Interactive Epistemology and Reasoning: On the Foundations of Game Theory

Game theory describes and analyzes strategic interaction. It is usually distinguished between static games, which are strategic situations in which the players choose only once as well as simultaneously, and dynamic games, which are strategic situations involving sequential choices. In addition, dynamic games can be further classified according to perfect and imperfect information. Indeed, a dynamic game is said to exhibit perfect information, whenever at any point of the game every player has full informational access to all choices that have been conducted so far. However, in the case of imperfect information some players are not fully informed about some choices. Game-theoretic analysis proceeds in two steps. Firstly, games are modelled by so-called form structures which extract and formalize the significant parts of the underlying strategic interaction. The basic and most commonly used models of games are the normal form, which rather sparsely describes a game merely in terms of the players' strategy sets and utilities, and the extensive form, which models a game in a more detailed way as a tree. In fact, it is standard to formalize static games with the normal form and dynamic games with the extensive form. Secondly, solution concepts are developed to solve models of games in the sense of identifying the choices that should be taken by rational players. Indeed, the ultimate objective of the classical approach to game theory, which is of normative character, is the development of a solution concept that is capable of identifying a unique choice for every player in an arbitrary game. However, given the large variety of games, it is not at all certain whether it is possible to device a solution concept with such universal capability. Alternatively, interactive epistemology provides an epistemic approach to game theory of descriptive character. This rather recent discipline analyzes the relation between knowledge, belief and choice of game-playing agents in an epistemic framework. The description of the players' choices in a given game relative to various epistemic assumptions constitutes the fundamental problem addressed by an epistemic approach to game theory. In a general sense, the objective of interactive epistemology consists in characterizing existing game-theoretic solution concepts in terms of epistemic assumptions as well as in proposing novel solution concepts by studying the game-theoretic implications of refined or new epistemic hypotheses. Intuitively, an epistemic model of a game can be interpreted as representing the reasoning of the players. Indeed, before making a decision in a game, the players reason about the game and their respective opponents, given their knowledge and beliefs. Precisely these epistemic mental states on which players base their decisions are explicitly expressible in an epistemic framework. In this PhD thesis, we consider an epistemic approach to game theory from a foundational point of view. In Chapter 1, basic game-theoretic notions as well as Aumann's epistemic framework for games are expounded and illustrated. Also, Aumann's sufficient conditions for backward induction are presented and his conceptual views discussed. In Chapter 2, Aumann's interactive epistemology is conceptually analyzed. In Chapter 3, which is based on joint work with Conrad Heilmann, a three-stage account for dynamic games is introduced and a type-based epistemic model is extended with a notion of agent connectedness. Then, sufficient conditions for backward induction are derived. In Chapter 4, which is based on joint work with Jérémie Cabessa, a topological approach to interactive epistemology is initiated. In particular, the epistemic-topological operator limit knowledge is defined and some implications for games considered. In Chapter 5, which is based on joint work with Jérémie Cabessa and Andrés Perea, Aumann's impossibility theorem on agreeing to disagree is revisited and weakened in the sense that possible contexts are provided in which agents can indeed agree to disagree.

Dynamic stackelberg game with risk-averse players: optimal risk-sharing under asymmetric information

The objective of this paper is to clarify the interactive nature of the leader-follower relationship when both players are endogenously risk-averse. The analysis is placed in the context of a dynamic closed-loop Stackelberg game with private information. The case of a risk-neutral leader, very often discussed in the literature, is only a borderline possibility in the present study. Each player in the game is characterized by a risk-averse type which is unknown to his opponent. The goal of the leader is to implement an optimal incentive compatible risk-sharing contract. The proposed approach provides a qualitative analysis of adaptive risk behavior profiles for asymmetrically informed players in the context of dynamic strategic interactions modelled as incentive Stackelberg games.

The Multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria

A multiple-partners assignment game with heterogeneous sales and multiunit demands consists of a set of sellers that own a given number of indivisible units of (potentially many different) goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define a competitive equilibrium for this generalized assignment game and prove its existence by using only linear programming. In particular, we show how to compute equilibrium price vectors from the solutions of the dual linear program associated to the primal linear program defined to find optimal assignments. Using only linear programming tools, we also show (i) that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all optimal assignments, and vice versa; (ii) that the set of (restricted) equilibrium price vectors has a natural lattice structure; and (iii) how this structure is translated into the set of agents' utilities that are attainable at equilibrium.

On Cooperative solutions of a generalized assignment game: limit theorems to the set of competitive equilibria

We study two cooperative solutions of a market with indivisible goods modeled as a generalized assignment game: Set-wise stability and Core. We first establish that the Set-wise stable set is contained in the Core and it contains the non-empty set of competitive equilibrium payoffs. We then state and prove three limit results for replicated markets. First, the sequence of Cores of replicated markets converges to the set of competitive equilibrium payoffs when the number of replicas tends to infinity. Second, the Set-wise stable set of a two-fold replicated market already coincides with the set of competitive equilibrium payoffs. Third, for any number of replicas there is a market with a Core payoff that is not a competitive equilibrium payoff.

Development of a collection of bacteria causing meningitis in Rio de Janeiro from 1990 to 1991

From March 1990 to December 1992, the National Institute for Quality Control of Health-INCQS Research Collection received 1476 bacterial samples isolated from human cerebrospinal fluid of patients suspect of meningitis in Rio de Janeiro, from the São Sebastião State Institute of Infectious Diseases (IEISS). Neisseria meningitidis was found in most of these materials, followed in smaller number by Haemophilus sp. and Streptococcus pneumoniae. The great majority of N. meningitidis strains was serogroup B, followed by serogroup C and a few strains of serogroup W135. More than 50 of the isolated bacterial agents came from the predominant 0-4 years age group. The majority of the strains were from patients in the region known as "Baixada Fluminense" (Low Lands). The aim of the work presented here is to obtain samples of meningitis cases in at least 70 of the State of Rio de Janeiro and develop a collaborative research between INCQS-FIOCRUZ and the IEISS, in order to set up a collection of strains for future studies. However, despite work being carried out in a rather satisfactory way, difficulties still arise and have to be overcome, to survey data.

Report on a collection of Lutzomyia sand flies (Diptera: Psychodidae) from the middle Solimões (Amazonas, Brazil)

Fifty-two species of Lutzomyia sand flies were identified in contemporaneous samples totalling only 1875 individuals, collected at the same site in tall primary terra-firme rainforest, near the south bank of the Solimões River. The most abundant species belonged to the subgenera Trichophoromyia and Nyssomyia. The subgenera Psathyromyia, Nyssomyia and Psychodopygus represented the greatest number of species. A new, aberrant species of the subgenus Psathyromyia (L. cultellata) and the female of Lu. souzacastroi are described. The Phlebotominae are proposed as a suitable indicator group for biogeographic and diversity studies.

Detection of nandrolone metabolites in urine after a football game in professional and amateur players: a Bayesian comparison.

Nandrolone (19-nortestosterone) is a widely used anabolic steroid in sports where strength plays an essential role. Once nandrolone has been metabolised, two major metabolites are excreted in urine, 19-norandrosterone (NA) and 19-noretiocholanolone (NE). In 1997, in France, quite a few sportsmen had concentrations of 19-norandrosterone very close to the IOC cut off limit (2ng/ml). At that time, a debate took place about the capability of the human male body to produce by itself these metabolites without any intake of nandrolone or related compounds. The International Football Federation (FIFA) was very concerned with this problematic, especially because the World Cup was about to start in France. In this respect, a statistical study was held with all football players from the first and second divisions of the Swiss Football National League. All players gave a urine sample after effort and around 6% of them showed traces of 19-norandrosterone. These results were compared with amateur football players (control group) and around 6% of them had very small amounts of 19-norandrosterone and/or 19-noretiocholanolone in urine after effort, whereas none of them had detectable traces of one or the other metabolite before effort. The origin of these compounds in urine after a strenuous physical activity is still unknown, but three hypotheses can be put forward. First, an endogenous production of nandrolone metabolites takes place. Second, nandrolone metabolites are released from the fatty tissues after an intake of nandrolone, some related compounds or some contaminated nutritive supplements. Finally, the sportsmen may have taken something during or just before the football game.

The type specimens of mosquitoes (Diptera, Culicidae) deposited in the entomological collection of the Instituto Oswaldo Cruz, Rio de Janeiro, Brazil

A list of type specimens of 100 mosquito species deposited in the Entomological collection of the Instituto Oswaldo Cruz is presented. It includes five holotypes belonging to the subfamily Anophelinae; 56 holotypes of Culicinae and two of Toxorhynchitinae. A lectotype is designated for Toxorhynchites fluminensis. The holotypes of six nominal species - Psorophora chiquitana, Psorophora circunflava, Psorophora melanota, Psorophora lanei, Wyeomyia brucei and Uranotaenia noctivaga - previously considered non existent or of unknown location were found in the collection.

La presa de consciència de les actituds a l'educació física en la formació inicial de mestres de primària

Aquest treball és el resultat d’un procés de reflexió al voltant de les actituds dins la Formació Inicial de mestres de primària d’Educació física. Es tracta, d’una primera aproximació d’anàlisi i interpretació sobre la presa de consciència d’actituds que fan els estudiants en la pràctica de l’Educació física. Les preguntes que em plantejo en aquesta recerca són el resultat de les dues parts que configura aquest treball. La primera pregunta, es centra en el marc teòric de l’estudi, donant resposta a les relacions que s’estableixen entre l’educació física i l’educació en valors en el currículum de primària d’Educació física i en la Formació Inicial de mestres. La segona pregunta, pretén donar resposta a la proposta pràctica i així, esbrinar el paper del joc motor en el treball educatiu de les actituds en la Formació Inicial de mestres de primària. Els aspectes teòrics que estudio analitzen la relació que s’estableix entre l’Educació física i les actituds dins el marc educatiu de la Formació Inicial de mestres de primària. I serà, a partir de la proposta pràctica quan el joc motor esdevindrà element d’aproximació en la presa de consciència d’actituds En el context de la Facultat d’Educació de la Universitat de Vic, i en l’assignatura d’Educació física i la seva Didàctica de 2n curs, els estudiants de mestres de primària d’Educació física són protagonistes del seu propi procés d’aprenentatge. Tenen la possibilitat d’experimentar el paper de mestres, a partir de la posada en pràctica d’un joc motor. A partir d’aquesta pràctica, he volgut conèixer quins són els components de la pràctica que possibiliten la presa de consciència de les actituds presents a les sessions de classe per promoure l’educació en valors. Els instruments utilitzats, en la realització d’aquest treball, són un qüestionari elaborat a partir d’una selecció i justificació de continguts actitudinals, i l’observació d’una fitxa sessió després de la pràctica. El treball de recerca se situa en un paradigma interpretatiu i pràctic. Es planteja comprendre la importància que té, en les sessions de classe d’educació física, el desenvolupament de processos d’acció i de reflexió en la formació inicial dels mestres de primària i així examinar i perfeccionar futures intervencions pràctiques, tant del professorat com dels estudiants de mestre.

The Type Specimens of Apoidea (Hymenoptera) Deposited in the Entomological Collection of Instituto Oswaldo Cruz, Rio de Janeiro, RJ, Brazil

A list of 41 Apoidea (Hymenoptera) type specimens deposited in the Entomological Collection of the Instituto Oswaldo Cruz, Rio de Janeiro, RJ, Brazil is presented. The types previously belonged to the Zikán and Schrottky private collections. A total of 11 holotypes and 30 paratypes are listed with their respective data and literature

Role of disease activity for decision making ability in early multiple sclerosis

Background and purpose: Decision making (DM) has been defined as the process through which a person forms preferences, selects and executes actions, and evaluates the outcome related to a selected choice. This ability represents an important factor for adequate behaviour in everyday life. DM impairment in multiple sclerosis (MS) has been previously reported. The purpose of the present study was to assess DM in patients with MS at the earliest clinically detectable time point of the disease. Methods: Patients with definite (n=109) or possible (clinically isolated syndrome, CIS; n=56) MS, a short disease duration (mean 2.3 years) and a minor neurological disability (mean EDSS 1.8) were compared to 50 healthy controls aged 18 to 60 years (mean age 32.2) using the Iowa Gambling Task (IGT). Subjects had to select a card from any of 4 decks (A/B [disadvantageous]; C/D [advantageous]). The game consisted of 100 trials then grouped in blocks of 20 cards for data analysis. Skill in DM was assessed by means of a learning index (LI) defined as the difference between the averaged last three block indexes and first two block indexes (LI=[(BI-3+BI-4+BI-5)/3-(BI-1+B2)/2]). Non parametric tests were used for statistical analysis. Results: LI was higher in the control group (0.24, SD 0.44) than in the MS group (0.21, SD 0.38), however without reaching statistical significance (p=0.7). Interesting differences were detected when MS patients were grouped according to phenotype. A trend to a difference between MS subgroups and controls was observed for LI (p=0.06), which became significant between MS subgroups (p=0.03). CIS patients who confirmed MS diagnosis by presenting a second relapse after study entry showed a dysfunction in the IGT in comparison to the other CIS (p=0.01) and definite MS (p=0.04) patients. In the opposite, CIS patients characterised by not entirely fulfilled McDonald criteria at inclusion and absence of relapse during the study showed an normal learning pattern on the IGT. Finally, comparing MS patients who developed relapses after study entry, those who remained clinically stable and controls, we observed impaired performances only in relapsing patients in comparison to stable patients (p=0.008) and controls (p=0.03). Discussion: These results raise the assumption of a sustained role for both MS relapsing activity and disease heterogeneity (i.e. infra-clinical severity or activity of MS) in the impaired process of decision making.