximation method to the state-Action value functions, which significantly reduces the memory space for storing the function values. In addition, the preference learning is incorporated to speed up the convergence when dealing with the requests from users that have obvious content preferences. Simulation results confirm that the proposed scheme outperforms the baseline scheme in terms of convergence and system throughput, especially when the personal preference is concentrated to one or two contents

Converging an Overlay Network to a Gradient Topology

In this paper, we investigate the topology convergence problem for the gossip-based Gradient overlay network. In an overlay network where each node has a local utility value, a Gradient overlay network is characterized by the properties that each node has a set of neighbors with the same utility value (a similar view) and a set of neighbors containing higher utility values (gradient neighbor set), such that paths of increasing utilities emerge in the network topology. The Gradient overlay network is built using gossiping and a preference function that samples from nodes using a uniform random peer sampling service. We analyze it using tools from matrix analysis, and we prove both the necessary and sufficient conditions for convergence to a complete gradient structure, as well as estimating the convergence time and providing bounds on worst-case convergence time. Finally, we show in simulations the potential of the Gradient overlay, by building a more efficient live-streaming peer-to-peer (P2P) system than one built using uniform random peer sampling.Comment: Submitted to 50th IEEE Conference on Decision and Control (CDC 2011

Maximum Score Estimation of Preference Parameters for a Binary Choice Model under Uncertainty

This paper develops maximum score estimation of preference parameters in the binary choice model under uncertainty in which the decision rule is affected by conditional expectations. The preference parameters are estimated in two stages: we estimate conditional expectations nonparametrically in the first stage and then the preference parameters in the second stage based on Manski (1975, 1985)'s maximum score estimator using the choice data and first stage estimates. The paper establishes consistency and derives rate of convergence of the two-stage maximum score estimator. Moreover, the paper also provides sufficient conditions under which the two-stage estimator is asymptotically equivalent in distribution to the corresponding single-stage estimator that assumes the first stage input is known. These results are of independent interest for maximum score estimation with nonparametrically generated regressors. The paper also presents some Monte Carlo simulation results for finite-sample behavior of the two-stage estimator

Smallness of a commodity and partial equilibrium analysis

Partial equilibrium analysis has a conceptual dilemma that its object should be negligibly small in order to be free from income effect but then the consumer does not care for it and the notion of willingness to pay for it does not make sense. In the setting of a continuum of commodities, we propose a limiting procedure which transforms the general many-commodity framework into a partial single-commodity framework. In the limit, willingness to pay for a commodity is established as a density notion and it is shown to be free from income effect. This pins down an exact relationship between general equilibrium analysis and partial equilibrium analysis