This thesis consists of five papers, presented as separate chapters within three parts: Industrial Organization, Evolutionary Game Theory and Game Theory. The common basis of these parts is research in the field of game theory and more specifically, equilibrium selection in different frameworks. The first part, Industrial Organization, consists of one paper co-authored with Prajit Dutta and Jörgen Weibull. Forward-looking consumers are analysed in a Bertrand framework. It is assumed that if firms can anticipate a price war and act accordingly, so can consumers. The second part, Evolutionary Game Theory, contains three chapters. All models in these papers are based on Young’s (1993, 1998) approach. In Chapter 2, the Saez Marti and Weibull’s (1999) model is generalized from the Nash Demand Game to generic two-player games. In Chapter 3, co-authored with Jens Josephson, a special set of stochastically stable states is introduced, minimal construction, which is the long-run prediction under imitation behavior in normal form games. In Chapter 4, best reply and imitation rules are considered on extensive form games with perfect information. / Diss. Stockholm : Handelshögsk., 2001

Kooperatives Verhalten lässt sich in vielen Bereichen menschlichen Zusammenlebens sowie im gesamten Tierreich beobachten. In evolutionären Modellen wurde gezeigt, dass Netzwerkstrukturen die Kooperation erhöhen können. Empirische Studien versuchten vergeblich diesen Mechanismus auch bei Menschen nachzuweisen. Es scheint, als würden Netzwerke nur dann die Kooperation erhöhen, wenn die Strukturen nicht statisch sind, sondern dynamisch. Das heißt, dass die Individuen die Möglichkeit haben, ihre Partner zu wechseln. Eine wichtige – aber bislang unerforschte – Eigenschaft dynamischer Netzwerke ist jedoch, dass derartige Wechsel von Partnern in der Regel Kosten verursachen, ob in Form von Zeit oder Ressourcen. Kapitel I meiner Arbeit schließt diese Lücke, in dem es sich mit den Effekten von Kosten auf dynamischen Netzwerken befasst. Ich konnte nachweisen, dass Menschen seltener Interaktionen mit Partnern beendeten, wenn die Kontaktaufnahme mit einem neuen Partner mit Kosten verbunden war. Bei sehr hohen Kosten, wurden Partner so selten gewechselt, dass das Netzwerk fast statisch war. Interessanterweise blieb die Kooperation dennoch sehr hoch. Das bedeutet, dass für kooperatives Verhalten entscheidend ist, ob man die Möglichkeit hat, Partner zu wechseln. Im Gegensatz zu bisherigen Annahmen ist es daher nicht wichtig, wie oft tatsächlich Partner gewechselt werden, sondern lediglich ob es die Möglichkeit dazu gibt. In Kapitel II beschäftige ich mich mit optimalem Entscheidungsverhalten. Im sogenannten Judge-Advisor-System geht es darum, dass eine Person, der Judge, eine unbekannte numerische Größe schätzen will. Dazu erhält der Judge eine zweite unabhängige Schätzung als Rat von einer zweiten Person, des Advisor. Schließlich ist die Frage, wie der Judge optimal den Rat verwerten kann um seine Anfangsschätzung zu verbessern. Bisherige Forschung konzentrierte sich hauptsächlich auf zwei mögliche Methoden, (i) das Bilden des Mittelwerts und (ii) das Wählen der besseren Anfangsschätzung. Das Hauptargument für diese einfachen Methoden ist deren häufige Verwendung in bisherigen Experimenten. Allerdings wurden sehr wohl auch andere Gewichtungen beobachtet und daher ist eine gründliche Analyse der optimalen Gewichtung erforderlich. In der vorliegenden Arbeit leitete ich ein normatives Modell her, das beschreibt, unter welchen Bedingungen welche Methode das bestmögliche Ergebnis liefert. Es wurden drei Methoden verglichen: (i) das Bilden des Durchschnitts, (ii) das Wählen der besseren Anfangsschätzung, und (iii) das Bilden eines gewichtetet Mittelwerts, wobei das Gewicht vom Kompetenzunterschied abhängt. Welche Methode optimal ist, hängt davon ab, wie groß der Kompetenzunterschied ist und wie gut er vom Judge erkannt wird. Die Durchschnittbildung ist immer dann vorteilhaft, wenn der Kompetenzunterschied nicht groß ist, oder nur schwer richtig eingeschätzt werden kann. Wenig überraschend lohnt sich das Wählen der besseren Anfangsschätzung, wenn der Kompetenzunterschied hinreichend groß ist, vorausgesetzt es wird tatsächlich die bessere Anfangsschätzung gewählt. Wenn der Kompetenzunterschied vom Judge gut eingeschätzt werden kann, ist eine Entsprechende Gewichtung immer die beste Methode, unabhängig vom tatsächlichen Unterschied. In Übereinstimmung mit bisheriger Forschung wurde auch die Kombination von Durchschnittbildung und Wählen der besseren Anfangsschätzung untersucht. Diese Kombinationsmethode beruht darauf, bei als gering eingeschätztem Kompetenzunterschied den Durchschnitt zu bilden und ansonsten die bessere Anfangsschätzung zu wählen. Interessanterweise schneidet diese Kombinationsmethode sehr schlecht ab, was hauptsächlich daran liegt, dass zu oft die falsche Anfangsschätzung genommen würde. Insgesamt ist das gewichtete Mittel also eine geeignete Methode für einen großen Parameterbereich.

[pt] Um dos principais desafios do mundo moderno é equilibrar o desenvolvimento econômico com a responsabilidade ambiental, de forma a alcançar um crescimento sustentável que minimize os impactos gerados no meio ambiente. Isto tem feito com que muitos governos e empresas estabeleçam políticas ambientais como instrumentos para a garantia de um futuro com sustentabilidade e que favoreçam o bem estar social. A proposta desta dissertação é utilizar a teoria dos jogos evolucionários para analisar as interações entre agentes reguladores de políticas ambientais de comando e controle e os agentes (firmas) que impulsionam o desenvolvimento econômico, porém que impactam de alguma forma o meio ambiente. Enquanto os primeiros precisam determinar as melhores ações estratégicas para implementar a política e aumentar o bem estar social, os segundos só irão se adequar à regulamentação ambiental estabelecida se esta escolha lhe render um maior retorno (payoff). Os resultados mostram que o custo de fiscalização é determinante para estabelecer a política ambiental mais adequada e, dependendo da magnitude deste custo, existem diferentes formas de iniciar sua implementação a fim de favorecer o melhor resultado possível sob o ponto de vista do bem estar social. / [en] The modern world faces the great challenge of balancing economic development and environmental responsibility in order to achieve sustainable growth that minimizes the impacts generated on the environment. This has forced some governments and firms establish environmental policies as instruments to guarantee a future with sustainability and favors social welfare. Using evolutionary games theory, this work aims to analyze the interactions between environmental policies regulators and firms that provide economic development impacting the environment. While the firsts need to choose the best strategic actions to established and inspect environmental standards sets to increase social welfare, the company will only complies if this choice yields a better payoff. The results show how the inspection cost is decisive for establishing the better environmental policy and depending on the magnitude of this cost, there are different ways to introduce it in order to provide a better social welfare result.

Existe um interesse crescente do mercado por aplicações de multimídia em streaming via rede. Particularmente, as aplicações de live streaming que utilizam a tecnologia de redes P2P para a disseminação de conteúdo têm sido alvo de grande atenção. Aplicações como PPLive e PPStream provam que as aplicações de live streaming em redes P2P são uma realidade com relação à tecnologia atual. Os sistemas de live streaming fornecem um serviço de multicast no nível de aplicação para transmissões ao vivo na Internet. Essas aplicações de live streaming, quando executadas em redes P2P, têm potencial para serem altamente robustas, escaláveis e adaptativas devido à redundância e não dependência de recursos particulares dentre os nodos participantes. Porém, para fazer uso de todas as vantagens disponíveis, a aplicação deve contornar alguns desafios: i) manter a qualidade de playback mesmo com a inerente dinamicidade das redes P2P; ii) impedir que nodos incorretos escondam ações maliciosas atrás do anonimato que existe em P2P; iii) manter a taxa de upload dos nodos participantes da aplicação em um nível aceitável. A taxa de upload dos nodos é muito importante porque a aplicação de live streaming em P2P é uma aplicação cooperativa. Desta forma, esperase que todo novo usuário ajude a aplicação retransmitindo pacotes para outros usuários, mantendo, desta forma, a capacidade global de upload do sistema. Infelizmente, manter a cooperação em live streaming não é uma tarefa trivial, visto que cada nodo enfrenta o dilema social do interesse próprio (individualmente é melhor explorar a cooperação dos outros usuários sem reciprocidade) versus a cooperação para com o grupo. A principal contribuição deste trabalho consiste na apresentação de um modelo matemático baseado em Teoria dos Jogos Evolucionários, cujo objetivo é ajudar a compreender as aplicações de live streaming em redes P2P e os fatores que influenciam o seu correto funcionamento. Como contribuição secundária, este trabalho fornece uma análise estatística do comportamento do download e upload observado nestas aplicações. A análise estatística mostra que existe um decaimento da variância temporal de download e upload nas aplicações de live streaming, e que tal decaimento segue uma lei de potência. Os resultados evolucionários do modelo indicam que, se a queda do índice de satisfação dos usuários com a taxa de download for suave, e se a redução da satisfação devido ao custo de upload for insignificante, então existe um ambiente propício para que a cooperação entre os nodos cresça. De forma inversa, se a queda do índice de satisfação dos usuários com a taxa de download for abrupta, e a redução da satisfação devido ao custo de upload for significativa, então existe um ambiente propício para proliferação de nodos oportunistas. A realização e descrição desta pesquisa é composta de quatro etapas principais: i) a delimitação do cenário de live streaming e a definição do jogo para modelagem; ii) a definição do conjunto de estratégias e da função de utilidade; iii) a criação do modelo; iv) a análise do modelo e a apresentação dos resultados de simulação. A análise do modelo abrange três fases: i) análise estatística e comparação das características de download e upload dos dois simuladores utilizados; ii) avaliação do modelo de Teoria dos Jogos Evolucionários através de simulações; e iii) análise dos resultados evolucionários gerados pelo simulador de Teoria dos Jogos Evolucionários. / There is a growing interest in the market for networked multimedia applications. Live streaming applications that use the technology of P2P networks for distribution of live content have specially been the subject of great attention. Applications such as PPLive and PPStrem demonstrate that P2P live streaming applications are already possible with our present technology. Live streaming systems provide a multicast service in the application level for live broadcasts to users through the Internet. These systems executing in P2P networks have the potential to be highly robust, scalable and adaptive due to the characteristics of these scenarios. However, to take advantage of these potential properties, they must overcome some challenges: i) to maintain the playback quality even with the inherent dynamics of P2P networks; ii) to prevent that incorrect peers hide malicious behavior behind their anonymity; iii) to maintain the upload contribution of peers at acceptable levels. The upload contribution of peers is highly important because live streaming applications are cooperative applications. Therefore, every new user must help the application forwarding packets to other users, thereby maintaining the global upload capacity of the system. Unfortunately, the maintenance of cooperation in live streaming system is not a trivial task, since each node faces the social dilemma of self-interest (individually is always better to explore the cooperation of other users without reciprocity) versus cooperation to the group. The main contribution of this dissertation is the presentation of a mathematical model based on Evolutionary Game Theory, whose goal is to help understanding live streaming P2P applications and the factors that influence their correct operation. As a secondary contribution, this work provides a statistical analysis of download and upload behaviors of peers in live streaming P2P systems. The statistical analysis indicates that there is a decay in the download and upload variances, and that this decay follows a power law. The evolutionary results of the model indicate that, if the satisfaction of users with the download rate is smooth, and the reduction of satisfaction due to the upload cost is negligible, then there is a favorable environment for the growth of cooperation. Conversely, if the satisfaction of users with the download rate is abrupt, and the reduction of satisfaction due to the upload cost is significant, then there is a favorable environment to the proliferation of opportunistic nodes. The realization and description of this research is composed of four main steps: i) the definition of the live streaming scenario and the definition of the game to model this scenario; ii) the definition of the strategy set and of the utility function; iii) the suggestion of a model; iv) the analysis of the proposed model and the presentation of obtained results. The model analysis comprehends three phases: i) the statistical analysis and the comparison of the characteristics of download and upload of the two simulators used in this work; ii) the evaluation of the Evolutionary Game Theory model through simulation; and iii) the analysis of the results generated by the Evolutionary Game Theory simulator.

Existe um interesse crescente do mercado por aplicações de multimídia em streaming via rede. Particularmente, as aplicações de live streaming que utilizam a tecnologia de redes P2P para a disseminação de conteúdo têm sido alvo de grande atenção. Aplicações como PPLive e PPStream provam que as aplicações de live streaming em redes P2P são uma realidade com relação à tecnologia atual. Os sistemas de live streaming fornecem um serviço de multicast no nível de aplicação para transmissões ao vivo na Internet. Essas aplicações de live streaming, quando executadas em redes P2P, têm potencial para serem altamente robustas, escaláveis e adaptativas devido à redundância e não dependência de recursos particulares dentre os nodos participantes. Porém, para fazer uso de todas as vantagens disponíveis, a aplicação deve contornar alguns desafios: i) manter a qualidade de playback mesmo com a inerente dinamicidade das redes P2P; ii) impedir que nodos incorretos escondam ações maliciosas atrás do anonimato que existe em P2P; iii) manter a taxa de upload dos nodos participantes da aplicação em um nível aceitável. A taxa de upload dos nodos é muito importante porque a aplicação de live streaming em P2P é uma aplicação cooperativa. Desta forma, esperase que todo novo usuário ajude a aplicação retransmitindo pacotes para outros usuários, mantendo, desta forma, a capacidade global de upload do sistema. Infelizmente, manter a cooperação em live streaming não é uma tarefa trivial, visto que cada nodo enfrenta o dilema social do interesse próprio (individualmente é melhor explorar a cooperação dos outros usuários sem reciprocidade) versus a cooperação para com o grupo. A principal contribuição deste trabalho consiste na apresentação de um modelo matemático baseado em Teoria dos Jogos Evolucionários, cujo objetivo é ajudar a compreender as aplicações de live streaming em redes P2P e os fatores que influenciam o seu correto funcionamento. Como contribuição secundária, este trabalho fornece uma análise estatística do comportamento do download e upload observado nestas aplicações. A análise estatística mostra que existe um decaimento da variância temporal de download e upload nas aplicações de live streaming, e que tal decaimento segue uma lei de potência. Os resultados evolucionários do modelo indicam que, se a queda do índice de satisfação dos usuários com a taxa de download for suave, e se a redução da satisfação devido ao custo de upload for insignificante, então existe um ambiente propício para que a cooperação entre os nodos cresça. De forma inversa, se a queda do índice de satisfação dos usuários com a taxa de download for abrupta, e a redução da satisfação devido ao custo de upload for significativa, então existe um ambiente propício para proliferação de nodos oportunistas. A realização e descrição desta pesquisa é composta de quatro etapas principais: i) a delimitação do cenário de live streaming e a definição do jogo para modelagem; ii) a definição do conjunto de estratégias e da função de utilidade; iii) a criação do modelo; iv) a análise do modelo e a apresentação dos resultados de simulação. A análise do modelo abrange três fases: i) análise estatística e comparação das características de download e upload dos dois simuladores utilizados; ii) avaliação do modelo de Teoria dos Jogos Evolucionários através de simulações; e iii) análise dos resultados evolucionários gerados pelo simulador de Teoria dos Jogos Evolucionários. / There is a growing interest in the market for networked multimedia applications. Live streaming applications that use the technology of P2P networks for distribution of live content have specially been the subject of great attention. Applications such as PPLive and PPStrem demonstrate that P2P live streaming applications are already possible with our present technology. Live streaming systems provide a multicast service in the application level for live broadcasts to users through the Internet. These systems executing in P2P networks have the potential to be highly robust, scalable and adaptive due to the characteristics of these scenarios. However, to take advantage of these potential properties, they must overcome some challenges: i) to maintain the playback quality even with the inherent dynamics of P2P networks; ii) to prevent that incorrect peers hide malicious behavior behind their anonymity; iii) to maintain the upload contribution of peers at acceptable levels. The upload contribution of peers is highly important because live streaming applications are cooperative applications. Therefore, every new user must help the application forwarding packets to other users, thereby maintaining the global upload capacity of the system. Unfortunately, the maintenance of cooperation in live streaming system is not a trivial task, since each node faces the social dilemma of self-interest (individually is always better to explore the cooperation of other users without reciprocity) versus cooperation to the group. The main contribution of this dissertation is the presentation of a mathematical model based on Evolutionary Game Theory, whose goal is to help understanding live streaming P2P applications and the factors that influence their correct operation. As a secondary contribution, this work provides a statistical analysis of download and upload behaviors of peers in live streaming P2P systems. The statistical analysis indicates that there is a decay in the download and upload variances, and that this decay follows a power law. The evolutionary results of the model indicate that, if the satisfaction of users with the download rate is smooth, and the reduction of satisfaction due to the upload cost is negligible, then there is a favorable environment for the growth of cooperation. Conversely, if the satisfaction of users with the download rate is abrupt, and the reduction of satisfaction due to the upload cost is significant, then there is a favorable environment to the proliferation of opportunistic nodes. The realization and description of this research is composed of four main steps: i) the definition of the live streaming scenario and the definition of the game to model this scenario; ii) the definition of the strategy set and of the utility function; iii) the suggestion of a model; iv) the analysis of the proposed model and the presentation of obtained results. The model analysis comprehends three phases: i) the statistical analysis and the comparison of the characteristics of download and upload of the two simulators used in this work; ii) the evaluation of the Evolutionary Game Theory model through simulation; and iii) the analysis of the results generated by the Evolutionary Game Theory simulator.

abstract: This dissertation investigates the dynamics of evolutionary games based on the framework of interacting particle systems in which individuals are discrete, space is explicit, and dynamics are stochastic. Its focus is on 2-strategy games played on a d-dimensional integer lattice with a range of interaction M. An overview of related past work is given along with a summary of the dynamics in the mean-field model, which is described by the replicator equation. Then the dynamics of the interacting particle system is considered, first when individuals are updated according to the best-response update process and then the death-birth update process. Several interesting results are derived, and the differences between the interacting particle system model and the replicator dynamics are emphasized. The terms selfish and altruistic are defined according to a certain ordering of payoff parameters. In these terms, the replicator dynamics are simple: coexistence occurs if both strategies are altruistic; the selfish strategy wins if one strategy is selfish and the other is altruistic; and there is bistability if both strategies are selfish. Under the best-response update process, it is shown that there is no bistability region. Instead, in the presence of at least one selfish strategy, the most selfish strategy wins, while there is still coexistence if both strategies are altruistic. Under the death-birth update process, it is shown that regardless of the range of interactions and the dimension, regions of coexistence and bistability are both reduced. Additionally, coexistence occurs in some parameter region for large enough interaction ranges. Finally, in contrast with the replicator equation and the best-response update process, cooperators can win in the prisoner's dilemma for the death-birth process in one-dimensional nearest-neighbor interactions. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2016

Evolutionary game theory originated from the application of mathematical game theory to biological studies. Well-known examples in evolutionary game theory are the prisoner's dilemma, predator-prey models, the rock-paper-scissors game, etc. Recently, such well-known models have attracted increased interest in population dynamics to understand the emergence of biodiversity and species coexistence. Meanwhile, it has been realized that techniques from statistical physics can aid us to gain novel insights into this interdisciplinary field. In our research, we mainly employ individual-based Monte Carlo simulations to study emerging spatio-temporal patterns, spatial correlations, and the influence of quenched spatial disorder in rock-paper-scissors systems either with or without conserved total population number. In balanced rock-paper-scissors systems far away from the ``corner'' of configuration space, it is shown that quenched spatial disorder in the reaction rates has only minor effects on the co-evolutionary dynamics. However, in model variants with strongly asymmetric rates (i.e., ``corner'' rock-paper-scissors systems), we find that spatial rate variability can greatly enhance the fitness of both minor species in``corner'' systems, a phenomenon already observed in two-species Lotka-Volterra predator-prey models. Moreover, we numerically study the influence of either pure hopping processes or exchange processes on the emergence of spiral patterns in spatial rock-paper-scissors systems without conservation law (i.e., May-Leonard model). We also observe distinct extinction features for small spatial May-Leonard systems when the mobility rate crosses the critical threshold which separates the active coexistence state from an inactive absorbing state. In addition, through Monte Carlo simulation on a heterogeneous interacting agents model, we investigate the universal scaling properties in financial markets such as the fat-tail distributions in return and trading volume, the volatility clustering, and the long-range correlation in volatility. It is demonstrated that the long-tail feature in trading volume distribution results in the fat-tail distribution of asset return, and furthermore it is shown that the long tail in trading volume distribution is caused by the heterogeneity in traders' sensitivities to market risk. / Ph. D.

Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: There are many examples of cooperation in action in society and in nature. In some cases cooperation leads to the increase of the overall welfare of those involved, and in other cases cooperation may be to the detriment of the larger society. The presence of cooperation seems natural if there is a direct bene t to individuals who choose to cooperate. However, in examples of cooperation this bene t is not always immediately obvious. The so called prisoner's dilemma is often used as an analogy to study cooperation and tease out the factors that lead to cooperation. In classical game theory, each player is assumed to be rational and hence typically seeks to select his strategy in such a way as to maximise his own expected pay-o . In the case of the classical prisoner's dilemma, this causes both players to defect. In evolutionary game theory, on the other hand, it is assumed that players have limited knowledge of the game and only bounded rationality. Games in evolutionary game theory are repeated in rounds and players are a orded the opportunity to adapt and learn as this repetition occurs. Past studies have revealed that cooperation may be a viable strategy if the prisoner's dilemma is placed in an evolutionary context, where the evolutionary tness of a strategy is directly related to the pay-o achieved by the player adopting the strategy. One of the mechanisms that promote the persistence of cooperation in the evolutionary prisoner's dilemma is structured interaction between players. A mathematical framework for representing the evolutionary prisoner's dilemma (ESPD) is developed in this thesis. The mathematical framework is used to undertake an analytical approach (i.e. avoiding the use of simulation) towards investigating the dynamics of the ESPD with a path, cycle, plane grid or toroidal grid as underlying graph. The objective of this investigation is to determine the likelihood of the emergence of persistent cooperation between players. The ESPD on a path or a cycle admits two fundamentally di erent parameter regions; large values of the temptation-to-defect parameter are not capable of inducing persistent cooperation, while small values of this parameter allow for the possibility of persistent cooperation. It is found that the likelihood of cooperation increases towards certainty as the order of the underlying graph increases if the underlying graph is a path or cycle. The state space of the ESPD with a plane or toroidal grid graph as underlying graph grows very quickly as a function of the graph order. The automorphism classes of game states are enumerated to determine exactly how fast the size of the state space of the game grows as a function of the order of the underlying graph. Finally, the dynamics of the ESPD is investigated for a grid graph as underlying graph (in cases where the state space is small enough) by means of constructing the corresponding state graphs of the ESPD. / AFRIKAANSE OPSOMMING: Daar is baie voorbeelde van samewerking in the gemeenskap en in die natuur. In sommige gevalle lei samewerking tot 'n toename in die algehele welvaart van die betrokkenes, terwyl samewerking in ander gevalle tot nadeel van die bre er gemeenskap mag wees. Die voorkoms van samewerking blyk natuurlik te wees indien daar 'n direkte voordeel vir die individue is wat kies om saam te werk. In voorbeelde van samewerking is s o 'n voordeel egter nie altyd voor-diehand- liggend nie. Die sogenaamde prisoniersdilemma word dikwels as voorbeeld in die studie van samewerking gebruik om die faktore wat na samewerking lei, te ontbloot. In klassieke speleteorie word daar aangeneem dat elke speler rasioneel is en dus poog om sy spelstrategie op s o 'n manier te kies dat sy eie verwagte uitbetaling gemaksimeer word. In die geval van die klassieke prisoniersdilemma veroorsaak dit dat beide spelers mekaar verraai. In evolusion^ere speleteorie, daarenteen, word daar slegs aangeneem dat elke speler oor beperkte kennis van die spel en begrensde rasionaliteit beskik. Spele in evolusion^ere speleteorie word in rondtes herhaal en spelers word die geleentheid gebied om gedurende hierdie herhalingsproses aan te pas en te leer. Vorige studies het getoon dat samewerking 'n lewensvatbare strategie is indien die prisoniersdilemma in 'n evolusion^ere konteks gespeel word, waar die evolusion^ere ksheid van 'n strategie direk afhang van die uitbetaling van 'n speler wat die strategie volg. Een van die meganismes wat volhoubare samewerking in die evolusion^ere prisoniersdilemma voortbring, is gestruktureerde interaksie tussen spelers. 'n Wiskundige raamwerk word vir die voorstelling van die evolusion^ere prisoniersdilemma in hierdie tesis ontwikkel. Hierdie wiskundige raamwerk word gebruik om 'n analitiese studie (met ander woorde sonder die gebruik van simulasie) van die dinamika van die prisoniersdilemma op 'n pad, siklus, rooster in die vlak, of rooster op die torus as onderliggende gra ek van stapel te stuur. Die doel van hierdie studie is om die waarskynlikheid vir die ontstaan van volhoubare samewerking tussen spelers te bepaal. Die prisoniersdilemma op 'n pad of siklus as onderliggende gra ek het twee fundamenteel verskillende parametergebiede tot gevolg; groot waardes van die versoeking-om-te-verraai parameter lei nie tot volhoubare samewerking nie, terwyl volhoubare samewerking wel vir klein waardes van hierdie parameter moontlik is. Daar word gevind dat die kans vir volhoubare samewerking toeneem tot sekerheid namate die orde van die onderliggende gra ek groei. Die toestandsruimte van die prisoniersdilemma met 'n rooster in die vlak of 'n rooster op die torus as onderliggende gra ek groei baie vinnig as 'n funksie van die orde van die gra ek. Die outomor smeklasse van die speltoestande word getel met die doel om te bepaal presies hoe vinnig die toestandsruimte van die spel as 'n funksie van die orde van die onderliggende gra ek groei. Die dinamika van die prisoniersdilemma met 'n rooster in die vlak of 'n rooster op die torus as onderliggende gra ek word laastens deur middel van konstruksies van die ooreenstemmende toestandsgra eke ondersoek (in gevalle waar die toestandsruimte klein genoeg is).

本文主要探討存戶決策對銀行投資組合決策之影響，及其可能引發之系統性風險的程度。以代表性銀行開始分析，假設銀行投資於安全性資產與風險性資產，而存戶依其決策可能會產生兩個均衡同時存在之情形。本文利用演化的力量，發展出以風險性資產報酬率作為均衡選擇之標準：當風險性資產報酬率低於某一水準時，擠兌的均衡會單獨發生。並比較銀行考慮擠兌發生可能性時，其投資組合承擔風險之程度，及可能引發的銀行倒閉機率大小。推廣至二家模型，發現愈多家銀行在作投資決策考慮存戶擠兌之可能性，愈會增加經濟體系中之系統性風險，顯示銀行與存戶之衝突與金融體系之脆弱性。最後討論資本適足性管制與央行最後貸款人角色能否有效降低銀行倒閉機率。

Main weakness of economics of crime is that it focuses on rational offender who is isolated from society. This thesis gives overview of game theory models, which take into account possible reactions of other actors to offender`s actions. I show that some variables of crime are dependent on individual`s social environment and I analyze them using moral costs of crime, where some gains and losses from crime are interconnected between people. Two own models are presented. First model deals with aggregated crime with significant role of moral costs of crime. Second model is a modification of Inspection game which includes moral costs of crime and is than modeled using evolutionary game theory. Result of first model is higher volatility of crime than in standard models of rational offender. Crime is maximally volatile in time in the second model. There is a critical level of moral costs of crime and after reaching this level, assumptions of inspection game are violated and society converges to state with zero crime. It is demonstrated on both models that crime is a self- propagating phenomenon, because of social interactions.