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Chapter 1: Evolution of reciprocator preferences when agents can pay for information. A benchmark result in the evolutionary games literature is that a preference for reciprocity will evolve if preferences are observable (at zero cost), since reciprocators can cooperate with each other rather than with materialists, thereby achieving a fitness advantage. I investigate how a preference for reciprocity evolves if individuals can observe an opponent's preferences only by bearing a fitness cost. My main result applies when observing an opponent's type is cheap, but cooperating only gives a modest fitness advantage or the preference for reciprocity is intense. In this case, a preference for reciprocity cannot evolve from a small starting share in the mix of preferences, even if discovering an opponent's preferences is arbitrarily cheap. This is in sharp contrast to the benchmark result. Chapter 2: A theory of conditional cooperation on networks (with Julien Gagnon) Chapter 2 is a study of reciprocity on social networks. We model a group of connected agents who play a one-shot public good game. Some players are materialists and others are reciprocators. We characterise the maximal Nash equilibrium (ME) of this game for any network and a broad class of reciprocal preferences. At the ME, a novel concept, the q-linked set, fully determines the set of players who contribute. We show that influential players are those connected to players who are sufficiently interconnected, but not too much. Finally, we study the decision of a planner faced with an uncertain type profile who designs the network to maximise expected contributions. The ex ante optimal network comprises isolated cliques of degree k*, with k* decreasing with the incidence of materialists. We discuss an important application of our results: the workplace. Chapter 3: Ideological games Chapter 3 is a theory of ideology. I define a preference type to be a set of first-order preferences over the outcomes of a `game of life', together with a set of (`meta-') preferences over all players' first-order preferences. Players can influence each other's preferences via costly investment: if player A invests and B does not, B's preferences becomes those of A. Players may invest for instrumental reasons (i.e. to achieve better outcomes in the game of life) or `ideological' reasons (i.e. they want their opponents to have the same preferences they do). I characterise `strongly ideological', `weakly ideological' and `pragmatic' types. Weakly ideological types wish to preserve their own type, as do strongly ideological types, who also seek to convert others. A pragmatic player, in contrast, is willing to have her type changed if her new type would prefer the resulting equilibrium of the game of life to the status quo. I show that if two players of different ideological types meet, there is an equilibrium investment profile with lower aggregate welfare than the no-invest profile. If at least one type is strongly ideological, there is a unique such equilibrium. Finally, a `perfectly ideological' type is a strongly ideological type which, if held by all players, results in the best outcome of the game of life as judged by that type. If a perfectly ideological player plays a pragmatic player, aggregate welfare is always greater than in the no-invest profile.

Roughgarden et al. (2006) proposed a theory called social selection as a behavioral game theoretic model for sexual reproduction that incorporates both competition and cooperation in 2006. Players oscillate between playing competitively to maximize their individual fitness, leading to a Nash Competitive Equilibrium, and playing cooperatively to maximize a team fitness function, leading to a Nash Bargaining Solution. Roughgarden et al. (2006) gives rates of change for both the competitive state and the cooperative state, but does not explain her rates or how to switch between the states in sufficient detail. We test and rederive the rates, critiquing an assumption that the derivation of such a rate must make, as well as create a probabilistic model that switches between the two states. We test our model on the reproductive behaviors of Symphodus tinca, the peacock wrasse. The results follow the trajectory of the reproductive strategies for the wrasse throughout the breeding system, suggesting that cooperation could be a mechanism through which wrasse change their reproductive behaviors. However, the inputs to the model need to be analyzed more critically. Future work could include deriving rates for competitive play and cooperative play that do not rely on assumptions of being able to quantify strategy allocation proportion and refining the model and drawing generalized conclusions about it.

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.

Evolutionary game theory has recently emerged as a key paradigm in various behavioral science disciplines. In particular it provides powerful tools and a conceptual framework for the analysis of the time evolution of strategic interdependence among players and its consequences, especially when the players are spatially distributed and linked in a complex social network. We develop various evolutionary game models, analyze these models using appropriate techniques, and study their applications to complex phenomena. In the second chapter, we derive integro-differential equations as deterministic approximations of the microscopic updating stochastic processes. These generalize the known mean-field ordinary differential equations and provide powerful tools to investigate the spatial effects on the time evolutions of the agents' strategy choices. The deterministic equations allow us to identify many interesting features of the evolution of strategy profiles in a population, such as standing and traveling waves, and pattern formation, especially in replicator-type evolutions. We introduce several methods of decomposition of two player normal form games in the third chapter. Viewing the set of all games as a vector space, we exhibit explicit orthonormal bases for the subspaces of potential games, zero-sum games, and their orthogonal complements which we call anti-potential games and anti-zero-sum games, respectively. Perhaps surprisingly, every anti-potential game comes either from Rock-paper-scissors type games (in the case of symmetric games) or from Matching Pennies type games (in the case of asymmetric games). Using these decompositions, we prove old (and some new) cycle criteria for potential and zero-sum games (as orthogonality relations between subspaces). We illustrate the usefulness of our decompositions by (a) analyzing the generalized Rock-Paper-Scissors game, (b) completely characterizing the set of all null-stable games, (c) providing a large class of strict stable games, (d) relating the game decomposition to the Hodge decomposition of vector fields for the replicator equations, (e) constructing Lyapunov functions for some replicator dynamics, (f) constructing Zeeman games -games with an interior asymptotically stable Nash equilibrium and a pure strategy ESS. The hierarchical modeling of evolutionary games provides flexibility in addressing the complex nature of social interactions as well as systematic frameworks in which one can keep track of the interplay of within-group dynamics and between-group competitions. For example, it can model husbands and wives' interactions, playing an asymmetric game with each other, while engaging coordination problems with the likes in other families. In the fourth chapter, we provide hierarchical stochastic models of evolutionary games and approximations of these processes, and study their applications

Les opérateurs et les constructeurs des réseaux sans fil sont amenés à développer de nouvelles stratégies afin de faire face à l'augmentation rapide des flux de données générés par les nouvelles applications telles que le streaming vidéo. D'une part, la récente saturation des réseaux cellulaires peut être en partie résorbée en diversifiant, pour chaque mobile, les technologies d'accès au réseau. Par exemple, la plupart des téléphones mobiles possède aujourd'hui la capacité de se connecter à des points d'accès Wifi en plus des réseaux cellulaires classiques. D'autre part, une gestion fine des allocations des mobiles sur les différents points d'accès permet une utilisation plus efficace des ressources (énergie, fréquences radio...), et augmente la capacité d'accueil des mobiles, sans nécessairement avoir recours à une onéreuse densification de la couverture radio. Cette thèse s'inscrit dans la problématique de l'auto-optimisation des réseaux en général et des réseaux sans fil en particulier. En raison de la nature très dynamique des réseaux sans fil, les algorithmes d'optimisation doivent être capables de s'adapter aux changements aléatoires de l'environnement de façon autonome. Dans cette thèse, nous proposons d'abord un algorithme de contrôle dynamique qui optimise l'allocation des mobiles tout en prenant en compte les contraintes de capacité. Bien que difficile à mettre en oeuvre en pratique, cet algorithme donne une borne supérieure des performances qu'il est possible d'atteindre. En raison de l'aspect fortement décentralisé des problèmes d'optimisation, nous avons été amenés à développer des méthodes de coopération inspirées de la théorie des jeux. Finalement, nous avons confronté plusieurs algorithmes stochastiques d'optimisation en terme d'efficacité et de robustesse qui sont en cours de prototypage dans un laboratoire industriel. / Operators and manufacturers of wireless networks are required to develop new strategies to cope with the increase fast data streams generated by new applications such as streaming video. On the one hand, the recent saturation cellular networks can be partly resolved by diversifying to each mobile, network access technologies. For example, Most mobile phones now has the ability to connect to WiFi access points in addition to cellular networks classic. In addition, careful management of allocations of mobile the various access points allows more efficient use resources (energy, radio frequency ...), and increases capacity mobile home, without necessarily resorting to a densification expensive radio coverage. This thesis is part of the problem of self-optimization networks in general and wireless networks in particular. Because of the highly dynamic nature of wireless networks, algorithms optimization must be able to adapt to changes random environment independently. In this thesis, First we propose a dynamic control algorithm optimizes the allocation of mobile while taking into account the capacity constraints. Although difficult to implement in practice, this algorithm gives an upper bound performance it is achievable. Due to the high aspect decentralized optimization problems, we have been led to develop methods of cooperation inspired by the theory of games. Finally, we compared several algorithms Stochastic optimization in terms of efficiency and robustness which are currently prototyping in an industrial laboratory.

Orientador: Prof. Dr. Cristian Fabio Coletti / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Matemática , 2017. / Nessa dissertação estudamos a Dinâmica de Melhor Resposta de Evilsizor e Lanchier (3). Foram revisadas as demonstrações em busca de equilíbrios evolucionariamente estáveis e analisando simulações para todos os casos pertinentes. Além desta revisão, neste trabalho introduzimos o conceito de nós teimosos e os adicionamos ao modelo a fim de desestabilizar o equilíbrio no caso estudado em (3). Através das simulações, criamos a intuição de que até nos casos onde não existem equilíbrios evolucionariamente estáveis há também um equilíbrio, porém com coexistência de estratégias. Conjecturamos que esse resultado vale para o caso geral, porém conseguimos prová-lo apenas para dois casos particulares. / In this thesis we studied the Best-Response Dynamics model of Evilsizor e Lanchier (3). We reviewed proofs in search for an Evolutionary Stable Equilibrium analysing simulations for all relevant cases. Besides this revision, we introduced the concept of stubborn players and added it to the Best-Response Dynamics model hoping destabilize the Evolutionary Stable Equilibrium. Through those simulations, we conjectured that even when there is not an Evolutionary Stable Equilibrium, the model converges to another kind of equilibrium, that has coexistent strategies. We conjectured that it states for all altruistic/altruistic cases, but we only could prove it for two specific sub-cases.

Ce manuscrit présente les fondements dynamiques des jeux de population avec un nombre variable de joueurs ainsi que leurs concepts de solutions et de stabilités. Nous introduisons d'abord les dynamiques de jeux avec retard et étudions leurs stabilités. Nous les appliquons aux réseaux filaires et aux réseaux sans fils. Ensuite nous nous intéressons aux aspects de mobilité et aux distributions spatiales des joueurs sur le réseau. Cela nous conduit à une nouvelle classe de dynamique de jeux à stratégies vectorielles avec des contraintes de migrations, appelée dynamique de jeux d'évolution avec migration. Nous dérivons de telles dynamiques pour les réseaux hybrides et appliquons aux problèmes de contrôle de puissance dans les réseaux hétérogènes, choix entre plusieurs technologies et migration entre plusieurs classes d'utilisateurs. Ensuite nous nous focalisons aux jeux stochastiques de population avec plusieurs classes de joueurs dans lesquels chaque joueur possède son propre état et fait face un vecteur qui évolue dans le temps. Des applications à la gestion d'énergie dans les réseaux sont présentées. Finalement, nous étudions une classe de jeux à champ moyen. Lorsque la taille de la population devient très grande, les asymptotiques du système conduisent à des dynamiques appelées dynamiques de jeux à champ moyen. Cette classe de dynamiques contient les dynamiques standard basées sur des révisions de stratégies. Nous utilisons ce modèle pour analyser les problèmes accès aléatoires à des ressources dans un environnement où les utilisateurs et les ressources sont spatialement distribuées. Nous établissons un lien entre les jeux à champ moyen et les jeux différentiels de population dans lesquels chaque joueur a son état individuel et optimise son paiement à long terme pendant son temps de séjour dans le système sous contraintes que le profil de population évolue selon une dynamique de jeux à champ moyen / His manuscript presents dynamic foundations of population games with variable number of players and their solutions and stability concepts. We first introduce delayed evolutionary game dynamics and study their stability. Applications to both wired and wireless networks are presented. We then introduce mobility and spatial aspects of players distribution into the network dynamics. This leads to a new class of game dynamics with multicomponent strategies and migration constraints called evolutionary game dynamics with migration. We derived such dynamics for hybrid systems such as power control in heterogenous networks, switching between technologies and migration between different classes of users. After that we focus on stochastic population games with multiple classes of players in which each player has its own state and facing to an evolving vector which represents the population profile. We use this model to analyze resource and energy constrained interactions in wireless networks. Finally, we present a class of mean field games. When taking the asymptotics of finite systems, we derive a new class of game dynamics called mean field game dynamics. This class contains the standard evolutionary game dynamics based on revision of pure actions. We apply this model to analyze spatial random access game and dynamic resource competition game with individual states. We establish a link betweenmean field games and differential population games inwhich each player optimizes its long-term objective during its sojourn time in the system subject to the constraint that the population profile evolves according to some mean field game dynamics

O dilema do prisioneiro é geralmente visto como o ponto de partida para entender o problema da cooperação. Em comparação com o dilema do prisioneiro discreto e iterado, poucos estudos existem sobre o dilema do prisioneiro contínuo e iterado. A maioria dos trabalhos que investigaram o dilema do prisioneiro contínuo e iterado concentrou-se no período de 1990 a 2000, não obtendo resultados conclusivos sobre a melhor estratégia a ser adotada neste tipo de jogo. Duas estratégias diferentes se destacam neste tipo de dilema. A primeira é a estratégia RTS (Raise-the-Stakes) de Roberts e Sherrat (1998) que testa o terreno antes de aumentar os investimentos na relação. A segunda deriva do modelo LRS (Linear Reactive Strategies) de Wahl e Nowak (1999a). Esta última estratégia estando em equilíbrio de Nash cooperativo apresenta três características: (i) generosidade, i.e., investir o máximo possível no início da relação de cooperação; (ii) otimismo, i.e., contar com o melhor cenário para as próximas rodadas, e (iii) intransigência. Esta pesquisa tem como objetivo principal contrapor as estratégias RTS e LRS num dilema do prisioneiro contínuo e iterado, na presença e ausência de ruído, com jogadas simultâneas e alternadas e para diferentes valores do parâmetro w (probabilidade de interagir novamente). Restringimos a nossa análise a um conjunto de seis estratégias: ALLC, ALLD, TFT, RTS, LRS e RTSM. O método utilizado foi o da simulação baseada em agente (ABM) no formato de torneios, semelhante ao de Axelrod (2006), Roberts & Sherratt (1998), Nowak & Sigmund (1992) e Nowak & Sigmund (1993). Utilizamos o software Netlogo e documentamos todo o processo da concepção e construção do modelo por meio da ferramenta TRACE (TRAnsparent and Comprehensive model Evaludation). Os resultados mostram que as estratégias mais cooperativas são mais favorecidas quando o jogo consiste em jogadas alternadas ao invés de simultâneas. A estratégia RTS teve melhor desempenho em jogos simultâneos para valores intermediários de w, na presença ou ausência de ruído. Por sua vez, a estratégia LRS teve melhor desempenho nos jogos simultâneos, na presença ou ausência de ruído, ou alternados e na presença de ruído, em ambos os casos para valores grandes de w / The prisoner\'s dilemma is generally seen as the starting point for understanding the problem of cooperation. In comparison with the discreet and iterated prisoner\'s dilemma, few studies exist on the continuous iterated prisoner\'s dilemma. Most of the works that have investigated the continuous iterated prisoner\'s dilemma has concentrated in the period from 1990 to 2000, not getting conclusive results on the best strategy to be adopted in this type of game. Two different strategies stand out in this kind of dilemma. The first is the RTS strategy (Raise-the-Stakes) of Roberts and Sherrat (1998) that tests the ground before increasing investment in the relationship. The second is the model deriva LRS (Linear Reactive Strategies) de Wahl and Nowak (1999a). This last strategy being in Nash equilibrium cooperative presents three characteristics: (i) generosity, i.e., investing as much as possible at the beginning of the cooperation relationship; (ii) optimism, i.e., rely on the best scenario for the next rounds, and (iii) intransigence. This research has as main goal to reconcile opposing RTS strategies and LRS in a continuous iterated prisoner\'s dilemma, in the presence and absence of noise, with simultaneous moves and alternate and for different values of the parameter w (probability of interacting again). We restrict our analysis to a set of six strategies: ALLC, ALLD, TFT, RTS, LRS and RTSM (halfway between RTS and LRS). The method used was the agent-based simulation (ABM) in tournament format, similar to that of Axelrod (2006), Roberts (1998), Sherratt & Nowak & Sigmund (1992) and Nowak & Sigmund (1993). We use the NetLogo software and document the whole process of design and construction of the tool model TRACE (TRAnsparent and Comprehensive model Evaludation). The results show that most strategies are more favoured unions when the game consists of alternating plays rather than simultaneous. The RTS strategy had better performance in simultaneous games for intermediate values of w, in the presence or absence of noise. In turn, the IRS strategy had better performance when simultaneous games, in the presence or absence of noise, or switched, and in the presence of noise, in both cases, for large values of w

O dilema do prisioneiro é geralmente visto como o ponto de partida para entender o problema da cooperação. Em comparação com o dilema do prisioneiro discreto e iterado, poucos estudos existem sobre o dilema do prisioneiro contínuo e iterado. A maioria dos trabalhos que investigaram o dilema do prisioneiro contínuo e iterado concentrou-se no período de 1990 a 2000, não obtendo resultados conclusivos sobre a melhor estratégia a ser adotada neste tipo de jogo. Duas estratégias diferentes se destacam neste tipo de dilema. A primeira é a estratégia RTS (Raise-the-Stakes) de Roberts e Sherrat (1998) que testa o terreno antes de aumentar os investimentos na relação. A segunda deriva do modelo LRS (Linear Reactive Strategies) de Wahl e Nowak (1999a). Esta última estratégia estando em equilíbrio de Nash cooperativo apresenta três características: (i) generosidade, i.e., investir o máximo possível no início da relação de cooperação; (ii) otimismo, i.e., contar com o melhor cenário para as próximas rodadas, e (iii) intransigência. Esta pesquisa tem como objetivo principal contrapor as estratégias RTS e LRS num dilema do prisioneiro contínuo e iterado, na presença e ausência de ruído, com jogadas simultâneas e alternadas e para diferentes valores do parâmetro w (probabilidade de interagir novamente). Restringimos a nossa análise a um conjunto de seis estratégias: ALLC, ALLD, TFT, RTS, LRS e RTSM. O método utilizado foi o da simulação baseada em agente (ABM) no formato de torneios, semelhante ao de Axelrod (2006), Roberts & Sherratt (1998), Nowak & Sigmund (1992) e Nowak & Sigmund (1993). Utilizamos o software Netlogo e documentamos todo o processo da concepção e construção do modelo por meio da ferramenta TRACE (TRAnsparent and Comprehensive model Evaludation). Os resultados mostram que as estratégias mais cooperativas são mais favorecidas quando o jogo consiste em jogadas alternadas ao invés de simultâneas. A estratégia RTS teve melhor desempenho em jogos simultâneos para valores intermediários de w, na presença ou ausência de ruído. Por sua vez, a estratégia LRS teve melhor desempenho nos jogos simultâneos, na presença ou ausência de ruído, ou alternados e na presença de ruído, em ambos os casos para valores grandes de w / The prisoner\'s dilemma is generally seen as the starting point for understanding the problem of cooperation. In comparison with the discreet and iterated prisoner\'s dilemma, few studies exist on the continuous iterated prisoner\'s dilemma. Most of the works that have investigated the continuous iterated prisoner\'s dilemma has concentrated in the period from 1990 to 2000, not getting conclusive results on the best strategy to be adopted in this type of game. Two different strategies stand out in this kind of dilemma. The first is the RTS strategy (Raise-the-Stakes) of Roberts and Sherrat (1998) that tests the ground before increasing investment in the relationship. The second is the model deriva LRS (Linear Reactive Strategies) de Wahl and Nowak (1999a). This last strategy being in Nash equilibrium cooperative presents three characteristics: (i) generosity, i.e., investing as much as possible at the beginning of the cooperation relationship; (ii) optimism, i.e., rely on the best scenario for the next rounds, and (iii) intransigence. This research has as main goal to reconcile opposing RTS strategies and LRS in a continuous iterated prisoner\'s dilemma, in the presence and absence of noise, with simultaneous moves and alternate and for different values of the parameter w (probability of interacting again). We restrict our analysis to a set of six strategies: ALLC, ALLD, TFT, RTS, LRS and RTSM (halfway between RTS and LRS). The method used was the agent-based simulation (ABM) in tournament format, similar to that of Axelrod (2006), Roberts (1998), Sherratt & Nowak & Sigmund (1992) and Nowak & Sigmund (1993). We use the NetLogo software and document the whole process of design and construction of the tool model TRACE (TRAnsparent and Comprehensive model Evaludation). The results show that most strategies are more favoured unions when the game consists of alternating plays rather than simultaneous. The RTS strategy had better performance in simultaneous games for intermediate values of w, in the presence or absence of noise. In turn, the IRS strategy had better performance when simultaneous games, in the presence or absence of noise, or switched, and in the presence of noise, in both cases, for large values of w