Mathematical models with fixed parameters have a long history of use in describing the dynamics of populations in ecological interactions. However, in many instances, evolutionary changes in species characteristics can have a significant influence on these dynamics. Using evolutionary game theory, we incorporate evolution into population dynamic models and apply the resulting “Darwinian dynamic” models to study the effects that evolutionary changes can have on populations in several ecological scenarios. We start with a single species (Chapter 2), then add a competitor (Chapter 3), and a predator (Chapter 4). In Chapter 2, a rigorous mathematical analysis of the Darwinian logistic model for a single species shows that stable equilibria occur at strategies that maximize population size rather than growth rate. We apply this model to the data obtained from an experimental study on genetically perturbed populations of the flour beetle Tribolium castaneum. In Chapter 3, we apply a Darwinian dynamic modification of the Lotka-Volterra model to investigate circumstances under which evolution will change expected competitive outcomes. We compare the results of our Darwinian Lotka-Volterra model to studies in which unusual observations were made in studies of the flour beetles T. castaneum and T. confusum, including a reversal in the “winner” of competitive exclusion, and evolution from exclusion to coexistence. Chapters 2 and 3 provide one of the few examples in which evolutionary game theory has been successfully applied to empirical data. From a foundation provided by the Darwinian logistic equation, we build Darwinian dynamic models with two and three trophic levels to study effects of evolution on some basic ecological interactions in Chapter 4. We show how a consumer can cause a resource (producer) species to evolve to a mean strategy that increases its growth rate rather than its population size. We also briefly study how predation on the consumer species can affect equilibrium strategies of species lower in the food chain. Our results show how evolutionary game theoretic methods can be useful for studying both theoretical and applied problems that arise due to evolutionary processes, even when they occur on a ecological time scale. They provide a foundation for the future study of evolutionary effects in larger complex networks of interacting species.

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Uma das características que nos distinguem de outros seres vivos é nossa cultura. Entretanto, como comportamentos não fossilizam, é difícil reconstruir o passado para gerar insights sobre por que nos tornamos o que somos hoje. Juntamente com dados etnográficos e experimentais, os modelos matemáticos têm sido utilizados para abordar a questão sobre como nossos comportamentos foram moldados pela evolução. Esta tese está dividida em duas partes. Na primeira parte, discutiremos sobre seleção multinível e sobre como o framework matemático chamado Two-level Fisher Wright (TLFW) pode nos ajudar a entender a evolução da cooperação em populações humanas. Após descrevermos o problema da cooperação através do uso de ferramentas de teoria dos jogos, revisamos algumas das teorias atuais sobre por que a cooperação evoluiu. Em seguida, empregamos o framework TLFW ao problema da emergência de altruísmo em populações de caçadores-coletores, considerando uma situação em que o conflito entre grupos direciona a seleção. Na segunda parte, abordamos o tópico de diversidade linguística e apresentamos a importância de se estudar a competição entre línguas para ajudar a preservá-las. Traçando um paralelo entre a evolução das línguas e a evolução de normas sociais, introduzimos um modelo para analisar a persistência de dialetos, quando existe competição com uma língua padrão nacional. / One of the features that distinguish human beings from other living species is our culture. However, since behaviors do not fossilize, it is difficult to reconstruct the past to get insights about why we are who we are. Along with ethnographic and experimental data, mathematical models have been used to address the question of how our behaviors were shaped by evolution. This thesis is divided into two parts. In the first part, we will discuss multilevel selection and how the mathematical framework Two-Level Fisher-Wright (TLFW) can help us to understand the evolution of cooperation in human populations. After describing the problem of cooperation by using game theory, we review some of the present theories about why cooperation has evolved. Then, we apply the TLFW framework to the problem of the evolution of altruism in populations of hunter-gatherers, considering a situation in which group conflict drives selection. In the second part, we discuss language diversity and present the importance of studying the competition between languages for helping to preserve them. By drawing a parallel between the evolution of language and social norms, we introduce a mathematical model to analyze the persistence of dialects competing against a national standard language.

Uma das características que nos distinguem de outros seres vivos é nossa cultura. Entretanto, como comportamentos não fossilizam, é difícil reconstruir o passado para gerar insights sobre por que nos tornamos o que somos hoje. Juntamente com dados etnográficos e experimentais, os modelos matemáticos têm sido utilizados para abordar a questão sobre como nossos comportamentos foram moldados pela evolução. Esta tese está dividida em duas partes. Na primeira parte, discutiremos sobre seleção multinível e sobre como o framework matemático chamado Two-level Fisher Wright (TLFW) pode nos ajudar a entender a evolução da cooperação em populações humanas. Após descrevermos o problema da cooperação através do uso de ferramentas de teoria dos jogos, revisamos algumas das teorias atuais sobre por que a cooperação evoluiu. Em seguida, empregamos o framework TLFW ao problema da emergência de altruísmo em populações de caçadores-coletores, considerando uma situação em que o conflito entre grupos direciona a seleção. Na segunda parte, abordamos o tópico de diversidade linguística e apresentamos a importância de se estudar a competição entre línguas para ajudar a preservá-las. Traçando um paralelo entre a evolução das línguas e a evolução de normas sociais, introduzimos um modelo para analisar a persistência de dialetos, quando existe competição com uma língua padrão nacional. / One of the features that distinguish human beings from other living species is our culture. However, since behaviors do not fossilize, it is difficult to reconstruct the past to get insights about why we are who we are. Along with ethnographic and experimental data, mathematical models have been used to address the question of how our behaviors were shaped by evolution. This thesis is divided into two parts. In the first part, we will discuss multilevel selection and how the mathematical framework Two-Level Fisher-Wright (TLFW) can help us to understand the evolution of cooperation in human populations. After describing the problem of cooperation by using game theory, we review some of the present theories about why cooperation has evolved. Then, we apply the TLFW framework to the problem of the evolution of altruism in populations of hunter-gatherers, considering a situation in which group conflict drives selection. In the second part, we discuss language diversity and present the importance of studying the competition between languages for helping to preserve them. By drawing a parallel between the evolution of language and social norms, we introduce a mathematical model to analyze the persistence of dialects competing against a national standard language.

Network reciprocity describes the emergence of cooperative behaviour where interactions are constrained by incomplete network connectivity. It has been widely studied as an enabling mechanism for the emergence of cooperation and may be of particular interest in explaining cooperative behaviours amongst unrelated individuals or in organisms of lower cognitive abilities. Research in this area has been galvanised by the finding that heterogeneous topology promotes cooperation. Consequently there has been a strong focus on scale-free networks; however, such networks typically presuppose formative mechanisms based on preferential attachment, a process which has no general explanation. This assumption may give rise to models of cooperation that implicitly encode capabilities only generally found in more complex forms of life, thus constraining their relevance with regards to the real world. By considering the connectivity of populations to be dynamic, rather than fixed, cooperation can exist at lower levels of heterogeneity. This thesis demonstrates that a model of network fluctuation, based on random rather than preferential growth, supports cooperative behaviour in simulated social networks of only moderate heterogeneity, thus overcoming difficulties associated with explanations based on scale-free networks. In addition to illustrating the emergence and persistence of cooperation in existing networks, we also demonstrate how cooperation may evolve in networks during their growth. In particular our model supports the emergence of cooperation in populations where it is originally absent. The combined impact of our findings increases the generality of reciprocity as an explanation for cooperation in networks.

Interpersonal trust is a one-sided social dilemma. Building on the binary trust game, we ask how trust and trustworthiness can evolve in a population where partners are matched randomly and agents sometimes act as trustors and sometimes as trustees. Trustors have the option to costly check a trustee's last action and to condition their behavior on the signal they receive. We show that the resulting population game admits two components of Nash equilibria. Nevertheless, the long-run outcome of an evolutionary social learning process modeled by the best response dynamics is unique. Even if unconditional distrust initially abounds, the trustors' checking option leads trustees to build a reputation for trustworthiness by honoring trust. This invites free-riders among the trustors who save the costs of checking and trust blindly, until it does no longer pay for trustees to behave in a trustworthy manner. This results in cyclical convergence to a mixed equilibrium with behavioral heterogeneity where suspicious checking and blind trusting coexist while unconditional distrust vanishes. (author's abstract) / Series: Department of Economics Working Paper Series

Vaccination has been used to control the spread of infectious diseases for centuries with widespread success. Deterministic models studying the spread of infectious disease often use the assumption of mass vaccination; however, these models do not allow for the inclusion of human behaviour. Since current vaccination campaigns are voluntary in nature, it is important to extend the study of infectious disease models to include the effects of human behaviour. To model the effects of vaccination behaviour on the spread of influenza, we examine a series of models in which individuals vaccinate according to memory or individual decision-making processes based upon self-interest. Allowing individuals to vaccinate proportionally to an exponentially decaying memory function of disease prevalence, we demonstrate the existence of a Hopf bifurcation for short memory spans. Using a game-theoretic influenza model, we determine that lowering the perceived vaccine risk may be insufficient to increase coverage to established target levels. Utilizing evolutionary game theory, we examine models with imitation dynamics both with and without a decaying memory function and show that, under certain conditions, periodic dynamics occur without seasonal forcing. Our results suggest that maintaining diseases at low prevalence with voluntary vaccination campaigns could lead to subsequent epidemics following the free-rider dilemma and that future research in disease control reliant on individual-based decision-making need to include the effects of human behaviour.

[pt] O papel das agências de rating de crédito no mercado de capitais tem evoluído ao longo dos últimos anos, passando de um provedor de informação aos agentes financeiros a um quase-regulador do mercado. Em princípio, supõe-se que as avaliações concedidas pelas agências de rating são imparciais e, consequentemente, indicadoras de qualidade de crédito dos mais diversos instrumentos financeiros. Porém, deve ser observado que à medida que esses instrumentos disponíveis no mercado foram se tornando mais complexos, o valor agregado das avaliações das agências diminuiu consideravelmente. A fim de analisar o problema da imparcialidade das agências de rating, conforme proposto por Hirth (2014), fez-se uso da estrutura espacial em comparação à solução analítica apresentada como condição de equilíbrio para o jogo evolucionário, com população well-mixed. Sendo assim, para a modelagem do problema apresentado, foi criado um programa computacional baseado a fim de apresentar uma solução compatível com a literatura sobre Teoria dos Jogos, expandindo seus conceitos e aplicações para uma Estrutura de Jogos Espaciais. Por fim, foi desenvolvida uma extensão ao programa, a qual, dentro do meu melhor conhecimento, representa uma inovação à literatura ao estender as abordagens de Chan et al. (2013), Hauert (2004) e Zhong et al. (2006), considerando a Estrutura de Jogos Espaciais, para o conceito de duas populações. A partir dos casos estudados, pode-se concluir que a população ser well-mixed ou estar disposta ao longo de um grid espacial não implica em diferenças significativas nos resultados para os mesmos valores dos parâmetros. / [en] The role of the credit rating agencies in the capital market has evolved in the last years, turning from a data provider to financial agents into a market quasi-regulator . Primarily, it is supposed that the evaluations provided by the rating agencies are impartial and, consequently, indicative of credit quality of a wide range of financial instruments. Nevertheless, it is important to note that as these instruments available in the market became more complex, the aggregate value of evaluations of agencies decrease considerably. In order to analyze the rating agencies impartiality issues, as proposed by Hirth (2014), this study uses the spatial structure in comparison to the analytical solution presented as equilibrium condition to the evolutionary game, with well-mixed population. Therefore, in order to model the presented problem, this study presents a computational program that aims to present a solution that matches the Game Theory literature, expanding its concepts and applications to a Spatial Games Structure. Finally, we created an extension of the program, which, in my best knowledge, is an innovation to the literature since it extends the approaches of Chan et al. (2013), Hauert (2004) e Zhong et al. (2006), regarding the Spatial Games Structure, to the concept of two populations. From the studied cases, we concluded that the fact of the population being well-mixed or disposed in a spatial grid does not imply differences of significance in the results to the same parameters values.

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.

Thesis advisor: Katherine McAuliffe / Thesis advisor: Angela Johnston / Human cooperation is unparalleled in the natural world and is a defining feature of human social life—it shapes nearly every social interaction we experience, from geopolitical conflict, to collective bargaining, to team collaboration. However, cooperation also presents a challenge—it is often personally costly or risky to cooperate. How are humans able to overcome these costs and risks in favor of the interest of the group? To address this question, it is important to investigate the cognitive abilities that allow us to successfully cooperate with others. One important ability for cooperation is mentalizing—the ability to represent other agents’ beliefs, knowledge, desires, and intentions. The ability to think about other agents’ minds in order to predict how they will behave (e.g., whether they will cooperate or free-ride) is an important component of our own cooperative behavior, particularly in the context of coordination—a type of cooperative interaction where cooperation is mutually beneficial but risky. I test the idea that our ability to represent the beliefs of others plays a critical role in successful cooperation. Studies 1 and 2 examine one cognitive ability for representing others’ knowledge—common knowledge—that underlies cooperation by reducing uncertainty about others’ cooperative behavior. Studies 3 and 4 investigate how we make inferences about others’ beliefs from how they behave and how that influences our own cooperative behavior in the context of social norms. Studies 2 and 4 take a developmental approach to investigate how early emerging mentalizing is for cooperative behavior to better understand how foundational it is in social cognition. Altogether, the results of these studies suggest that the ability to represent other agents’ beliefs in order to predict their behavior plays a fundamental role in supporting successful cooperation. / Thesis (PhD) — Boston College, 2023. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Psychology.