Designing Free Sofware for Marketing: A Game Theoretic Approach

We develop a vertical differentiation game-theoretic model that addresses the issue of designing free software samples for attaining follow-on sales. When software samples are akin to durable goods, a Monopolist giving a free sample away is likely to engender the cannibalization of sales of its commercial product. We analyze the optimal design of free software according to two characteristics: the trial time allotted for sampling (potentially renewable) and the proportion of features included in the sample. We find that these two dimensions play different roles whenever the software product is innovative or standard. We draw implications regarding the effectiveness of marketing strategies depending on the type of software product offered by a Monopolist.Vertical Differentiation, Monopolist, Free sample, Software, Durable goods, Sales Cannibalization, Optimal Design.

Objective Improvement in Information-Geometric Optimization

Information-Geometric Optimization (IGO) is a unified framework of stochastic algorithms for optimization problems. Given a family of probability distributions, IGO turns the original optimization problem into a new maximization problem on the parameter space of the probability distributions. IGO updates the parameter of the probability distribution along the natural gradient, taken with respect to the Fisher metric on the parameter manifold, aiming at maximizing an adaptive transform of the objective function. IGO recovers several known algorithms as particular instances: for the family of Bernoulli distributions IGO recovers PBIL, for the family of Gaussian distributions the pure rank-mu CMA-ES update is recovered, and for exponential families in expectation parametrization the cross-entropy/ML method is recovered. This article provides a theoretical justification for the IGO framework, by proving that any step size not greater than 1 guarantees monotone improvement over the course of optimization, in terms of q-quantile values of the objective function f. The range of admissible step sizes is independent of f and its domain. We extend the result to cover the case of different step sizes for blocks of the parameters in the IGO algorithm. Moreover, we prove that expected fitness improves over time when fitness-proportional selection is applied, in which case the RPP algorithm is recovered

Cache Hierarchy Inspired Compression: a Novel Architecture for Data Streams

We present an architecture for data streams based on structures typically found in web cache hierarchies. The main idea is to build a meta level analyser from a number of levels constructed over time from a data stream. We present the general architecture for such a system and an application to classification. This architecture is an instance of the general wrapper idea allowing us to reuse standard batch learning algorithms in an inherently incremental learning environment. By artificially generating data sources we demonstrate that a hierarchy containing a mixture of models is able to adapt over time to the source of the data. In these experiments the hierarchies use an elementary performance based replacement policy and unweighted voting for making classification decisions