Publications

Clustering is widely used in unsupervised learning to find homogeneous groups of observations within a dataset. However, clustering mixed-type data remains a challenge, as few existing approaches are suited for this task. This study presents the state-of-the-art of these approaches and compares them using various simulation models. The compared methods include the distance-based approaches k-prototypes, PDQ, and convex k-means, and the probabilistic methods KAy-means for MIxed LArge data (KAMILA), the mixture of Bayesian networks (MBNs), and latent class model (LCM). The aim is to provide insights into the behavior of different methods across a wide range of scenarios by varying some experimental factors such as the number of clusters, cluster overlap, sample size, dimension, proportion of continuous variables in the dataset, and clusters’ distribution. The degree of cluster overlap and the proportion of continuous variables in the dataset and the sample size have a significant impact on the observed performances. When strong interactions exist between variables alongside an explicit dependence on cluster membership, none of the evaluated methods demonstrated satisfactory performance. In our experiments KAMILA, LCM, and k-prototypes exhibited the best performance, with respect to the adjusted rand index (ARI). All the methods are available in R.

In many emerging economies with antiquated laws, bribes paid to government officials reduce economic impediments and serve as a device to improve market competition, thereby contributing to the modernization of an economy. In this context, this paper uses a simple two-stage game theoretic model to investigate the effects of the US Foreign Corrupt Practices Act (FCPA) on such economies. We demonstrate, among others, that while an increase in fines under FCPA reduces overall corruption, it leads to a deterioration in the market quality in an emerging economy. In the presence of FCPA, an increase in the US firm's technological advantage unambiguously leads to a decrease in the market quality in an emerging economy.

Most studies assessing animal decision-making under risk rely on probabilities that are typically larger than 10%. To study Decision-Making in uncertain conditions, we explore a novel experimental and modelling approach that aims at measuring the extent to which rats are sensitive - and how they respond - to outcomes that are both rare (probabilities smaller than 1%) and extreme in their consequences (deviations larger than 10 times the standard error). In a four-armed bandit task, stochastic gains (sugar pellets) and losses (time-out punishments) are such that extremely large - but rare - outcomes materialize or not depending on the chosen options. All rats feature both limited diversification, mixing two options out of four, and sensitivity to rare and extreme outcomes despite their infrequent occurrence, by combining options with avoidance of extreme losses (Black Swans) and exposure to extreme gains (Jackpots). Notably, this sensitivity turns out to be one-sided for the main phenotype in our sample: it features a quasi-complete avoidance of Black Swans, so as to escape extreme losses almost completely, which contrasts with an exposure to Jackpots that is partial only. The flip side of observed choices is that they entail smaller gains and larger losses in the frequent domain compared to alternatives. We have introduced sensitivity to Black Swans and Jackpots in a new class of augmented Reinforcement Learning models and we have estimated their parameters using observed choices and outcomes for each rat. Adding such specific sensitivity results in a good fit of the selected model - and simulated behaviors that are close - to behavioral observations, whereas a standard Q-Learning model without sensitivity is rejected for almost all rats. This model reproducing the main phenotype suggests that frequent outcomes are treated separately from rare and extreme ones through different weights in Decision-Making.

We study a simple model in which two vertically differentiated firms compete in prices and mass advertising on an initially uninformed market. Consumers differ in their preference for quality. There is an upper bound on prices since consumers cannot spend more on the good than a fixed amount (say, their income). Depending on this income and on the ratio between the advertising cost and quality differential (relative advertising cost), either there is no equilibrium in pure strategies or there exists one of the following three types: (1) an interior equilibrium, where both firms have positive natural markets and charge prices lower than the consumer’s income; (2) a constrained interior equilibrium, where both firms have positive natural markets, and the high-quality firm charges the consumer’s income or (3) a corner equilibrium, where the low-quality firm has no natural market selling only to uninformed customers. We show that no corner equilibrium exists in which the high-quality firm would have a null natural market. At an equilibrium (whenever there exists one), the high-quality firm always advertises more, charges a higher price and makes a higher profit than the low-quality one. As the relative advertising cost goes to infinity, prices become equal and the advertising intensities converge to zero as well as the profits. Finally, the advertising intensities are, at least globally, increasing with the quality differential. Finally, in all cases, as the advertising parameter cost increases unboundedly, both prices converge increasingly towards the consumer’s income.