Interdependent network reciprocity in evolutionary games

Besides the structure of interactions within networks, also the interactions between networks are of the outmost importance. We therefore study the outcome of the public goods game on two interdependent networks that are connected by means of a utility function, which determines how payoffs on both networks jointly influence the success of players in each individual network. We show that an unbiased coupling allows the spontaneous emergence of interdependent network reciprocity, which is capable to maintain healthy levels of public cooperation even in extremely adverse conditions. The mechanism, however, requires simultaneous formation of correlated cooperator clusters on both networks. If this does not emerge or if the coordination process is disturbed, network reciprocity fails, resulting in the total collapse of cooperation. Network interdependence can thus be exploited effectively to promote cooperation past the limits imposed by isolated networks, but only if the coordination between the interdependent networks is not disturbe

Win-stay-lose-learn promotes cooperation in the spatial prisoner's dilemma game

Holding on to one's strategy is natural and common if the later warrants success and satisfaction. This goes. against widespread simulation practices of evolutionary games, where players frequently consider changing their strategy even though their payoffs may be marginally different than those of the other players. Inspired by this observation, we introduce an aspiration-based win-stay-lose-learn strategy updating rule into the spatial prisoner's dilemma game. The rule is simple and intuitive, foreseeing strategy changes only by dissatisfied players, who then attempt to adopt the strategy of one of their nearest neighbors, while the strategies of satisfied players are not subject to change. We find that the proposed win-stay-lose-learn rule promote the evolution of cooperation, and it does so very robustly and independently of the initial conditions. I fact, we show that even a minute initial fraction of cooperators may be sufficient to eventually secure a higly cooperative final state. In addition to extensive simulation results that support our conclusions, we also present results obtained by means of the pair approximation of the studied game. Our findings continue the success story of related win-stay strategy updating rules, and by doing so reveal new ways of resolving the prisoner's dilemma

Simulating Evolutionary Games: A Python-Based Introduction

This paper is an introduction to agent-based simulation using the Python programming language. The core objective of the paper is to enable students, teachers, and researchers immediately to begin social-science simulation projects in a general purpose programming language. This objective is facilitated by design features of the Python programming language, which we very briefly discuss. The paper has a 'tutorial' component, in that it is enablement-focused and therefore strongly application-oriented. As our illustrative application, we choose a classic agent-based simulation model: the evolutionary iterated prisoner's dilemma. We show how to simulate the iterated prisoner's dilemma with code that is simple and readable yet flexible and easily extensible. Despite the simplicity of the code, it constitutes a useful and easily extended simulation toolkit. We offer three examples of this extensibility: we explore the classic result that topology matters for evolutionary outcomes, we show how player type evolution is affected by payoff cardinality, and we show that strategy evaluation procedures can affect strategy persistence. Social science students and instructors should find that this paper provides adequate background to immediately begin their own simulation projects. Social science researchers will additionally be able to compare the simplicity, readability, and extensibility of the Python code with comparable simulations in other languages.Agent-Based Simulation, Python, Prisoner's Dilemma

Leave and let leave: A sufficient condition to explain the evolutionary emergence of cooperation

The option to leave your current partner in response to his behavior, also known as conditional dissociation, is a mechanism that has been shown to promote the emergence and stability of cooperation in many social interactions. This mechanism, nevertheless, has always been studied in combination with other factors that are known to support cooperation by themselves. In this paper, we isolate the effect of conditional dissociation on the evolution of cooperation and show that this mechanism is enough to sustain a significant level of cooperation if the expected lifetime of individuals is sufficiently longACCESS (EU, 12-120610), SIMULPAST (MICINN, CSD2010-00034) and SPPORT (JCyL, VA056A12-2). L.R.I. Spanish Ministry of Education for grant JC2009-0026

Coevolution of risk aversion, trust and trustworthiness: an agent-based approach

The research presented here deals with the evolution of personality features of humans engaged in strategic interactions. The evolution of risk aversion and trustworthiness is modelled and simulated in the context of a binary trust game, seeking the origin and end-points of an evolutionary process, accounting for different degrees of locality. This research has employed computer simulations in order to get dynamic equilibria in populations of players that keep evolving. The locality or global nature of interaction plays an important role. Risk aversion evolves together with trust and trustworthiness. Trust behaviour follows reciprocation attributes. Results of the simulations are equal to the ones elicited in empirical studies

Game theoretic modeling and analysis : A co-evolutionary, agent-based approach

Ph.DDOCTOR OF PHILOSOPH

Public good games with incentives

Public good games dienen als Modell für den Konflikt zwischen Allgemeinwohl und individuellem Vorteil: Während der Erfolg eines gemeinschaftlichen Projekts oft vom Einsatz aller Beteiligten abhängt, kann für den Einzelnen der Anreiz zum Trittbrettfahren bestehen. In dieser Dissertation untersuche ich das Zusammenspiel von Kooperation und Anreizsystemen mit Hilfe der evolutionären Spieltheorie. Es wird gezeigt, dass Belohnungen zwar individuelle Kooperation anstoßen können, dass aber Bestrafungsmöglichkeiten notwendig sind um die Zusammenarbeit aufrechtzuerhalten. Dabei liefert die individuelle Reputation der Spieler einen Anreiz, die Einhaltung von Normen zu überwachen und Abweichungen zu sanktionieren. Im Gegensatz zu früheren Studien werden Bestrafungsmechanismen jedoch nicht zur Stabilisierung von beliebigen Normen und Verhaltensvorschriften verwendet. Stattdessen werden Sanktionen gezielt dazu eingesetzt um die soziale Wohlfahrt zu verbessern. In dieser Dissertation stelle ich auch einige mathematischeWerkzeuge und methodische Konzepte vor, die bei der Untersuchung von Public good games hilfreich sind. Dazu wird die Theorie der Rollenspiele erweitert und eine modifizierte Replikatorgleichung eingeführt. Unter dieser lokalen Replikatordynamik können sich selbst dominierte Strategien durchsetzen, falls diese zu einem relativen Vorteil führen.Public good games reflect the common conflict between group interest and self interest: While collaborative projects depend on joint efforts of all participants, each individual performs best by free-riding on the others’ contributions. In this thesis I use evolutionary game dynamics to study the interplay of cooperation and incentives. I demonstrate that rewards may act as a catalyst for individual contributions, while punishment is needed to maintain mutual cooperation. In this process, reputation plays a key role: It helps to mitigate the second-order free-rider problem and prevents subjects from being spiteful. In contrast to previous studies, I do not find that punishment can promote any behaviour (as long as deviations from that norm are punished). Instead, sanctions are targeted at noncooperators only, and lead to stable cooperation. Furthermore, this thesis provides some mathematical tools for the study of public good games with incentives. It extends the theory of role games and it introduces a modified replicator dynamcis that allows to investigate the consequences of local competition. Under this local replicator dynamics, even dominated strategies may prevail if they lead to a relative payoff advantage – which can be considered as a basic model for the evolution of spite

An investigation into cooperative behaviour : altruism and evolutionary computing

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Behaviour from an evolutionary point of view: experimental studies on fish and humans

Evolutionary theory based on natural selection states that individuals of a population vary in certain traits and pass these traits on to their offspring. Furthermore, individuals continuously compete with each other for limited resources, such as food items, mating partners, and territories. As a consequence, those individuals that feature traits enabling them to cope better with the current environmental conditions have an advantage in accessing and exploiting these resources and can, therefore, allocate more resources to reproduction. Thus, they will outcompete those individuals not having such advantageous traits and the respective traits will spread in the population. Disadvantageous traits will diminish. The result of evolution is ever better adapted organisms. However, there are many traits that do not seem to be advantageous to the individual, but they still have evolved. The present work focuses on two such phenomena that are disadvantageous and costly at the first sight: sexual reproduction and human cooperation. Sexual reproduction is disadvantageous, because only one half of the population can bear offspring. Furthermore, it is costly to the individual, because, among other things, individuals have to search for mates. It has been suggested that sexually reproducing organisms have an advantage due to a higher genetic recombination rate. Thus, they are supposed to have an increased ability to adapt to environmental changes. A potential source of such changes are parasites: Organisms potentially need to continuously develop better adapted immune defence (e.g., genes of the major histocompatibility complex, MHC) to successfully fight parasites. This exerts selection pressure on the parasites which have to adapt subsequently. The result is an arms race between host and parasites in which it would be advantageous for the host to achieve a high genetic recombination rate and, hence, a high adaptability by sexual reproduction. A crucial behaviour connected to sexual reproduction is mate choice, and the threespined stickleback is a perfectly suited model organism to investigate this behaviour in more detail. It is known that female sticklebacks base their mating decision on various visual and olfactory male cues, such as red breeding colouration (visual cue) and MHC peptides (olfactory cue). Adding on to previous work, Chapter 1 deals with seasonal variation of male olfactory attractiveness to female sticklebacks. Our results document that, besides the MHC signal, a further cue conveys information about potential mates; male olfactory attractiveness to females peaked in summer while the males maintained a nest. This finding suggests that males release special substances during nest maintenance that indicate male reproductive status to females. Evidently, female olfactory mate choice is not only based on the MHC signal, but on a combination of at least two cues. A second experiment (Chapter 2) examined the evolutionary consequences of mate choice in sticklebacks under semi-natural conditions. Thereby, the focus was on MHC-based mate choice, and actual matings were analysed in six enclosure facilities in the lake Großer Plöner See. The obtained results are consistent with previous studies that linked MHC genetics with fitness related traits, and show that individuals with an intermediate number of MHC variants ultimately achieve the highest reproductive output. Consequently, choosing the right mate bearing the best MHC genotype might confer the individual advantage needed to cope with an ever changing environment of parasites. This finding is in line with the hypothesis that parasite pressure is a potential cause of the evolution and maintenance of sexual reproduction. Another seemingly paradoxical phenomenon for evolutionary biologists is the evolution and maintenance of cooperation. Cooperation describes behaviour that is beneficial for another individual, but costly for the cooperator. Thus, a cooperator is someone who invests his own resources in order to help others. Evidently, a defector (i.e., someone who does not cooperate) does not bear the costs of cooperation and, therefore, has more resources to himself. But why is cooperative behaviour so abundant if it is costly? This is especially puzzling in the case of humans which tend to cooperate even with unrelated individuals in one-shot encounters. In general, university students played computer-based games that served as experimental setup for the research presented in the second part of this thesis. Analysing the participants’ behaviour provided further insight into the phenomenon of human cooperation. A first study (Chapter 3) has elucidated whether the evolved strategies also enable humans to solve modern social dilemmas. Thereby, we focused in Chapter 3 on a global dilemma that we characterised as a collective-risk social dilemma: the prevention of dangerous climate change. To reduce the risk of dangerous climate change, greenhouse gas emissions need to be reduced to ~50% of the present level by 2050. Thus, states, companies, but also private individuals need to invest in environmentally friendly technologies and practices. In order to reduce greenhouse gas emissions down to a certain threshold, we need to invest in climate protection up to a certain threshold. Otherwise we will face substantial human, ecological, and economic losses. This scenario was simulated in an experimental game with 30 groups of six students each. The participants’ investments in climate protection had to reach a known threshold to prevent dangerous climate change. Participants only reached this threshold if the risk of personal loss was high. Thus, we conclude that humans are able to solve the real climate dilemma if they are convinced about the extreme risk of losses. Further experiments on cooperation (Chapters 4 and 5) are based on the finding that humans tend to direct their help towards people that have previously helped others. This so called indirect reciprocity can explain high levels of cooperation and is based on the reputation of the other person. But how do people get to know the reputation of others? Evidently, we cannot observe all the people we possibly interact with during our entire life, therefore various scientists proposed gossip as a possible means of spreading and gathering this information. In this thesis, this proposed function of gossip has been investigated experimentally. The first study in this context (Chapter 4) has shown that gossip indeed can serve as a vector for social, reputation-relevant information. Participants described the observed behaviour of others truthfully; this gossip was perceived as positive or negative in accordance with the author’s intention; and, last, participants reacted on positive gossip with cooperative behaviour, and on negative gossip with defection towards the person who was described by that gossip. Yet, gossip also seems to have a strong manipulative potential; people’s decisions were influenced by gossip designed by the experimenter even if they knew hard facts (i.e., past behaviour) about the other person. In a follow-up study (Chapter 5), this effect was examined in more detail. The effect of multiple gossip statements was examined with respect to elicited cooperation from the people encountering them. The participants’ response was compared to the same people’s response based on a single gossip statement or direct observation. The results indicate that an increased number of gossip statements helps to reduce the risk of manipulation and to direct cooperative behaviour towards cooperators. Furthermore, this study suggests a strong connection between reputation, reciprocity, and trust: Participants who gained a high reputation through reciprocating were also perceived as more trustworthy. This connection might have fostered cooperative behaviour up to the present level in modern human societies. These findings support the hypothesis that gossip and, hence, the use of language, is connected to the high level of human cooperation.Summary__________________________________________________________________ 7 Zusammenfassung _________________________________________________________ 10 Introduction ______________________________________________________________ 13 Sexual reproduction ____________________________________________________________ 14 Human Cooperation ____________________________________________________________ 17 Outline __________________________________________________________________ 21 Mate choice in the three-spined stickleback __________________________________________ 21 Human cooperation_____________________________________________________________ 22 Chapter 1 Seasonal Variation of Male Attractiveness in Sticklebacks ________________ 24 Abstract______________________________________________________________________ 24 Introduction___________________________________________________________________ 25 Materials and Methods __________________________________________________________ 26 Results_______________________________________________________________________ 28 Discussion____________________________________________________________________ 30 Acknowledgements_____________________________________________________________ 31 Chapter 2 Lifetime Reproductive Success and the MHC __________________________ 32 Abstract______________________________________________________________________ 32 Introduction___________________________________________________________________ 33 Material and methods ___________________________________________________________ 34 Results_______________________________________________________________________ 37 Discussion____________________________________________________________________ 41 Acknowledgments______________________________________________________________ 43 Chapter 3 Preventing Dangerous Climate Change: a Collective-Risk Social Dilemma __ 44 Abstract______________________________________________________________________ 44 Introduction___________________________________________________________________ 45 Results and Discussion __________________________________________________________ 47 Methods______________________________________________________________________ 51 Acknowledgements_____________________________________________________________ 51 Chapter 4 Gossip as an Alternative for Direct Observation ________________________ 52 Abstract______________________________________________________________________ 52 Introduction___________________________________________________________________ 53 Results_______________________________________________________________________ 55 Discussion____________________________________________________________________ 59 Materials and Methods __________________________________________________________ 61 Acknowledgements_____________________________________________________________ 63 Chapter 5 Multiple Gossip Statements, Reputation, and Trust ______________________ 64 Abstract______________________________________________________________________ 64 Introduction___________________________________________________________________ 65 Materials and Methods __________________________________________________________ 66 Results_______________________________________________________________________ 68 Discussion____________________________________________________________________ 72 Acknowledgements_____________________________________________________________ 75 Conclusion _______________________________________________________________ 76 Acknowledgements _________________________________________________________ 78 References________________________________________________________________ 80 Appendix A ______________________________________________________________ 104 Appendix B ______________________________________________________________ 106 Appendix C ______________________________________________________________ 111 Appendix D ______________________________________________________________ 122 Appendix E ______________________________________________________________ 128 Curriculum vitae__________________________________________________________ 13

Behaviour from an evolutionary point of view: experimental studies on fish and humans

Evolutionary theory based on natural selection states that individuals of a population vary in certain traits and pass these traits on to their offspring. Furthermore, individuals continuously compete with each other for limited resources, such as food items, mating partners, and territories. As a consequence, those individuals that feature traits enabling them to cope better with the current environmental conditions have an advantage in accessing and exploiting these resources and can, therefore, allocate more resources to reproduction. Thus, they will outcompete those individuals not having such advantageous traits and the respective traits will spread in the population. Disadvantageous traits will diminish. The result of evolution is ever better adapted organisms. However, there are many traits that do not seem to be advantageous to the individual, but they still have evolved. The present work focuses on two such phenomena that are disadvantageous and costly at the first sight: sexual reproduction and human cooperation. Sexual reproduction is disadvantageous, because only one half of the population can bear offspring. Furthermore, it is costly to the individual, because, among other things, individuals have to search for mates. It has been suggested that sexually reproducing organisms have an advantage due to a higher genetic recombination rate. Thus, they are supposed to have an increased ability to adapt to environmental changes. A potential source of such changes are parasites: Organisms potentially need to continuously develop better adapted immune defence (e.g., genes of the major histocompatibility complex, MHC) to successfully fight parasites. This exerts selection pressure on the parasites which have to adapt subsequently. The result is an arms race between host and parasites in which it would be advantageous for the host to achieve a high genetic recombination rate and, hence, a high adaptability by sexual reproduction. A crucial behaviour connected to sexual reproduction is mate choice, and the threespined stickleback is a perfectly suited model organism to investigate this behaviour in more detail. It is known that female sticklebacks base their mating decision on various visual and olfactory male cues, such as red breeding colouration (visual cue) and MHC peptides (olfactory cue). Adding on to previous work, Chapter 1 deals with seasonal variation of male olfactory attractiveness to female sticklebacks. Our results document that, besides the MHC signal, a further cue conveys information about potential mates; male olfactory attractiveness to females peaked in summer while the males maintained a nest. This finding suggests that males release special substances during nest maintenance that indicate male reproductive status to females. Evidently, female olfactory mate choice is not only based on the MHC signal, but on a combination of at least two cues. A second experiment (Chapter 2) examined the evolutionary consequences of mate choice in sticklebacks under semi-natural conditions. Thereby, the focus was on MHC-based mate choice, and actual matings were analysed in six enclosure facilities in the lake Großer Plöner See. The obtained results are consistent with previous studies that linked MHC genetics with fitness related traits, and show that individuals with an intermediate number of MHC variants ultimately achieve the highest reproductive output. Consequently, choosing the right mate bearing the best MHC genotype might confer the individual advantage needed to cope with an ever changing environment of parasites. This finding is in line with the hypothesis that parasite pressure is a potential cause of the evolution and maintenance of sexual reproduction. Another seemingly paradoxical phenomenon for evolutionary biologists is the evolution and maintenance of cooperation. Cooperation describes behaviour that is beneficial for another individual, but costly for the cooperator. Thus, a cooperator is someone who invests his own resources in order to help others. Evidently, a defector (i.e., someone who does not cooperate) does not bear the costs of cooperation and, therefore, has more resources to himself. But why is cooperative behaviour so abundant if it is costly? This is especially puzzling in the case of humans which tend to cooperate even with unrelated individuals in one-shot encounters. In general, university students played computer-based games that served as experimental setup for the research presented in the second part of this thesis. Analysing the participants’ behaviour provided further insight into the phenomenon of human cooperation. A first study (Chapter 3) has elucidated whether the evolved strategies also enable humans to solve modern social dilemmas. Thereby, we focused in Chapter 3 on a global dilemma that we characterised as a collective-risk social dilemma: the prevention of dangerous climate change. To reduce the risk of dangerous climate change, greenhouse gas emissions need to be reduced to ~50% of the present level by 2050. Thus, states, companies, but also private individuals need to invest in environmentally friendly technologies and practices. In order to reduce greenhouse gas emissions down to a certain threshold, we need to invest in climate protection up to a certain threshold. Otherwise we will face substantial human, ecological, and economic losses. This scenario was simulated in an experimental game with 30 groups of six students each. The participants’ investments in climate protection had to reach a known threshold to prevent dangerous climate change. Participants only reached this threshold if the risk of personal loss was high. Thus, we conclude that humans are able to solve the real climate dilemma if they are convinced about the extreme risk of losses. Further experiments on cooperation (Chapters 4 and 5) are based on the finding that humans tend to direct their help towards people that have previously helped others. This so called indirect reciprocity can explain high levels of cooperation and is based on the reputation of the other person. But how do people get to know the reputation of others? Evidently, we cannot observe all the people we possibly interact with during our entire life, therefore various scientists proposed gossip as a possible means of spreading and gathering this information. In this thesis, this proposed function of gossip has been investigated experimentally. The first study in this context (Chapter 4) has shown that gossip indeed can serve as a vector for social, reputation-relevant information. Participants described the observed behaviour of others truthfully; this gossip was perceived as positive or negative in accordance with the author’s intention; and, last, participants reacted on positive gossip with cooperative behaviour, and on negative gossip with defection towards the person who was described by that gossip. Yet, gossip also seems to have a strong manipulative potential; people’s decisions were influenced by gossip designed by the experimenter even if they knew hard facts (i.e., past behaviour) about the other person. In a follow-up study (Chapter 5), this effect was examined in more detail. The effect of multiple gossip statements was examined with respect to elicited cooperation from the people encountering them. The participants’ response was compared to the same people’s response based on a single gossip statement or direct observation. The results indicate that an increased number of gossip statements helps to reduce the risk of manipulation and to direct cooperative behaviour towards cooperators. Furthermore, this study suggests a strong connection between reputation, reciprocity, and trust: Participants who gained a high reputation through reciprocating were also perceived as more trustworthy. This connection might have fostered cooperative behaviour up to the present level in modern human societies. These findings support the hypothesis that gossip and, hence, the use of language, is connected to the high level of human cooperation.Summary__________________________________________________________________ 7 Zusammenfassung _________________________________________________________ 10 Introduction ______________________________________________________________ 13 Sexual reproduction ____________________________________________________________ 14 Human Cooperation ____________________________________________________________ 17 Outline __________________________________________________________________ 21 Mate choice in the three-spined stickleback __________________________________________ 21 Human cooperation_____________________________________________________________ 22 Chapter 1 Seasonal Variation of Male Attractiveness in Sticklebacks ________________ 24 Abstract______________________________________________________________________ 24 Introduction___________________________________________________________________ 25 Materials and Methods __________________________________________________________ 26 Results_______________________________________________________________________ 28 Discussion____________________________________________________________________ 30 Acknowledgements_____________________________________________________________ 31 Chapter 2 Lifetime Reproductive Success and the MHC __________________________ 32 Abstract______________________________________________________________________ 32 Introduction___________________________________________________________________ 33 Material and methods ___________________________________________________________ 34 Results_______________________________________________________________________ 37 Discussion____________________________________________________________________ 41 Acknowledgments______________________________________________________________ 43 Chapter 3 Preventing Dangerous Climate Change: a Collective-Risk Social Dilemma __ 44 Abstract______________________________________________________________________ 44 Introduction___________________________________________________________________ 45 Results and Discussion __________________________________________________________ 47 Methods______________________________________________________________________ 51 Acknowledgements_____________________________________________________________ 51 Chapter 4 Gossip as an Alternative for Direct Observation ________________________ 52 Abstract______________________________________________________________________ 52 Introduction___________________________________________________________________ 53 Results_______________________________________________________________________ 55 Discussion____________________________________________________________________ 59 Materials and Methods __________________________________________________________ 61 Acknowledgements_____________________________________________________________ 63 Chapter 5 Multiple Gossip Statements, Reputation, and Trust ______________________ 64 Abstract______________________________________________________________________ 64 Introduction___________________________________________________________________ 65 Materials and Methods __________________________________________________________ 66 Results_______________________________________________________________________ 68 Discussion____________________________________________________________________ 72 Acknowledgements_____________________________________________________________ 75 Conclusion _______________________________________________________________ 76 Acknowledgements _________________________________________________________ 78 References________________________________________________________________ 80 Appendix A ______________________________________________________________ 104 Appendix B ______________________________________________________________ 106 Appendix C ______________________________________________________________ 111 Appendix D ______________________________________________________________ 122 Appendix E ______________________________________________________________ 128 Curriculum vitae__________________________________________________________ 13