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.

Relève en médecine interne générale: enjeux et perspectives [Perspectives and challenges to guarantee training and renewal in general internal medicine]

Training new doctors in general internal medicine represents a challenge. This requires to define future needs, which result from interest that are not necessarily convergent between patients, doctors, insurers and politicians. Problems related to medical demography in Switzerland, with the ageing of the population, the increase in health care costs and the place of Switzerland within the European Community require the implementation of specific objectives to train new physicians in general internal medicine. The success of these opportunities depends on social factors, political choices and choices from physician's association. In this article we will approach these challenges by formulating some proposals--nonexhaustive--in order to guarantee sufficient renewal in general internal medicine.

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.

Altruism, dispersal, and phenotype-matching kin recognition.

We investigate the coevolution between philopatry and altruism in island-model populations when kin recognition occurs through phenotype matching. In saturated environments, a good discrimination ability is a necessary prerequisite for the emergence of sociality. Discrimination decreases not only with the average phenotypic similarity between immigrants and residents (i.e., with environmental homogeneity and past gene flow) but also with the sampling variance of similarity distributions (a negative function of the number of traits sampled). Whether discrimination should rely on genetically or environmentally determined traits depends on the apportionment of phenotypic variance and, in particular, on the relative values of e (the among-group component of environmental variance) and r (the among-group component of genetic variance, which also measures relatedness among group members). If r exceeds e, highly heritable cues do better. Discrimination and altruism, however, remain low unless philopatry is enforced by ecological constraints. If e exceeds r, by contrast, nonheritable traits do better. High e values improve discrimination drastically and thus have the potential to drive sociality, even in the absence of ecological constraints. The emergence of sociality thus can be facilitated by enhancing e, which we argue is the main purpose of cue standardization within groups, as observed in many social insects, birds, and mammals, including humans.

The genetical theory of social behaviour.

We survey the population genetic basis of social evolution, using a logically consistent set of arguments to cover a wide range of biological scenarios. We start by reconsidering Hamilton's (Hamilton 1964 J. Theoret. Biol. 7, 1-16 (doi:10.1016/0022-5193(64)90038-4)) results for selection on a social trait under the assumptions of additive gene action, weak selection and constant environment and demography. This yields a prediction for the direction of allele frequency change in terms of phenotypic costs and benefits and genealogical concepts of relatedness, which holds for any frequency of the trait in the population, and provides the foundation for further developments and extensions. We then allow for any type of gene interaction within and between individuals, strong selection and fluctuating environments and demography, which may depend on the evolving trait itself. We reach three conclusions pertaining to selection on social behaviours under broad conditions. (i) Selection can be understood by focusing on a one-generation change in mean allele frequency, a computation which underpins the utility of reproductive value weights; (ii) in large populations under the assumptions of additive gene action and weak selection, this change is of constant sign for any allele frequency and is predicted by a phenotypic selection gradient; (iii) under the assumptions of trait substitution sequences, such phenotypic selection gradients suffice to characterize long-term multi-dimensional stochastic evolution, with almost no knowledge about the genetic details underlying the coevolving traits. Having such simple results about the effect of selection regardless of population structure and type of social interactions can help to delineate the common features of distinct biological processes. Finally, we clarify some persistent divergences within social evolution theory, with respect to exactness, synergies, maximization, dynamic sufficiency and the role of genetic arguments.

Emergence of Cooperation on Static and Dynamic Networks

Game theory is a branch of applied mathematics used to analyze situation where two or more agents are interacting. Originally it was developed as a model for conflicts and collaborations between rational and intelligent individuals. Now it finds applications in social sciences, eco- nomics, biology (particularly evolutionary biology and ecology), engineering, political science, international relations, computer science, and philosophy. Networks are an abstract representation of interactions, dependencies or relationships. Net- works are extensively used in all the fields mentioned above and in many more. Many useful informations about a system can be discovered by analyzing the current state of a network representation of such system. In this work we will apply some of the methods of game theory to populations of agents that are interconnected. A population is in fact represented by a network of players where one can only interact with another if there is a connection between them. In the first part of this work we will show that the structure of the underlying network has a strong influence on the strategies that the players will decide to adopt to maximize their utility. We will then introduce a supplementary degree of freedom by allowing the structure of the population to be modified along the simulations. This modification allows the players to modify the structure of their environment to optimize the utility that they can obtain.

The stationary distribution of a continuously varying strategy in a class-structured population under mutation-selection-drift balance.

Many traits and/or strategies expressed by organisms are quantitative phenotypes. Because populations are of finite size and genomes are subject to mutations, these continuously varying phenotypes are under the joint pressure of mutation, natural selection and random genetic drift. This article derives the stationary distribution for such a phenotype under a mutation-selection-drift balance in a class-structured population allowing for demographically varying class sizes and/or changing environmental conditions. The salient feature of the stationary distribution is that it can be entirely characterized in terms of the average size of the gene pool and Hamilton's inclusive fitness effect. The exploration of the phenotypic space varies exponentially with the cumulative inclusive fitness effect over state space, which determines an adaptive landscape. The peaks of the landscapes are those phenotypes that are candidate evolutionary stable strategies and can be determined by standard phenotypic selection gradient methods (e.g. evolutionary game theory, kin selection theory, adaptive dynamics). The curvature of the stationary distribution provides a measure of the stability by convergence of candidate evolutionary stable strategies, and it is evaluated explicitly for two biological scenarios: first, a coordination game, which illustrates that, for a multipeaked adaptive landscape, stochastically stable strategies can be singled out by letting the size of the gene pool grow large; second, a sex-allocation game for diploids and haplo-diploids, which suggests that the equilibrium sex ratio follows a Beta distribution with parameters depending on the features of the genetic system.

Exposure to superfluous information reduces cooperation and increases antisocial punishment in reputation-based interactions

Human cooperation is often based on reputation gained from previous interactions with third parties. Such reputation can be built on generous or punitive actions, and both, one's own reputation and the reputation of others have been shown to influence decision making in experimental games that control for confounding variables. Here we test how reputation-based cooperation and punishment react to disruption of the cognitive processing in different kinds of helping games with observers. Saying a few superfluous words before each interaction was used to possibly interfere with working memory. In a first set of experiments, where reputation could only be based on generosity, the disruption reduced the frequency of cooperation and lowered mean final payoffs. In a second set of experiments where reputation could only be based on punishment, the disruption increased the frequency of antisocial punishment (i.e. of punishing those who helped) and reduced the frequency of punishing defectors. Our findings suggest that working memory can easily be constraining in reputation-based interactions within experimental games, even if these games are based on a few simple rules with a visual display that provides all the information the subjects need to play the strategies predicted from current theory. Our findings also highlight a weakness of experimental games, namely that they can be very sensitive to environmental variation and that quantitative conclusions about antisocial punishment or other behavioral strategies can easily be misleading.

Conformity, upstream reciprocity and social diversity: secondary mechanisms for the evolution of cooperation

Cooperation is ubiquitous in nature: genes cooperate in genomes, cells in muti- cellular organims, and individuals in societies. In humans, division of labor and trade are key elements of most known societies, where social life is regulated by- moral systems specifying rights and duties often enforced by third party punish¬ment. Over the last decades, several primary mechanisms, such as kin selection, direct and indirect reciprocity, have been advanced to explain the evolution of cooperation from a naturalistic approach. In this thesis, I focus on the study of three secondary mechanisms which, although insufficient to allow for the evo¬lution of cooperation, have been hypothesized to further promote it when they are linked to proper primary mechanisms: conformity (the tendency to imitate common behaviors), upstream reciprocity (the tendency to help somebody once help has been received from somebody else) and social diversity (heterogeneous social contexts). I make use of mathematical and computational models in the formal framework of evolutionary game theory in order to investigate the theoret¬ical conditions under which conformity, upstream reciprocity and social diversity are able to raise the levels of cooperation attained in evolving populations. - La coopération est ubiquitaire dans la nature: les gènes coopèrent dans les génomes, les cellules dans les organismes muticellulaires, et les organismes dans les sociétés. Chez les humains, la division du travail et le commerce sont des éléments centraux de la plupart des sociétés connues, où la vie sociale est régie par des systèmes moraux établissant des droits et des devoirs, souvent renforcés par la punition. Au cours des dernières décennies, plusieurs mécanismes pri¬maires, tels que la sélection de parentèle et les réciprocités directe et indirecte, ont été avancés pour expliquer l'évolution de la coopération d'un point de vue nat¬uraliste. Dans cette thèse, nous nous concentrons sur l'étude de trois mécanismes secondaires qui, bien qu'insuffisants pour permettre l'évolution de la coopération, sont capables de la promouvoir davantage s'ils sont liés aux mécanismes primaires appropriés: la conformité (tendance à imiter des comportements en commun), la 'réciprocité en amont' (tendance à aider quelqu'un après avoir reçu l'aide de quelqu'un d'autre) et la diversité sociale (contextes sociaux hétérogènes). Nous faisons usage de modèles mathématiques et informatiques dans le cadre formel de la théorie des jeux évolutionnaires afin d'examiner les conditions théoriques dans lesquelles la conformité, la 'réciprocité en amont' et la diversité sociale sont capables d'élever le niveau de coopération des populations en évolution.

Risk and global change : developing scientific methods for advocacy and awareness raising

Les catastrophes sont souvent perçues comme des événements rapides et aléatoires. Si les déclencheurs peuvent être soudains, les catastrophes, elles, sont le résultat d'une accumulation des conséquences d'actions et de décisions inappropriées ainsi que du changement global. Pour modifier cette perception du risque, des outils de sensibilisation sont nécessaires. Des méthodes quantitatives ont été développées et ont permis d'identifier la distribution et les facteurs sous- jacents du risque.¦Le risque de catastrophes résulte de l'intersection entre aléas, exposition et vulnérabilité. La fréquence et l'intensité des aléas peuvent être influencées par le changement climatique ou le déclin des écosystèmes, la croissance démographique augmente l'exposition, alors que l'évolution du niveau de développement affecte la vulnérabilité. Chacune de ses composantes pouvant changer, le risque est dynamique et doit être réévalué périodiquement par les gouvernements, les assurances ou les agences de développement. Au niveau global, ces analyses sont souvent effectuées à l'aide de base de données sur les pertes enregistrées. Nos résultats montrent que celles-ci sont susceptibles d'être biaisées notamment par l'amélioration de l'accès à l'information. Elles ne sont pas exhaustives et ne donnent pas d'information sur l'exposition, l'intensité ou la vulnérabilité. Une nouvelle approche, indépendante des pertes reportées, est donc nécessaire.¦Les recherches présentées ici ont été mandatées par les Nations Unies et par des agences oeuvrant dans le développement et l'environnement (PNUD, l'UNISDR, la GTZ, le PNUE ou l'UICN). Ces organismes avaient besoin d'une évaluation quantitative sur les facteurs sous-jacents du risque, afin de sensibiliser les décideurs et pour la priorisation des projets de réduction des risques de désastres.¦La méthode est basée sur les systèmes d'information géographique, la télédétection, les bases de données et l'analyse statistique. Une importante quantité de données (1,7 Tb) et plusieurs milliers d'heures de calculs ont été nécessaires. Un modèle de risque global a été élaboré pour révéler la distribution des aléas, de l'exposition et des risques, ainsi que pour l'identification des facteurs de risque sous- jacent de plusieurs aléas (inondations, cyclones tropicaux, séismes et glissements de terrain). Deux indexes de risque multiples ont été générés pour comparer les pays. Les résultats incluent une évaluation du rôle de l'intensité de l'aléa, de l'exposition, de la pauvreté, de la gouvernance dans la configuration et les tendances du risque. Il apparaît que les facteurs de vulnérabilité changent en fonction du type d'aléa, et contrairement à l'exposition, leur poids décroît quand l'intensité augmente.¦Au niveau local, la méthode a été testée pour mettre en évidence l'influence du changement climatique et du déclin des écosystèmes sur l'aléa. Dans le nord du Pakistan, la déforestation induit une augmentation de la susceptibilité des glissements de terrain. Les recherches menées au Pérou (à base d'imagerie satellitaire et de collecte de données au sol) révèlent un retrait glaciaire rapide et donnent une évaluation du volume de glace restante ainsi que des scénarios sur l'évolution possible.¦Ces résultats ont été présentés à des publics différents, notamment en face de 160 gouvernements. Les résultats et les données générées sont accessibles en ligne (http://preview.grid.unep.ch). La méthode est flexible et facilement transposable à des échelles et problématiques différentes, offrant de bonnes perspectives pour l'adaptation à d'autres domaines de recherche.¦La caractérisation du risque au niveau global et l'identification du rôle des écosystèmes dans le risque de catastrophe est en plein développement. Ces recherches ont révélés de nombreux défis, certains ont été résolus, d'autres sont restés des limitations. Cependant, il apparaît clairement que le niveau de développement configure line grande partie des risques de catastrophes. La dynamique du risque est gouvernée principalement par le changement global.¦Disasters are often perceived as fast and random events. If the triggers may be sudden, disasters are the result of an accumulation of actions, consequences from inappropriate decisions and from global change. To modify this perception of risk, advocacy tools are needed. Quantitative methods have been developed to identify the distribution and the underlying factors of risk.¦Disaster risk is resulting from the intersection of hazards, exposure and vulnerability. The frequency and intensity of hazards can be influenced by climate change or by the decline of ecosystems. Population growth increases the exposure, while changes in the level of development affect the vulnerability. Given that each of its components may change, the risk is dynamic and should be reviewed periodically by governments, insurance companies or development agencies. At the global level, these analyses are often performed using databases on reported losses. Our results show that these are likely to be biased in particular by improvements in access to information. International losses databases are not exhaustive and do not give information on exposure, the intensity or vulnerability. A new approach, independent of reported losses, is necessary.¦The researches presented here have been mandated by the United Nations and agencies working in the development and the environment (UNDP, UNISDR, GTZ, UNEP and IUCN). These organizations needed a quantitative assessment of the underlying factors of risk, to raise awareness amongst policymakers and to prioritize disaster risk reduction projects.¦The method is based on geographic information systems, remote sensing, databases and statistical analysis. It required a large amount of data (1.7 Tb of data on both the physical environment and socio-economic parameters) and several thousand hours of processing were necessary. A comprehensive risk model was developed to reveal the distribution of hazards, exposure and risk, and to identify underlying risk factors. These were performed for several hazards (e.g. floods, tropical cyclones, earthquakes and landslides). Two different multiple risk indexes were generated to compare countries. The results include an evaluation of the role of the intensity of the hazard, exposure, poverty, governance in the pattern and trends of risk. It appears that the vulnerability factors change depending on the type of hazard, and contrary to the exposure, their weight decreases as the intensity increases.¦Locally, the method was tested to highlight the influence of climate change and the ecosystems decline on the hazard. In northern Pakistan, deforestation exacerbates the susceptibility of landslides. Researches in Peru (based on satellite imagery and ground data collection) revealed a rapid glacier retreat and give an assessment of the remaining ice volume as well as scenarios of possible evolution.¦These results were presented to different audiences, including in front of 160 governments. The results and data generated are made available online through an open source SDI (http://preview.grid.unep.ch). The method is flexible and easily transferable to different scales and issues, with good prospects for adaptation to other research areas. The risk characterization at a global level and identifying the role of ecosystems in disaster risk is booming. These researches have revealed many challenges, some were resolved, while others remained limitations. However, it is clear that the level of development, and more over, unsustainable development, configures a large part of disaster risk and that the dynamics of risk is primarily governed by global change.

Fitness, inclusive fitness, and optimization

Individual-as-maximizing agent analogies result in a simple understanding of the functioning of the biological world. Identifying the conditions under which individuals can be regarded as fitness maximizing agents is thus of considerable interest to biologists. Here, we compare different concepts of fitness maximization, and discuss within a single framework the relationship between Hamilton's (J Theor Biol 7: 1-16, 1964) model of social interactions, Grafen's (J Evol Biol 20: 1243-1254, 2007a) formal Darwinism project, and the idea of evolutionary stable strategies. We distinguish cases where phenotypic effects are additive separable or not, the latter not being covered by Grafen's analysis. In both cases it is possible to define a maximand, in the form of an objective function phi(z), whose argument is the phenotype of an individual and whose derivative is proportional to Hamilton's inclusive fitness effect. However, this maximand can be identified with the expression for fecundity or fitness only in the case of additive separable phenotypic effects, making individual-as-maximizing agent analogies unattractive (although formally correct) under general situations of social interactions. We also feel that there is an inconsistency in Grafen's characterization of the solution of his maximization program by use of inclusive fitness arguments. His results are in conflict with those on evolutionary stable strategies obtained by applying inclusive fitness theory, and can be repaired only by changing the definition of the problem.

Local Competition, Inbreeding, and the Evolution of Sex-Biased Dispersal.

Using game theory, we developed a kin-selection model to investigate the consequences of local competition and inbreeding depression on the evolution of natal dispersal. Mating systems have the potential to favor strong sex biases in dispersal because sex differences in potential reproductive success affect the balance between local resource competition and local mate competition. No bias is expected when local competition equally affects males and females, as happens in monogamous systems and also in polygynous or promiscuous ones as long as female fitness is limited by extrinsic factors (breeding resources). In contrast, a male-biased dispersal is predicted when local mate competition exceeds local resource competition, as happens under polygyny/promiscuity when female fitness is limited by intrinsic factors (maximal rate of processing resources rather than resources themselves). This bias is reinforced by among-sex interactions: female philopatry enhances breeding opportunities for related males, while male dispersal decreases the chances that related females will inbreed. These results meet empirical patterns in mammals: polygynous/promiscuous species usually display a male-biased dispersal, while both sexes disperse in monogamous species. A parallel is drawn with sex-ratio theory, which also predicts biases toward the sex that suffers less from local competition. Optimal sex ratios and optimal sex-specific dispersal show mutual dependence, which argues for the development of coevolution models.

Evolutionary games on complex networks : the emergence and maintenance of cooperation

Abstract The object of game theory lies in the analysis of situations where different social actors have conflicting requirements and where their individual decisions will all influence the global outcome. In this framework, several games have been invented to capture the essence of various dilemmas encountered in many common important socio-economic situations. Even though these games often succeed in helping us understand human or animal behavior in interactive settings, some experiments have shown that people tend to cooperate with each other in situations for which classical game theory strongly recommends them to do the exact opposite. Several mechanisms have been invoked to try to explain the emergence of this unexpected cooperative attitude. Among them, repeated interaction, reputation, and belonging to a recognizable group have often been mentioned. However, the work of Nowak and May (1992) showed that the simple fact of arranging the players according to a spatial structure and only allowing them to interact with their immediate neighbors is sufficient to sustain a certain amount of cooperation even when the game is played anonymously and without repetition. Nowak and May's study and much of the following work was based on regular structures such as two-dimensional grids. Axelrod et al. (2002) showed that by randomizing the choice of neighbors, i.e. by actually giving up a strictly local geographical structure, cooperation can still emerge, provided that the interaction patterns remain stable in time. This is a first step towards a social network structure. However, following pioneering work by sociologists in the sixties such as that of Milgram (1967), in the last few years it has become apparent that many social and biological interaction networks, and even some technological networks, have particular, and partly unexpected, properties that set them apart from regular or random graphs. Among other things, they usually display broad degree distributions, and show small-world topological structure. Roughly speaking, a small-world graph is a network where any individual is relatively close, in terms of social ties, to any other individual, a property also found in random graphs but not in regular lattices. However, in contrast with random graphs, small-world networks also have a certain amount of local structure, as measured, for instance, by a quantity called the clustering coefficient. In the same vein, many real conflicting situations in economy and sociology are not well described neither by a fixed geographical position of the individuals in a regular lattice, nor by a random graph. Furthermore, it is a known fact that network structure can highly influence dynamical phenomena such as the way diseases spread across a population and ideas or information get transmitted. Therefore, in the last decade, research attention has naturally shifted from random and regular graphs towards better models of social interaction structures. The primary goal of this work is to discover whether or not the underlying graph structure of real social networks could give explanations as to why one finds higher levels of cooperation in populations of human beings or animals than what is prescribed by classical game theory. To meet this objective, I start by thoroughly studying a real scientific coauthorship network and showing how it differs from biological or technological networks using divers statistical measurements. Furthermore, I extract and describe its community structure taking into account the intensity of a collaboration. Finally, I investigate the temporal evolution of the network, from its inception to its state at the time of the study in 2006, suggesting also an effective view of it as opposed to a historical one. Thereafter, I combine evolutionary game theory with several network models along with the studied coauthorship network in order to highlight which specific network properties foster cooperation and shed some light on the various mechanisms responsible for the maintenance of this same cooperation. I point out the fact that, to resist defection, cooperators take advantage, whenever possible, of the degree-heterogeneity of social networks and their underlying community structure. Finally, I show that cooperation level and stability depend not only on the game played, but also on the evolutionary dynamic rules used and the individual payoff calculations. Synopsis Le but de la théorie des jeux réside dans l'analyse de situations dans lesquelles différents acteurs sociaux, avec des objectifs souvent conflictuels, doivent individuellement prendre des décisions qui influenceront toutes le résultat global. Dans ce cadre, plusieurs jeux ont été inventés afin de saisir l'essence de divers dilemmes rencontrés dans d'importantes situations socio-économiques. Bien que ces jeux nous permettent souvent de comprendre le comportement d'êtres humains ou d'animaux en interactions, des expériences ont montré que les individus ont parfois tendance à coopérer dans des situations pour lesquelles la théorie classique des jeux prescrit de faire le contraire. Plusieurs mécanismes ont été invoqués pour tenter d'expliquer l'émergence de ce comportement coopératif inattendu. Parmi ceux-ci, la répétition des interactions, la réputation ou encore l'appartenance à des groupes reconnaissables ont souvent été mentionnés. Toutefois, les travaux de Nowak et May (1992) ont montré que le simple fait de disposer les joueurs selon une structure spatiale en leur permettant d'interagir uniquement avec leurs voisins directs est suffisant pour maintenir un certain niveau de coopération même si le jeu est joué de manière anonyme et sans répétitions. L'étude de Nowak et May, ainsi qu'un nombre substantiel de travaux qui ont suivi, étaient basés sur des structures régulières telles que des grilles à deux dimensions. Axelrod et al. (2002) ont montré qu'en randomisant le choix des voisins, i.e. en abandonnant une localisation géographique stricte, la coopération peut malgré tout émerger, pour autant que les schémas d'interactions restent stables au cours du temps. Ceci est un premier pas en direction d'une structure de réseau social. Toutefois, suite aux travaux précurseurs de sociologues des années soixante, tels que ceux de Milgram (1967), il est devenu clair ces dernières années qu'une grande partie des réseaux d'interactions sociaux et biologiques, et même quelques réseaux technologiques, possèdent des propriétés particulières, et partiellement inattendues, qui les distinguent de graphes réguliers ou aléatoires. Entre autres, ils affichent en général une distribution du degré relativement large ainsi qu'une structure de "petit-monde". Grossièrement parlant, un graphe "petit-monde" est un réseau où tout individu se trouve relativement près de tout autre individu en termes de distance sociale, une propriété également présente dans les graphes aléatoires mais absente des grilles régulières. Par contre, les réseaux "petit-monde" ont, contrairement aux graphes aléatoires, une certaine structure de localité, mesurée par exemple par une quantité appelée le "coefficient de clustering". Dans le même esprit, plusieurs situations réelles de conflit en économie et sociologie ne sont pas bien décrites ni par des positions géographiquement fixes des individus en grilles régulières, ni par des graphes aléatoires. De plus, il est bien connu que la structure même d'un réseau peut passablement influencer des phénomènes dynamiques tels que la manière qu'a une maladie de se répandre à travers une population, ou encore la façon dont des idées ou une information s'y propagent. Ainsi, durant cette dernière décennie, l'attention de la recherche s'est tout naturellement déplacée des graphes aléatoires et réguliers vers de meilleurs modèles de structure d'interactions sociales. L'objectif principal de ce travail est de découvrir si la structure sous-jacente de graphe de vrais réseaux sociaux peut fournir des explications quant aux raisons pour lesquelles on trouve, chez certains groupes d'êtres humains ou d'animaux, des niveaux de coopération supérieurs à ce qui est prescrit par la théorie classique des jeux. Dans l'optique d'atteindre ce but, je commence par étudier un véritable réseau de collaborations scientifiques et, en utilisant diverses mesures statistiques, je mets en évidence la manière dont il diffère de réseaux biologiques ou technologiques. De plus, j'extrais et je décris sa structure de communautés en tenant compte de l'intensité d'une collaboration. Finalement, j'examine l'évolution temporelle du réseau depuis son origine jusqu'à son état en 2006, date à laquelle l'étude a été effectuée, en suggérant également une vue effective du réseau par opposition à une vue historique. Par la suite, je combine la théorie évolutionnaire des jeux avec des réseaux comprenant plusieurs modèles et le réseau de collaboration susmentionné, afin de déterminer les propriétés structurelles utiles à la promotion de la coopération et les mécanismes responsables du maintien de celle-ci. Je mets en évidence le fait que, pour ne pas succomber à la défection, les coopérateurs exploitent dans la mesure du possible l'hétérogénéité des réseaux sociaux en termes de degré ainsi que la structure de communautés sous-jacente de ces mêmes réseaux. Finalement, je montre que le niveau de coopération et sa stabilité dépendent non seulement du jeu joué, mais aussi des règles de la dynamique évolutionnaire utilisées et du calcul du bénéfice d'un individu.

Cumulative cultural dynamics and the coevolution of cultural innovation and transmission: an ESS model for panmictic and structured populations.

When individuals in a population can acquire traits through learning, each individual may express a certain number of distinct cultural traits. These traits may have been either invented by the individual himself or acquired from others in the population. Here, we develop a game theoretic model for the accumulation of cultural traits through individual and social learning. We explore how the rates of innovation, decay, and transmission of cultural traits affect the evolutionary stable (ES) levels of individual and social learning and the number of cultural traits expressed by an individual when cultural dynamics are at a steady-state. We explore the evolution of these phenotypes in both panmictic and structured population settings. Our results suggest that in panmictic populations, the ES level of learning and number of traits tend to be independent of the social transmission rate of cultural traits and is mainly affected by the innovation and decay rates. By contrast, in structured populations, where interactions occur between relatives, the ES level of learning and the number of traits per individual can be increased (relative to the panmictic case) and may then markedly depend on the transmission rate of cultural traits. This suggests that kin selection may be one additional solution to Rogers's paradox of nonadaptive culture.