It is well known that in contrast to the Prisoner's Dilemma, the snowdrift game can lead to a stable coexistence of cooperators and cheaters. Recent theoretical evidence on the snowdrift game suggests that gradual evolution for individuals choosing to contribute in continuous degrees can result in the social diversification to a 100% contribution and 0% contribution through so-called evolutionary branching. Until now, however, game-theoretical studies have shed little light on the evolutionary dynamics and consequences of the loss of diversity in strategy. Here, we analyze continuous snowdrift games with quadratic payoff functions in dimorphic populations. Subsequently, conditions are clarified under which gradual evolution can lead a population consisting of those with 100% contribution and those with 0% contribution to merge into one species with an intermediate contribution level. The key finding is that the continuous snowdrift game is more likely to lead to assimilation of different cooperation levels rather than maintenance of diversity. Importantly, this implies that allowing the gradual evolution of cooperative behavior can facilitate social inequity aversion in joint ventures that otherwise could cause conflicts that are based on commonly accepted notions of fairness. (authors' abstract)

Random Forest (RF) is an ensemble classification technique that was developed by Leo Breiman over a decade ago. Compared with other ensemble techniques, it has proved its accuracy and superiority. Many researchers, however, believe that there is still room for optimizing RF further by enhancing and improving its performance accuracy. This explains why there have been many extensions of RF where each extension employed a variety of techniques and strategies to improve certain aspect(s) of RF. The main focus of this dissertation is to develop new extensions of RF using new optimization techniques that, to the best of our knowledge, have never been used before to optimize RF. These techniques are clustering, the local outlier factor, diversified weighted subspaces, and replicator dynamics. Applying these techniques on RF produced four extensions which we have termed CLUB-DRF, LOFB-DRF, DSB-RF, and RDB-DR respectively. Experimental studies on 15 real datasets showed favorable results, demonstrating the potential of the proposed methods. Performance-wise, CLUB-DRF is ranked first in terms of accuracy and classifcation speed making it ideal for real-time applications, and for machines/devices with limited memory and processing power.

At the beginning of my Master's thesis we define basic terms such as payoff, strategy, best reply and Nash equilibrium. Furthermore, we introduce the population perspective, in which during a random meeting of a pair of players, these players interact according to their strategies and they receive payoffs. We define the criterion of evolutionary stability, which shows a link between payoffs in the game and strategy spreading among population. The most common description of this evolution is based on the replicator equations. We analyze their basic properties and examine the relationship between the stationary points of this system and the concepts of Nash equilibrium and evolutionary stability. In the following practical part, we apply the introduced theory to model the Cournot duopoly. Its aim is to analyze the model characteristics in terms of evolutionary stability and to determine the duopolist's behavior in the long run.

A synthetic proto-organism could be self-assembled by integrating a lipid proto-container with a proto-metabolic subsystem and a proto-genetic subsystem. This three-component system can use energy and nutrients by means of either redox or photo-chemical reactions, evolve its proto-genome by means of template directed replication, and ultimately die. The evolutionary dynamics of the proto-organism depends crucially on the chemical kinetics of its sub-systems and on their interplay. In this work the template replication kinetics is investigated and it is found that the product inhibition inherent in the ligation-like replication process allows for coexistence of unrelated self-replicating proto-genes in the lipid surface layer. The combined catalytic effects from the proto-genes on the metabolic production rates determine the fate of the strain protocell.

Satisficing game theory is an alternative to traditional non-cooperative game theory which offers increased flexibility in modeling players' social interactions. However, satisficing players with conflicting attitudes may implement dysfunctional behaviors, leading to poor performance. In this thesis, we present two attempts to "bridge the gap" between satisficing and non-cooperative game theory. First, we present an evolutionary method by which players adapt their attitudes to increase raw payoff, allowing players to overcome dysfunction. We extend the Nash equilibrium concept to satisficing games, showing that the evolutionary method presented leads the players toward an equilibrium in their attitudes. Second, we introduce the conditional utility functions of satisficing theory into an otherwise traditional non-cooperative framework. While the conditional structure allows increased social flexibility in the players' behaviors, players maximize individual utility in the traditional sense, allowing us to apply the Nash equilibrium. We find that, by adjusting players' attitudes, we may alter the Nash equilibria that result.

<p dir="ltr">This dissertation addresses three progressively fundamental problems for functional data analysis: (1) To do efficient inference for the functional mean model accounting for within-subject correlation, we propose the refined and bias-corrected empirical likelihood method. (2) To identify functional subjects potentially from different populations, we propose the dominant-set based unsupervised clustering method using the similarity matrix. (3) To learn the similarity matrix from various similarity metrics for functional data clustering, we propose the modularity guided and dominant-set based semi-supervised clustering method.</p><p dir="ltr">In the first problem, the empirical likelihood method is utilized to do inference for the mean function of functional data by constructing the refined and bias-corrected estimating equation. The proposed estimating equation not only improves efficiency but also enables practically feasible empirical likelihood inference by properly incorporating within-subject correlation, which has not been achieved by previous studies.</p><p dir="ltr">In the second problem, the dominant-set based unsupervised clustering method is proposed to maximize the within-cluster similarity and applied to functional data with a flexible choice of similarity measures between curves. The proposed unsupervised clustering method is a hierarchical bipartition procedure under the penalized optimization framework with the tuning parameter selected by maximizing the clustering criterion called modularity of the resulting two clusters, which is inspired by the concept of dominant set in graph theory and solved by replicator dynamics in game theory. The advantage offered by this approach is not only robust to imbalanced sizes of groups but also to outliers, which overcomes the limitation of many existing clustering methods.</p><p dir="ltr">In the third problem, the metric-based semi-supervised clustering method is proposed with similarity metric learned by modularity maximization and followed by the above proposed dominant-set based clustering procedure. Under semi-supervised setting where some clustering memberships are known, the goal is to determine the best linear combination of candidate similarity metrics as the final metric to enhance the clustering performance. Besides the global metric-based algorithm, another algorithm is also proposed to learn individual metrics for each cluster, which permits overlapping membership for the clustering. This is innovatively different from many existing methods. This method is superiorly applicable to functional data with various similarity metrics between functional curves, while also exhibiting robustness to imbalanced sizes of groups, which are intrinsic to the dominant-set based clustering approach.</p><p dir="ltr">In all three problems, the advantages of the proposed methods are demonstrated through extensive empirical investigations using simulations as well as real data applications.</p>

La théorie des jeux évolutionnaires est un outil qui permet d’étudier l’évolution des stratégies dans une population composée d’un grand nombre d’agents qui interagissent d’une façon continue et aléatoire. Dans cette théorie, il y a deux concepts essentiels qui sont la stratégie évolutivement stable (ESS), et la dynamique de réplication. Une stratégie évolutivement stable est une stratégie, qui, si adoptée par toute la population,ne peut pas être envahie par une autre stratégie ”mutante” utilisée par une petite fraction de la population. Ce concept statique est un raffinement de l’équilibre de Nash, et il ne peut pas renseigner, par exemple, sur la durée du temps nécessaire pour que l’ESS élimine la stratégie mutante. La dynamique de réplication, originalement proposée par Hawk-Dove, est un modèle dynamique qui permet de prédire l’évolution de la fraction de chaque stratégie dans la population en fonction du temps, en réponse aux gains des stratégies et l’état de la population.Dans cette thèse, nous proposons dans une première partie une extension de la dynamique de réplication classique en y introduisant des délais hétérogènes et aléatoires.En effet, la plupart des phénomènes qui se produisent prennent un temps incertain avant d’avoir des résultats. Nous étudions l’effet de la distribution des délais sur la stabilité de l’ESS dans la dynamique de réplication et nous considérons les distributions uniforme, exponentielle, et Gamma (ou Erlang). Dans les cas des distributions uniforme et Gamma, nous trouvons la valeur critique de la moyenne à laquelle la stabilité de l’équilibre est perdue et des oscillations permanentes apparaissent. Dans le cas de la distribution exponentielle, nous montrons que la stabilité de l’équilibre ne peut être perdue,et ce pour toute valeur de la moyenne de la distribution. Par ailleurs, nous montrons que la distribution exponentielle peut affecter la stabilité de l’ESS quand une seule stratégie subit un délai aléatoire issu de cette distribution. Nous étudions également le cas où les délais sont discrets et nous trouvons une condition suffisante et indépendante des valeurs des délais pour la stabilité de l’équilibre. Dans tous les cas, nous montrons que les délais aléatoires sont moins risqués que les délais constants pour la stabilité de l’équilibre, vu que la valeur moyenne critique des délais aléatoires est toujours supérieure de celle des délais constants. En outre, nous considérons comme paramètre de bifurcation la moyenne de la distribution des délais et nous étudions les propriétés de la solution périodique qui apparait à la bifurcation de Hopf, et ce en utilisant une méthode de perturbation non linéaire. En effet, à la bifurcation de Hopf, une oscillation périodique stable apparait dont l’amplitude est fonction de la moyenne de la distribution. Nous déterminons analytiquement l’amplitude de l’oscillation au voisinage de la bifurcation de Hopf en fonction du paramètre de bifurcation et de la matrice des jeux dans les cas des distributions de Dirac, uniforme, Gamma et discrète, et nous appuyons nos résultats avec des simulations numériques. Dans une deuxième partie, nous considérons une population hétérogène composée de plusieurs communautés qui interagissent d’une manière non-uniforme. Pour chaque communauté, nous définissons les matrices des jeux et les probabilités d’interaction avec les autres communautés. Dans ce contexte, nous définissons trois ESS avec différents niveaux de stabilité contre les mutations: un ESS fort, un ESS faible et un ESS intermédiaire. Nous définissons un ESS fort comme suit: si toute la population adopte l’ESS, alors l’ESS ne peut pas être envahi par une petite fraction de mutants composée d’agents de toutes les communautés. / In this dissertation, we study evolutionary game theory which is a mathematical tool used to model and predict the evolution of strategies in a population composed of a largenumber of players. In this theory, there are two basic concepts which are the evolutionarilystable strategy (ESS) and the replicator dynamics. The ESS is originally definedas follows [1]: if all the population adopts the ESS, then no alternative strategy used bya sufficiently small fraction of the population can invade the population.The ESS is astatic concept and a refinement of a Nash equilibrium. It does not allow us, for example,to estimate the time required for the ESS to overcome the mutant strategy, neither to predictthe asymptotic distribution of strategies in the population. The replicator dynamics,originally introduced in [2], is a model of evolution of strategies according to which the growth rate of a given strategy is proportional to how well this strategy performs relative to the average pay off in the population.In the first part of this work, we propose an extended version of the replicator dynamics which takes into account heterogeneous random delays. Indeed, in many situations,the presence of uncertain delays is ubiquitous. We first consider continuous delays and we study the effect of the distribution of delays on the asymptotic stability of the mixed equilibrium in the replicator dynamics. In the case of uniform and Gamma delay distributions,we find the critical mean delay at which a Hopf bifurcation is created and the stability of the mixed equilibrium is lost. When the distribution of delays is exponential, we prove that the stability of the equilibrium cannot be affected by the delays. However, when only one strategy is delayed according to the exponential distribution,the asymptotic stability of the ESS can be lost. In all the cases, we show that the critical mean delay value is higher than that of constant delays, and thus random delays are less threatening than constant delays. In addition, we consider discrete delays and one o four results is that, when the instantaneous term is dominant, that is when the probabilityof zero delay is sufficiently high, the stability of the ESS cannot be lost.Furthermore, by taking as a bifurcation parameter the mean delay distribution, we examine the properties of the bifurcating periodic solution created near the Hopf bifurcationusing a nonlinear perturbation method. Indeed, near the Hopf bifurcation, a stable periodic oscillation appears whose amplitude depends on the value of the bifurcation parameter. We give a closed-form expression of the amplitude of the periodic solution and we validate our results with numerical simulations.In the second part, we consider an heterogeneous population composed of several communities which interact in a nonuniform manner. Each community has its own set of strategies, payoffs, and interaction probabilities. Indeed, individuals of a population have many inherent differences that favor the appearance of groups or clusters. In this scenario, we define three ESS with different levels of stability against mutations: strong,weak, and intermediate ESS, and we examine their connection to each other. A strongESS is a strategy that, when adopted by all the population, cannot be invaded by a sufficientlysmall fraction of mutants composed of agents from all the communities. Incontrast, a weak ESS is a strategy wherein each community resists invasion by a sufficientlysmall fraction of mutants in that community (local mutants). In the intermediateESS, the population adopting the ESS cannot be invaded by a small fraction of mutantswhen we consider the total fitness of the population rather than the fitness of eachcommunity separately.

No description available.

Dans cette thèse, nous étudions les effets d'un environnement stochastique et de l'utilisation d'une stratégie d'opting-out sur l'évolution de la coopération dans les jeux évolutionnaires. La thèse contient 8 articles, dont 6 sont déjà publiés dans des revues avec comité de lecture. Outre l'introduction, la thèse est divisée en deux parties, la partie 1 composée de 5 articles et la partie 2 de 3 articles. La partie 1 étudie l'impact de gains randomisés dans les jeux évolutionnaires. L'article 1 introduit les concepts de stabilité pour les jeux avec matrice de paiement aléatoire 2x2 dans des populations infinies avec des générations discrètes sans chevauchement dans un environnement stochastique. On y donne les conditions pour qu'un équilibre, sur la frontière ou à l'intérieur du simplexe des fréquences des stratégies, soit stochastiquement localement stable ou instable. L'article 2 étend les résultats de l'article 1 au cas où la valeur sélective est une fonction exponentielle du gain attendu suite à des interactions aléatoires par paires et montre que, de manière inattendue, le bruit aléatoire environnemental peut rompre un cycle périodique et favoriser la stabilité d'un équilibre intérieur. L'article 3 discute des effets de la sélection faible. Alors que les conditions de stabilité dans un environnement aléatoire reviennent aux conditions du cas déterministe lorsque l'intensité de la sélection diminue, les fluctuations aléatoires des gains peuvent accélérer la vitesse de convergence vers un équilibre stable sous une sélection plus faible. L'article 4 applique la théorie de la stabilité évolutive stochastique à un jeu randomisé de dilemme du prisonnier. On y montre que l'augmentation de la variance des gains de défection est propice à l'évolution de la coopération. L'article 5 étudie les jeux matriciels randomisés dans des populations finies et donne les conditions pour que la sélection favorise l'évolution de la coopération dans le contexte du jeu randomisé de dilemme du prisonnier. La partie 2 considère un jeu répété de dilemme du prisonnier dans le cas où un comportement d'opting-out est adopté par chaque joueur dans les interactions par paires. L'article 6 étudie la dynamique évolutive de la coopération et de la défection dans ce contexte et montre une possible coexistence à long terme, en supposant une population infinie et un équilibre rapide (en fait, instantané) dans les fréquences des paires. L'article 7 rapporte des résultats expérimentaux avec 264 étudiants universitaires utilisant la stratégie d'opting-out qui soutiennent la prédiction théorique d'une coexistence à long terme de coopération et de défection. L'article 8 étend l'analyse du modèle avec la stratégie d'opting-out au cas d'une population finie et fournit une preuve rigoureuse des deux échelles de temps pour les fréquences de coopération et de défection d'une part et les fréquences de paires de stratégies d'autre part. / In this thesis, we study the effects of a stochastic environment and the use of an opting-out strategy on the evolution of cooperation in evolutionary games. The thesis contains 8 articles, among which 6 are already published in peer-reviewed journals. Apart from the introduction, the thesis is divided into two parts, Part 1 made with 5 articles and Part 2 with 3 articles. Part 1 studies randomized payoffs in evolutionary games. Article 1 introduces stability concepts for 2x2 matrix games in infinite populations undergoing discrete, non-overlapping generations in a stochastic environment and gives conditions for an equilibrium, either on the boundary or in the interior of the simplex of all strategy frequencies, to be stochastically locally stable or unstable. Article 2 extends the results of Article 1 to the case where fitness is an exponential function of expected payoff in random pairwise interactions and shows that, unexpectedly, environmental random noise can break a periodic cycle and promote stability of an interior equilibrium. Article 3 discusses the effects of weak selection. While stability conditions in a random environment return to conditions in the deterministic case as selection intensity diminishes, random fluctuations in payoffs can accelerate the speed of convergence toward a stable equilibrium under weaker selection. Article 4 applies stochastic evolutionary stability theory to a randomized Prisoner's dilemma game and shows that increasing the variance in payoffs for defection is conducive to the evolution of cooperation. Article 5 studies randomized matrix games in finite populations and gives conditions for selection to favor the evolution of cooperation in the context of a randomized Prisoner's dilemma. Part 2 considers a repeated Prisoner's dilemma game with an opting-out behavior adopted by every player in pairwise interactions. Article 6 studies the evolutionary dynamics of cooperation and defection in this context and shows possible long-term coexistence, assuming an infinite population and fast (actually, instantaneous) equilibrium in the pair frequencies. Article 7 reports experimental results with 264 university students using the opting-out strategy that support the theoretical prediction of a long-term coexistence of cooperation and defection. Article 8 extends the analysis of the model with the opting-out strategy to the case of a finite population and provides a rigorous proof of the two-time scales for the frequencies of cooperation and defection on one hand and the frequencies of strategy pairs on the other.