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.

Withdrawal, "serosorting" and "strategic positioning": use of risk reduction strategies with casual sex partners in men who have sex with men (MSM) in Switzerland, 2007

Introduction: 1) Withdrawal before ejaculation, "serosorting" (to choose a partner of same serostatus) and "strategic positioning" (only insertive vs. only receptive role in anal sex according to serostatus) are known to be used by MSM as alternatives to condom use. 2) Despite their questionable levels of effectiveness they are collectively labelled as "risk reduction strategies" (RRS). Objectives: The aim of this study is to estimate the prevalence and factors related to RRS in men who report unprotected anal intercourse (UAI) with occasional partners in the last 12 months. Methods: 1) In 2007, a module on RRS was included in a repeated national survey conducted among readers of gay newspapers, members of gay organizations and visitors of gay websites (N=2953). 2) Using an anonymous self-completed questionnaire, participants were asked whether, with the aim of avoiding HIV infection, RRS were used with occasional partners. Analysis: 1) Prevalences were calculated in participants who reported UAI with occasional partners in the last 12 months (n=416). 2) A logistic regression was performed, using "at least one RRS" as dependent variable. Number of partners in the last 12 months, HIV-status and usual socio-demographic characteristics were used as independent factors. Result : 1) 70% (292/416) of the participants reporting UAI used at least one RRS when they had unprotected sex with casual partners in the last 12 months (Table 1). 2) Withrawal before ejaculation was the most frequently reported strategy, followed by serosorting and strategic positioning (Table 1). 3) Participants who reported at least one RRS were more likely to be over 30 years and to belong to a gay organisation. HIV-positive and non-tested participants were less likely to report RRS than HIV-negative participants (Table 2). Conclusions: 1) The majority of MSM who reported UAI in the last 12 months tried to reduce risk of HIV transmission by using specific strategies (withdrawal, serosorting, strategic positioning). It is not known, however, to what extent the use of these strategies was systematic. 2) It is necessary to provide MSM with balanced information on these strategies and their respective level of effectiveness. 3) It is important to monitor the use of RRS in HIV behavioural surveillance surveys in MSM.

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.

Predictors of HIV-protection behaviour in HIV-positive men who have sex with casual male partners: a test of the explanatory power of an extended Information-Motivation-Behavioural Skills model.

This prospective study applies an extended Information-Motivation-Behavioural Skills (IMB) model to establish predictors of HIV-protection behaviour among HIV-positive men who have sex with men (MSM) during sex with casual partners. Data have been collected from anonymous, self-administered questionnaires and analysed by using descriptive and backward elimination regression analyses. In a sample of 165 HIV-positive MSM, 82 participants between the ages of 23 and 78 (M=46.4, SD=9.0) had sex with casual partners during the three-month period under investigation. About 62% (n=51) have always used a condom when having sex with casual partners. From the original IMB model, only subjective norm predicted condom use. More important predictors that increased condom use were low consumption of psychotropics, high satisfaction with sexuality, numerous changes in sexual behaviour after diagnosis, low social support from friends, alcohol use before sex and habitualised condom use with casual partner(s). The explanatory power of the calculated regression model was 49% (p<0.001). The study reveals the importance of personal and social resources and of routines for condom use, and provides information for the research-based conceptualisation of prevention offers addressing especially people living with HIV ("positive prevention").

"Michael's Game," a card game for the treatment of psychotic symptoms.

Objective: "Michael's Game" is a card game which aims at familiarizing healthcare professionals and patients with cognitive therapy of psychotic symptoms. The present study tests the feasibility and the impact of the intervention in naturalistic settings.Methods: 135 patients were recruited in 11 centres. They were assessed pre- and post-tests with the Beck Cognitive Insight Scale (BCIS) and the Peters Delusion Inventory-21 items (PDI-21).Results: Data about 107 patients were included in the entire analyses. Significant improvements were observed on BCIS subscales as well as a reduction of severity of conviction and preoccupation scores on the PDI-21. The intervention has a moderate effect on the PDI-21 preoccupation and conviction as well as the BCIS subscales. Patients who benefit the most from the program are patients who have a low degree of self-reflectiveness and patients who are concomitantly preoccupied by their symptoms.Conclusion: The present study supports the feasibility and effectiveness of "Michael's Game" in naturalistic settings.Practical implications: The game seems to be a useful tool for patients with psychotic disorders. (C) 2010 Elsevier Ireland Ltd. All rights reserved.

Men having sex with men serosorting with casual partners: who, how much, and what risk factors in Switzerland, 2007-2009.

BACKGROUND: Serosorting is practiced by men who have sex with men (MSM) to reduce human immunodeficiency virus (HIV) transmission. This study evaluates the prevalence of serosorting with casual partners, and analyses the characteristics and estimated numbers of serosorters in Switzerland 2007-2009. METHODS: Data were extracted from cross-sectional surveys conducted in 2007 and 2009 among self-selected MSM recruited online, through gay newspapers, and through gay organizations. Nested models were fitted to ascertain the appropriateness of pooling the datasets. Multiple logistic regression analysis was performed on pooled data to determine the association between serosorting and demographic, lifestyle-related, and health-related factors. Extrapolations were performed by applying proportions of various types of serosorters to Swiss population data collected in 2007. RESULTS: A significant and stable number of MSM (approximately 39% in 2007 and 2009) intentionally engage in serosorting with casual partners in Switzerland. Variables significantly associated with serosorting were: gay organization membership (aOR = 1.67), frequent internet use for sexual encounters (aOR = 1.71), having had a sexually transmitted infection (STI) at any time in the past 12 months (aOR = 1.70), HIV-positive status (aOR = 0.52), regularly frequenting sex-on-premises venues (aOR = 0.42), and unprotected anal intercourse (UAI) with partners of different or unknown HIV status in the past 12 months (aOR = 0.22). Approximately one-fifth of serosorters declared HIV negativity without being tested in the past 12 months; 15.8% reported not knowing their own HIV status. CONCLUSION: The particular risk profile of serosorters having UAI with casual partners (multiple partners, STI history, and inadequate testing frequency) requires specific preventive interventions tailored to HIV status.

Une nouvelle situation pour évaluer le fonctionnement familial: le jeu du pique-nique = A new situation to evaluate a family system's fuctioning: the picnic game.

Cet article présente une nouvelle situation, le Jeu du Pique-Nique, qui permet l'évaluation du fonctionnement familial, pris dans son ensemble, quel que soit le nombre d'enfants, âgés de quelques semaines à une douzaine d'années. L'évaluation est macroscopique, selon différentes dimensions comme le coparentage, la chaleur familiale, la dimension ludique, l'autonomie des enfants, etc. Pour illustrer la richesse des observations qu'offre cette situation, les jeux de trois familles contrastées sont présentés ainsi que leur codage. L'utilité en recherche ainsi qu'en clinique, et en particulier l'apport de la vision du film avec la famille, est discutée.

Coevolution of adaptive technology, maladaptive culture and population size in a producer-scrounger game.

Technology (i.e. tools, methods of cultivation and domestication, systems of construction and appropriation, machines) has increased the vital rates of humans, and is one of the defining features of the transition from Malthusian ecological stagnation to a potentially perpetual rising population growth. Maladaptations, on the other hand, encompass behaviours, customs and practices that decrease the vital rates of individuals. Technology and maladaptations are part of the total stock of culture carried by the individuals in a population. Here, we develop a quantitative model for the coevolution of cumulative adaptive technology and maladaptive culture in a 'producer-scrounger' game, which can also usefully be interpreted as an 'individual-social' learner interaction. Producers (individual learners) are assumed to invent new adaptations and maladaptations by trial-and-error learning, insight or deduction, and they pay the cost of innovation. Scroungers (social learners) are assumed to copy or imitate (cultural transmission) both the adaptations and maladaptations generated by producers. We show that the coevolutionary dynamics of producers and scroungers in the presence of cultural transmission can have a variety of effects on population carrying capacity. From stable polymorphism, where scroungers bring an advantage to the population (increase in carrying capacity), to periodic cycling, where scroungers decrease carrying capacity, we find that selection-driven cultural innovation and transmission may send a population on the path of indefinite growth or to extinction.

Social rationality and scales of action: inter-ethnic relations in cockfighting and game-fishing, Raiatea, French Polynesia

This article challenges the notion of economic rationality as a criterion for explaining ethnic boundary maintenance. It offers an ethnographic analysis of inter-ethnic relations in the context of games (cockfights and game-fishing contests) in the island of Raiatea (French Polynesia). Although all players engage in the same basic gambling practices, money is differentially scaled and mobilized by the Tahitian and Chinese participants. Building on recent pragmatic approaches to rationality, it is shown that the players' rationalities differ not from the point of view of economic maximization, but only in so far as they participate in social relations at different scales.