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.

Evolution, maintenance and ecological consequences of genetic caste determination in " Pogonomyrmex " harvester ants

Summary Division of labor between reproducers (queens) and helpers (workers) is the main characteristic of social insect societies and at the root of their ecological success. Kin selection models predict that phenotypic differences between queens and workers should result from environmental rather than from genetic differences. However, genetic effects on queen and worker differentiation were found in two populations-of Pogonomyrmex harvester ants. Each of the two populations is composed of two genetically distinct lineages. Queens (which can be of either lineage) generally mate with males of their own and of the alternate lineage and produce two types of female offspring, those fertilized by males of the queens' lineage which develop into queens and those fertilized by males of the alternate lineage which develop into workers. All four lineages were further suggested to be themselves of hybrid origin between-the species P: barbatus and P. rugosus, in which queens and workers do not differ genetically. In a first set of experiments, we tested if female caste determination (the differentiation into queens and workers) in the lineages was genetically hardwired and if it was associated with costs in terms of the ability to optimally allocate resources to the production of queens and workers. To this end we first mated queens of-two lineages to a single male. Queens mated to a male of the alternate lineage successfully raised worker offspring whereas queens mated to a male of their own lineage almost always failed to produce workers. This reveals that pure-lineage individuals have lost the ability to develop into workers. Second, we analyzed offspring produced by naturally mated queens. During the stage of colony founding when only workers are produced, naturally mated queens laid a high proportion of pure-lineage eggs but the large majority of these eggs failed to develop. As a consequence, the number of offspring produced by incipient colonies decreased linearly with the proportion of pure-lineage eggs laid by queens. Moreover, queens of the lineage most commonly represented in a given population produced more pure-lineage eggs, in line with the view that they mate randomly with the two types of males and indiscriminately use their sperm. Altogether these results predict frequency-dependent founding success for pairs of lineages because queens of the more common lineage will produce more pure-lineage eggs and their colonies be less successful during the stage of colony founding. To describe the distribution of populations characterized with genetic caste determination relative to the populations with environmental caste determination we genotyped queens and workers collected during a large survey of -additional populations. Genetic caste determination associated with pairs of interbreeding lineages was frequent and widespread in the studied range and we identified four additional lineages displaying genetic caste determination. Overall, there were thus eight highly differentiated lineages with genetic caste determination. These lineages always co-occurred in the same complementary lineage pairs. Three of the four lineage pairs appeared to have a common origin, while their relationship with the forth could not be resolved. The genetic survey also revealed that, in addition to being genetically isolated from one another, all eight lineages were genetically distinct from P. rugosus and P. barbatus, even when colonies of interbreeding lineages co-occurred with colonies of either putative parent at the same site. This raised the question of the mechanisms involved in the reproductive isolation between the lineages and the parental species and between the two lineages of a lineage pair. At a site where one lineage pair co-occurred with P. rugosus, we identified two pre-zygotic mechanisms (differences in timing for mating flights between P. rugosus and the lineage pair and assortative mating) and one post-zygotic mechanism (high levels of hybrid unviablility) which in combination may largely account for the reproductive isolation between the lineages and their parental species. The mechanisms accounting for the reproductive isolation between the two lineages of a lineage pair varied across lineage pairs. In one lineage pair, inter-lineage individuals exclusively occurred in the sterile worker caste, raising the possibility that inter-lineage eggs have completely lost the ability to develop into queens in this lineage pair and that there is thus no opportunity for gene flow. In each of the three remaining lineage pairs, inter-lineage queens were produced by a minority of colonies. In these lineage pairs, colonies headed by inter-lineage queens failed to grow sufficiently to produce reproductive individuals which may account for the reproductive isolation between co-occurring lineages in three lineage pairs. In conclusion, the results of this thesis show that genetic caste determination is costly but widespread in Pogonomyrmex harvester ants. Reproductive isolation among the lineages and between the lineages and the parental species as well as frequency-dependent founding success for co-occurring lineages may contribute to the persistence of this extraordinary system. Résumé La division du travail entre individus reproducteurs (les reines) et individus non-reproducteurs (ouvrières) représente la caractéristique principale des sociétés d'insectes et est à la base de leur succès écologique. Des modèles de sélection de parentèle prédisent que les différences phénotypiques entre reines et ouvrières devraient provenir d'effets environnementaux plutôt que de différences génétiques. Malgré ce fait, des effets génétiques sur la différentiation entre reines et ouvrières ont été montrés dans deux populations de fourmis moissonneuses du genre Pogonomyrmex. Chacune des deux populations est composée de deux lignées génétiquement distinctes. Les reines de chaque lignée s'accouplent en général avec des mâles de leur propre lignée ainsi qu'avec des mâles de l'autre lignée et produisent deux types d'oeufs, ceux qui sont fécondés par les mâles de leur propre lignée qui se développent en nouvelles reines et ceux qui sont fécondés par les mâles de l'autre lignée qui se développent en ouvrières. Il a été suggéré que les lignées sont elles-mêmes des hybrides entre les deux espèces P. barbatus et P. rugosus. Dans ces deux espèces, les reines et ouvrières ne sont pas génétiquement distinctes. Dans une première série d'expériences, nous avons testé si la détermination de la caste femelle (le développement en reine ou en ouvrière) est génétiquement rigide et si elle est associée à des coûts en terme de capacité à allouer de façon optimale les ressources pour la production de reines et d'ouvrières. Pour cela nous avons accouplé des reines de deux lignées avec un seul mâle. Les reines accouplées avec un mâle de l'autre lignée ont élevé de nouvelles ouvrières avec succès alors que les reines accouplées avec un mâle de leur propre lignée ont presque toujours échoué à produire des ouvrières. Ceci montre que les individus de lignée pure ont perdu la capacité de se développer en ouvrière. Deuxièmement, nous avons analysé la descendance de reines qui se sont accouplées naturellement. Durant le stade de fondation de la colonie, où seules des ouvrières sont élevées, les reines accouplées naturellement ont pondu une grande proportion d'oeufs de lignée pure mais la majorité de ces derniers ne se sont pas développés. En conséquence, le nombre de descendants produits par des colonies fondatrices diminuait linéairement avec la proportion des oeufs de lignée pure pondus par la reine en accord avec l'hypothèse que les reines s'accouplent au hasard avec les deux types de mâles et utilisent leur sperme aléatoirement. Dans l'ensemble; ces résultats prédisent un succès de fondation fréquence-dépendant pour les deux lignées, car les reines de la lignée la plus fréquente produiront .plus d'oeufs de lignée pure et leurs colonies auront moins de succès lors de la fondation de colonies par rapport aux colonies de la lignée la moins fréquente. Pour décrire la distribution des-populations caractérisées par une détermination génétique des castes par rapport aux populations caractérisées par une détermination environnementale des castes, nous avons génotypé des reines et des ouvrières qui ont été collectées lors d'une analyse de populations supplémentaires. La détermination génétique des castes associée à des croisements entre lignées est fréquente et largement répartie dans l'aire étudiée. Nous avons identifié quatre lignées supplémentaires, ayant une détermination génétique des castes, pour un total de huit lignées. Ces huit lignées forment quatre paires de lignées et on ne trouve jamais deux lignées de paires différentes, dans une population. Trois des quatre paires de lignées s'avèrent avoir une origine commune alors que leur relation avec la quatrième paire de lignées n'a pas pu être résolue. L'analyse génétique de populations supplémentaires a également révélé qu'en plus d'être génétiquement isolées les unes des autres, les huit lignées sont génétiquement distinctes de P. rugosus et P. barbatus même si les colonies d'une paire de lignées se trouvent en sympatrie avec l'une ou l'autre des espèces parentales. Ceci relève la question des mécanismes impliqués dans l'isolation reproductive entre les lignées et les espèces parentales ainsi qu'entre les deux lignées d'une paire. En étudiant un site où une paire de lignées se trouve en sympatrie avec P. rugosus, nous avons identifié deux mécanismes pré-zygotiques (des différences dans le timing du vol nuptial entre P. rugosus et les lignées et des accouplements assortis) ainsi qu'un mécanisme post-zygotique (un niveau élevé de non-viabilité des hybrides). En combinaison, ces mécanismes peuvent largement expliquer l'isolement reproductif entre les lignées et leurs espèces parentales. Les mécanismes contribuant à l'isolement reproductif entre les deux lignées d'une paire variaient entre paires de lignées. Dans une paire, les individus de génotype inter-lignée se trouvent uniquement dans la caste stérile des ouvrières, suggérant qu'il n'y a pas d'opportunité pour avoir du flux de gènes entre les deux lignées ce cette paire. Dans chacune des trois autres paires de lignées des nouvelles reines de génotype inter-lignée sont produites par une minorité de colonies. Par contre, les colonies avec une reine mère de génotype inter-lignée ne se développent pas suffisamment pour produire des individus reproducteurs. Ceci peut donc expliquer pourquoi il n'y a pas de flux de gènes entre les deux lignées de trois paires. En conclusion, les résultats de cette thèse montrent que la détermination génétique de la caste est coûteuse mais très répandue chez les fourmis. moissonneuses du genre Pogonomyrmex. L'isolement reproductif des lignées entre elles et avec les espèces parentales, ainsi qu'un succès de fondation fréquence-dépendant contribuent à la persistance de ce système extraordinaire.

How life history and demography promote or inhibit the evolution of helping behaviours.

In natural populations, dispersal tends to be limited so that individuals are in local competition with their neighbours. As a consequence, most behaviours tend to have a social component, e.g. they can be selfish, spiteful, cooperative or altruistic as usually considered in social evolutionary theory. How social behaviours translate into fitness costs and benefits depends considerably on life-history features, as well as on local demographic and ecological conditions. Over the last four decades, evolutionists have been able to explore many of the consequences of these factors for the evolution of social behaviours. In this paper, we first recall the main theoretical concepts required to understand social evolution. We then discuss how life history, demography and ecology promote or inhibit the evolution of helping behaviours, but the arguments developed for helping can be extended to essentially any social trait. The analysis suggests that, on a theoretical level, it is possible to contrast three critical benefit-to-cost ratios beyond which costly helping is selected for (three quantitative rules for the evolution of altruism). But comparison between theoretical results and empirical data has always been difficult in the literature, partly because of the perennial question of the scale at which relatedness should be measured under localized dispersal. We then provide three answers to this question.

The longitudinal association between social functioning and theory of mind in first episode psychosis

Introduction. There is some cross-sectional evidence that theory of mind ability is associated with social functioning in those with psychosis but the direction of this relationship is unknown. This study investigates the longitudinal association between both theory of mind and psychotic symptoms and social functioning outcome in first-episode psychosis. Methods. Fifty-four people with first-episode psychosis were followed up at 6 and 12 months. Random effects regression models were used to estimate the stability of theory of mind over time and the association between baseline theory of mind and psychotic symptoms and social functioning outcome. Results. Neither baseline theory of mind ability (regression coefficients: Hinting test 1.07 95% CI 0.74, 2.88; Visual Cartoon test 2.91 95% CI 7.32, 1.51) nor baseline symptoms (regression coefficients: positive symptoms 0.04 95% CI 1.24, 1.16; selected negative symptoms 0.15 95% CI 2.63, 2.32) were associated with social functioning outcome. There was evidence that theory of mind ability was stable over time, (regression coefficients: Hinting test 5.92 95% CI 6.66, 8.92; Visual Cartoon test score 0.13 95% CI 0.17, 0.44). Conclusions. Neither baseline theory of mind ability nor psychotic symptoms are associated with social functioning outcome. Further longitudinal work is needed to understand the origin of social functioning deficits in psychosis.

Recommandations de pratique clinique dans la schizophrénie: de la théorie à la mise en application = Clinical practice guidelines for the treatment of schizophrenia: from theory to practice

Dans le cadre d'une étude rétrospective au sein d'une unité de réhabilitation, nous avons cherché à examiner le degré de respect de recommandations de pratique clinique (RPC) abordant le traitement pharmacologique au long cours de la schizophrénie, par des médecins qui n'en ont qu'une connaissance indirecte. The Expert Consensus Guideline for the treatment of schizophrenia (ECGTS) a été retenu comme référence sur la base d'une comparaison avec cinq autres RPC principales. Sur un collectif de 20 patients, les recommandations de l'ECGTS sont totalement respectées dans 65 % des cas, partiellement respectées dans 10 % et non respectées dans 25 %, démontrant ainsi que la pratique clinique est clairement perfectible (principalement dans le traitement des symptômes psychotiques et dépressifs). Cependant, le respect des RPC ne garantit pas forcément la résolution de tous les problèmes cliniques rencontrés : 12 patients sur 20 présentent des effets secondaires à l'évaluation clinique et pour huit d'entre eux, les recommandations à ce niveau, sont respectées. Notre étude montre cependant que le choix et l'application d'une RPC ne sont pas simples. Les RPC actuelles donnent peu ou pas d'instruments de mesure, ni de critères précis pour évaluer les problèmes cliniques auxquels elles font référence. L'avenir appartient donc à des RPC qui proposent, outre les recommandations cliniques elles-mêmes, les moyens de leur vérification et de leur application sur le terrain.

Nest-box design for the study of diurnal raptors and owls is still an overlooked point in ecological, evolutionary and conservation studies: a review

The use of artificial nest-boxes has led to significant progress in bird conservation and in our understanding of the functional and evolutionary ecology of free-ranging birds that exploit cavities for roosting and reproduction. Nest-boxes and their improved accessibility have made it easier to perform comparative and experimental field investigations. However, concerns about the generality and applicability of scientific studies involving birds breeding in nest-boxes have been raised because the occupants of boxes may differ from conspecifics occupying other nest sites. Here we review the existing evidence demonstrating the importance of nest-box design to individual life-history traits in three falcon (Falconiformes) and seven owl (Strigiformes) species, as well as the extent to which publications on these birds describe the characteristics of exploited artificial nest-boxes in their 'methods' sections. More than 60% of recent publications did not provide any details on nest-box design (e.g. size, shape, material), despite several calls >15 years ago to increase the reporting of such information. We exemplify and discuss how variation in nest-box characteristics can affect or confound conclusions from nest-box studies and conclude that it is of overall importance to present details of nest-box characteristics in scientific publications.

Public sector rationing and private sector selection [paper accepted and forthcoming in Journal of Public Economic Theory]

We study the interaction between nonprice public rationing and prices in the private market. Under a limited budget, the public supplier uses a rationing policy. A private firm may supply the good to those consumers who are rationed by the public system. Consumers have different amounts of wealth, and costs of providing the good to them vary. We consider two regimes. First, the public supplier observes consumers' wealth information; second, the public supplier observes both wealth and cost information. The public supplier chooses a rationing policy, and, simultaneously, the private firm, observing only cost but not wealth information, chooses a pricing policy. In the first regime, there is a continuum of equilibria. The Pareto dominant equilibrium is a means-test equilibrium: poor consumers are supplied while rich consumers are rationed. Prices in the private market increase with the budget. In the second regime, there is a unique equilibrium. This exhibits a cost-effectiveness rationing rule; consumers are supplied if and only if their costbenefit ratios are low. Prices in the private market do not change with the budget. Equilibrium consumer utility is higher in the cost-effectiveness equilibrium than the means-test equilibrium [Authors]