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.

Dispersal strategies, few dominating or many coexisting: the effect of environmental spatial structure and multiple sources of mortality.

Interspecific competition, life history traits, environmental heterogeneity and spatial structure as well as disturbance are known to impact the successful dispersal strategies in metacommunities. However, studies on the direction of impact of those factors on dispersal have yielded contradictory results and often considered only few competing dispersal strategies at the same time. We used a unifying modeling approach to contrast the combined effects of species traits (adult survival, specialization), environmental heterogeneity and structure (spatial autocorrelation, habitat availability) and disturbance on the selected, maintained and coexisting dispersal strategies in heterogeneous metacommunities. Using a negative exponential dispersal kernel, we allowed for variation of both species dispersal distance and dispersal rate. We showed that strong disturbance promotes species with high dispersal abilities, while low local adult survival and habitat availability select against them. Spatial autocorrelation favors species with higher dispersal ability when adult survival and disturbance rate are low, and selects against them in the opposite situation. Interestingly, several dispersal strategies coexist when disturbance and adult survival act in opposition, as for example when strong disturbance regime favors species with high dispersal abilities while low adult survival selects species with low dispersal. Our results unify apparently contradictory previous results and demonstrate that spatial structure, disturbance and adult survival determine the success and diversity of coexisting dispersal strategies in competing metacommunities.

The role of phylogeny in the spatial distributions and assembly of mountain plant communities.

A major challenge in community ecology is a thorough understanding of the processes that govern the assembly and composition of communities in time and space. The growing threat of climate change to the vascular plant biodiversity of fragile ecosystems such as mountains has made it equally imperative to develop comprehensive methodologies to provide insights into how communities are assembled. In this perspective, the primary objective of this PhD thesis is to contribute to the theoretical and methodological development of community ecology, by proposing new solutions to better detect the ecological and evolutionary processes that govern community assembly. As phylogenetic trees provide by far, the most advanced tools to integrate the spatial, ecological and evolutionary dynamics of plant communities, they represent the cornerstone on which this work was based. In this thesis, I proposed new solutions to: (i) reveal trends in community assembly on phylogenies, depicted by the transition of signals at the nodes of the different species and lineages responsible for community assembly, (ii) contribute to evidence the importance of evolutionarily labile traits in the distribution of mountain plant species. More precisely, I demonstrated that phylogenetic and functional compositional turnover in plant communities was driven by climate and human land use gradients mostly influenced by evolutionarily labile traits, (iii) predict and spatially project the phylogenetic structure of communities using species distribution models, to identify the potential distribution of phylogenetic diversity, as well as areas of high evolutionary potential along elevation. The altitudinal setting of the Diablerets mountains (Switzerland) provided an appropriate model for this study. The elevation gradient served as a compression of large latitudinal variations similar to a collection of islands within a single area, and allowed investigations on a large number of plant communities. Overall, this thesis highlights that stochastic and deterministic environmental filtering processes mainly influence the phylogenetic structure of plant communities in mountainous areas. Negative density-dependent processes implied through patterns of phylogenetic overdispersion were only detected at the local scale, whereas environmental filtering implied through phylogenetic clustering was observed at both the regional and local scale. Finally, the integration of indices of phylogenetic community ecology with species distribution models revealed the prospects of providing novel and insightful explanations on the potential distribution of phylogenetic biodiversity in high mountain areas. These results generally demonstrate the usefulness of phylogenies in inferring assembly processes, and are worth considering in the theoretical and methodological development of tools to better understand phylogenetic community structure.

Spatial, temporal and subcellular localization of islet-brain 1 (IB1), a homologue of JIP-1, in mouse brain.

Islet-brain 1 (IB1) was recently identified as a DNA-binding protein of the GLUT2 gene promoter. The mouse IB1 is the rat and human homologue of the Jun-interacting protein 1 (JIP-1) which has been recognized as a key player in the regulation of c-Jun amino-terminal kinase (JNK) mitogen-activated protein kinase (MAPK) pathways. JIP-1 is involved in the control of apoptosis and may play a role in brain development and aging. Here, IB1 was studied in adult and developing mouse brain tissue by in situ hybridization, Northern and Western blot analysis at cellular and subcellular levels, as well as by immunocytochemistry in brain sections and cell cultures. IB1 expression was localized in the synaptic regions of the olfactory bulb, retina, cerebral and cerebellar cortex and hippocampus in the adult mouse brain. IB1 was also detected in a restricted number of axons, as in the mossy fibres from dentate gyrus in the hippocampus, and was found in soma, dendrites and axons of cerebellar Purkinje cells. After birth, IB1 expression peaks at postnatal day 15. IB1 was located in axonal and dendritic growth cones in primary telencephalon cells. By biochemical and subcellular fractionation of neuronal cells, IB1 was detected both in the cytosolic and membrane fractions. Taken together with previous data, the restricted neuronal expression of IB1 in developing and adult brain and its prominent localization in synapses suggest that the protein may be critical for cell signalling in developing and mature nerve terminals.

Spatial pattern and process at the plant neighbourhood scale: insights from communities dominated by the clonal grass Elymus repens (L.) Gould.

Question: How do clonal traits of a locally dominant grass (Elymus repens (L.) Gould.) respond to soil heterogeneity and shape spatial patterns of its tillers? How do tiller spatial patterns constrain seedling recruitment within the community?Locations: Artificial banks of the River Rhone, France.Material and Methods: We examined 45 vegetation patches dominated by Elymus repens. During a first phase we tested relationships between soil variables and three clonal traits (spacer length, number of clumping tillers and branching rate), and between the same clonal traits and spatial patterns (i.e. density and degree of spatial aggregation) of tillers at a very fine scale. During a second phase, we performed a sowing experiment to investigate effects of density and spatial patterns of E. repens on recruitment of eight species selected from the regional species pool.Results: Clonal traits had clear effects - especially spacer length - on densification and aggregation of E. repens tillers and, at the same time, a clear response of these same clonal traits as soil granulometry changed. The density and degree of aggregation of E. repens tillers was positively correlated to total seedling cover and diversity at the finest spatial scales.Conclusions: Spatial patterning of a dominant perennial grass responds to soil heterogeneity through modifications of its clonal morphology as a trade-off between phalanx and guerrilla forms. In turn, spatial patterns have strong effects on abundance and diversity of seedlings. Spatial patterns of tillers most probably led to formation of endogenous gaps in which the recruitment of new plant individuals was enhanced. Interestingly, we also observed more idiosyncratic effects of tiller spatial patterns on seedling cover and diversity when focusing on different growth forms of the sown species.

The impact of spatial resolution and respiratory motion on MR imaging of atherosclerotic plaque.

PURPOSE: To examine the impact of spatial resolution and respiratory motion on the ability to accurately measure atherosclerotic plaque burden and to visually identify atherosclerotic plaque composition. MATERIALS AND METHODS: Numerical simulations of the Bloch equations and vessel wall phantom studies were performed for different spatial resolutions by incrementally increasing the field of view. In addition, respiratory motion was simulated based on a measured physiologic breathing pattern. RESULTS: While a spatial resolution of > or = 6 pixels across the wall does not result in significant errors, a resolution of < or = 4 pixels across the wall leads to an overestimation of > 20%. Using a double-inversion T2-weighted turbo spin echo sequence, a resolution of 1 pixel across equally thick tissue layers (fibrous cap, lipid, smooth muscle) and a respiratory motion correction precision (gating window) of three times the thickness of the tissue layer allow for characterization of the different coronary wall components. CONCLUSIONS: We found that measurements in low-resolution black blood images tend to overestimate vessel wall area and underestimate lumen area.

Revisiting spatial distribution and biochemical composition of calcium-containing crystals in human osteoarthritic articular cartilage.

INTRODUCTION: Calcium-containing (CaC) crystals, including basic calcium phosphate (BCP) and calcium pyrophosphate dihydrate (CPP), are associated with destructive forms of osteoarthritis (OA). We assessed their distribution and biochemical and morphologic features in human knee OA cartilage. METHODS: We prospectively included 20 patients who underwent total knee replacement (TKR) for primary OA. CaC crystal characterization and identification involved Fourier-transform infra-red spectrometry and scanning electron microscopy of 8 to 10 cartilage zones of each knee, including medial and lateral femoral condyles and tibial plateaux and the intercondyle zone. Differential expression of genes involved in the mineralization process between cartilage with and without calcification was assessed in samples from 8 different patients by RT-PCR. Immunohistochemistry and histology studies were performed in 6 different patients. RESULTS: Mean (SEM) age and body mass index of patients at the time of TKR was 74.6 (1.7) years and 28.1 (1.6) kg/m², respectively. Preoperative X-rays showed joint calcifications (chondrocalcinosis) in 4 cases only. The medial femoro-tibial compartment was the most severely affected in all cases, and mean (SEM) Kellgren-Lawrence score was 3.8 (0.1). All 20 OA cartilages showed CaC crystals. The mineral content represented 7.7% (8.1%) of the cartilage weight. All patients showed BCP crystals, which were associated with CPP crystals for 8 joints. CaC crystals were present in all knee joint compartments and in a mean of 4.6 (1.7) of the 8 studied areas. Crystal content was similar between superficial and deep layers and between medial and femoral compartments. BCP samples showed spherical structures, typical of biological apatite, and CPP samples showed rod-shaped or cubic structures. The expression of several genes involved in mineralization, including human homolog of progressive ankylosis, plasma-cell-membrane glycoprotein 1 and tissue-nonspecific alkaline phosphatase, was upregulated in OA chondrocytes isolated from CaC crystal-containing cartilages. CONCLUSIONS: CaC crystal deposition is a widespread phenomenon in human OA articular cartilage involving the entire knee cartilage including macroscopically normal and less weight-bearing zones. Cartilage calcification is associated with altered expression of genes involved in the mineralisation process.

Vision, spatial cognition and intellectual disability.

Vision is the most synthetic sensory channel and it provides specific information about the relative position of distant landmarks during visual exploration. In this paper we propose that visual exploration, as assessed by the recording of eye movements, offers an original method to analyze spatial cognition and to reveal alternative adaptation strategies in people with intellectual disabilities (ID). Our general assumption is that eye movement exploration may simultaneously reveal whether, why, and how, compensatory strategies point to specific difficulties related to neurological symptoms. An understanding of these strategies will also help in the development of optimal rehabilitation procedures.

Metabolic activation pattern of distinct hippocampal subregions during spatial learning and memory retrieval.

Activation dynamics of hippocampal subregions during spatial learning and their interplay with neocortical regions is an important dimension in the understanding of hippocampal function. Using the (14C)-2-deoxyglucose autoradiographic method, we have characterized the metabolic changes occurring in hippocampal subregions in mice while learning an eight-arm radial maze task. Autoradiogram densitometry revealed a heterogeneous and evolving pattern of enhanced metabolic activity throughout the hippocampus during the training period and on recall. In the early stages of training, activity was enhanced in the CA1 area from the intermediate portion to the posterior end as well as in the CA3 area within the intermediate portion of the hippocampus. At later stages, CA1 and CA3 activations spread over the entire longitudinal axis, while dentate gyrus (DG) activation occurred from the anterior to the intermediate zone. Activation of the retrosplenial cortex but not the amygdala was also observed during the learning process. On recall, only DG activation was observed in the same anterior part of the hippocampus. These results suggest the existence of a functional segmentation of the hippocampus, each subregion being dynamically but also differentially recruited along the acquisition, consolidation, and retrieval process in parallel with some neocortical sites.