Evolutionary game theory tries to explain the emergence of stable behaviors observed in human and animal societies. Prominent examples of such behaviors are cooperative and conformist behaviors. In the first part of the thesis, we develop a model of indirect reciprocity with institutional screening to study how institutions may promote cooperative behavior. We show that cooperation can emerge if screening institutions are sufficiently reliable at identifying cooperators. The second part presents a large-population learning model in which individuals update their beliefs through time. In the model, only one individual updates his beliefs each period. We show that a population, playing a game with two strategies, eventually learns to play a Nash equilibrium. We focus on coordination games and prove that a unique behavior arises both when players use myopic and perturbed best replies. The third part studies the payoff calculation in an evolutionary setting. By introducing mutual consent as a requirement for game play, we provide a more realistic alternative way to compute payoffs. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Manuscript. Paper 3: Manuscript.</p>

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.

This thesis examines a series of problems with the goal of better understanding the fundamental dilemma of whether to invest effort in obtaining information that may lead to better opportunities in the future versus exploiting immediately available opportunities. In particular this work investigates how this dilemma is affected by competition in an evolutionary setting. To achieve this requires both the use of evolutionary game theory, and Markov decision procesess or stochastic dynamic programming. This thesis grows directly out of earlier work on the Social Learning Strategies Tournament. Although I cast the problem in the biological setting of optimal foraging theory, where it fills an obvious gap, this fundamental dilemma should also be of some interest to economists, operations researchers, as well as those working in ecology, evolution and behaviour. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2012-01-31 19:55:25.11

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We study game theoretic ecological models with cyclic competition in the case where the strategies can be mixed or pure. For both projects, reported in [49] and [50], we employ Monte Carlo simulations to study finite systems. In chapter 3 the results of a previously published paper [49] are presented and expanded upon, where we study the extinction time of four cyclically competing species on different lattice structures using Lotka-Volterra dynamics. We find that the extinction time of a well mixed system goes linearly with respect to the system size and that the probability distribution approximately takes the shape of a shifted exponential. However, this is not true for when spatial structure is added to the model. In that case we find that instead the probability distribution takes on a non-trivial shape with two characteristic slopes and that the mean goes as a power law with an exponent greater than one. This is attributed to neutral species pairs, species who do not interact, forming domains and coarsening. In chapter 4 the results of [50] are reported and expanded, where we allow agents to choose cyclically competing strategies out of a distribution. We first study the case of three strategies and find through both simulation and mean field equations that the probability distributions of the agents synchronize and oscillate with time in the limit where the agents probability distributions can be approximated as continuous. However, when we simulate the system on a one-dimensional lattice and the probability distributions are small and discretized, it is found that there is a drastic transition in stability, where the average extinction time of a strategy goes from being a power law with respect to system size to an exponential. This transition can also be observed in space time images with the emergence of tile patterns. We also look into the case of four cyclically competing strategies and find results similar to that of [49], such as the coarsening of neutral domains. However, the transition from power law to exponential for the average extinction time seen for three strategies is not observed, but we do find a transition from one power law to another with a different slope. This work was supported by the United States National Science Foundation through grants DMR-0904999 and DMR-1205309. / Ph. D.

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.

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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