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The notion of stochastic precedence between two random variables emerges as a relevant concept in several fields of applied probability. When one consider a vector of random variables X1,...,Xn, this notion has a preeminent role in the analysis of minima of the type $\min \limits _{j \in A} X_{j}$ for A ⊂{1,…n}. In such an analysis, however, several apparently controversial aspects can arise (among which phenomena of “non-transitivity”). Here we concentrate attention on vectors of non-negative random variables with absolutely continuous joint distributions, in which a case the set of the multivariate conditional hazard rate (m.c.h.r.) functions can be employed as a convenient method to describe different aspects of stochastic dependence. In terms of the m.c.h.r. functions, we first obtain convenient formulas for the probability distributions of the variables $\min \limits _{j \in A} X_{j}$ and for the probability of events $\{X_{i}=\min \limits _{j \in A} X_{j}\}$ . Then we detail several aspects of the notion of stochastic precedence. On these bases, we explain some controversial behavior of such variables and give sufficient conditions under which paradoxical aspects can be excluded. On the purpose of stimulating active interest of readers, we present several comments and pertinent examples.

Rational choice theory is the benchmark for Economics to model individual choice behavior because the utility function allows a practical representation of decision making. In reality, however, people do not always satisfy the consistency conditions imposed by the theory. Many common behaviors are then excluded, even if they are a form of bounded rationality. The first part of this PhD Thesis is devoted to the formal characterization of specific choice behaviors where the agent has limited capabilities and may be affected by a cognitive bias. Chapter 1 examines the choice behavior of an agent who faces incomparable alternatives. Two classic properties are weakened: completeness and transitivity of preferences. Several representation theorems are proposed. Chapter 2 focuses on the choice from lists when the agent can partially consider the available options. The structured presentation of alternatives highlights a possible limited attention. This choice behavior is rationalized and practical identification of individual parameters are investigated. In the second part, this PhD Thesis analyzes the determinants of customer loyalty with an econometric study based on real data from a distributor of office supplies. Chapter 3 focuses on the factors that influence repeat purchases by a consumer, that is his Customer Lifetime Duration. The effects of the purchase behavior and loyalty program on the survival of new customers are estimated. The effectiveness of the incentive system is evaluated., La théorie du choix rationnel est la référence en économie pour modéliser les comportements de choix individuel car la fonction d'utilité permet une représentation efficace du processus de décision. Cependant, dans la réalité, les individus ne satisfont pas toujours les hypothèses de cohérence imposées par cette théorie. De nombreux comportements usuels sont alors exclus, même s'ils relèvent d'une forme de rationalité limitée. La première partie de cette Thèse est donc consacrée à la caractérisation formelle de comportements de choix spécifiques dans lesquels l'agent a des capacités limitées ou est affecté par un biais cognitif. Le Chapitre 1 étudie le comportement de choix d'un agent qui fait face à des alternatives incomparables. Deux propriétés classiques sont affaiblies : la complétude et la transitivité des préférences. Plusieurs théorèmes de représentation sont proposés. Le Chapitre 2 est centré sur le processus de choix dans des listes lorsque l'agent peut considérer partiellement les options disponibles. La présentation structurée des alternatives met en évidence son éventuelle attention limitée. Ce comportement de choix est rationalisé et plusieurs identifications pratiques des paramètres individuels sont examinées. Dans une seconde partie, cette Thèse apporte une contribution sur les déterminants de la fidélisation client avec une étude économétrique à partir de données réelles d'un distributeur de fournitures de bureau. Le Chapitre 3 s'intéresse aux facteurs qui influencent les achats répétés d'un consommateur, c'est-à-dire sa "durée de vie". Les effets du comportement d'achat et d'un programme de fidélité sur la survie des nouveaux clients sont estimés. L'efficacité du système incitatif est évaluée.

Version of March 05, 2007. An extended abstract of the paper appeared in the Proceedings of the 2006 Prague Colloquium on "Reasoning about Vagueness and Uncertainty".; We compare three strategies to model the notion of vague knowledge in epistemic logic. Williamson's margin for error semantics typically uses non-transitive Kripke structures, but invalidates the principle of positive introspection. On the contrary, Halpern's two-dimensional semantics preserves the introspection principle, but using more complex uncertainty relations that are transitive. We present a modification of the standard epistemic semantics, which validates introspection over one-dimensional non-transitive structures, and study its correspondence with Halpern's approach. While the semantics can be seen as the diagonalization of an explicit two-dimensional semantics, it affords a more intuitive representation of the uncertainty characteristic of vague knowledge. We examine the implications of the semantics concerning higher-order vagueness and the status of the non-transitivity of perceptual indiscriminability. We respond to a potential objection against our approach by giving a dynamic model of the way subjects with inexact knowledge make successive approximations of their margin of error.

We present two alternative approaches to constructing 3 × 3 entangled quantum games, based on different formulations of mixed strategies in a quantum game. Although these formulations are quite similar in 2 × 2 games (2 players × 2 choices), their differences become pronounced in the 3 × 3 case. A 3 × 3 classical game is the simplest platform which allows for non-transitive strategies A, B, C, where A beats B, B beats C, and C beats A (A > B > C > A). We consider non-transitive strategies in both formulations of 3 × 3 quantum games, and show that non-transitivity survives in the quantum versions of the corresponding classical games. Some physical implications of these results are also considered., Predstavljamo dvije inačice pristupa za sastavljanje upletenih kvantnih igara, koji se zasnivaju na različitim obrascima miješanih strategija kvantne igre. Iako su ti obrasci u igrama 2 × 2 vrlo slični (2 igrača × 2 odabira), njihove razlike postaju istaknutije u slučaju 3×3. Klasična igra 3×3 je najjednostavnija osnova koja dozvoljava neprijenosne strategije A, B, C, gdje A nadjača B, B nadjača C, i C nadjača A (A > B > C > A). Razmatramo neprijenosne strategije za oba obrasca kvantnih igara 3 × 3, i pokazujemo kako se u kvantnim inačicama zadržava neprijenosnost odgovarajućih klasičnih igara. Razmatraju se fizičke posljedice tih ishoda.

Many structured overlay networks rely on a ring invariant as a core network connectivity element. The responsibility ranges of the participating peers and navigability principles (greedy routing) heavily depend on the ring structure. For correctness guarantees, each node needs to eagerly maintain its immediate neighboring links - the ring invariant. However, the ring maintenance is an expensive task and it may not even be possible to maintain the ring invariant continuously under high churn, particularly as the network size grows. Furthermore, routing anomalies in the network, peers behind firewalls and Network Address Translators (NATs) create non-transitivity effects, which inevitably lead to the violation of the ring invariant. We argue that reliance on the ring structure is a serious impediment for real life deployment and scalability of structured overlays. In this paper we propose an overlay called Fuzzynet, which does not rely on the ring invariant, yet has all the functionalities of structured overlays. Fuzzynet takes the idea of lazy overlay maintenance further by dropping any explicit connectivity and data maintenance requirement, relying merely on the actions performed when new Fuzzynet peers join the network. We show that with sufficient amount of neighbors (O(log N), comparable to traditional structured over-lays), even under high churn, data can be retrieved in Fuzzynet w.h.p. We validate our novel design principles by simulations as well as PlanetLab experiments and compare them with ring based overlays.