Asymptotic Behavior of Strategies in the Repeated Prisoner's Dilemma Game in the Presence of Errors

We examine the asymptotic behavior of a finite, but error-prone population, whose agents can choose one of ALLD (always defect), ALLC (always cooperate), or Pavlov (repeats the previous action if the opponent cooperated and changes action otherwise) to play the repeated Prisoner's Dilemma. A novelty of the study is that it allows for three types of errors that affect agents' strategies in distinct ways: (a) implementation errors, (b) perception errors of one's own action, and (c) perception errors of the opponent's action. We also derive numerical results based on the payoff matrix used in the tournaments of Axelrod (1984). Strategies' payoffs are monitored as the likelihood of committing errors increases from zero to one, which enables us to provide a taxonomy of best response strategies. We find that for some range of error levels, a unique best response (i.e. a dominant strategy) exists. In all other, the population composition can vary based on the proportion of each strategist's type and/or the payoffs of the matrix. Overall, our results indicate that the emergence of cooperation is considerably weak at most error levels

Reinforcement Learning Dynamics in Social Dilemmas

In this paper we replicate and advance Macy and Flache\'s (2002; Proc. Natl. Acad. Sci. USA, 99, 7229–7236) work on the dynamics of reinforcement learning in 2�2 (2-player 2-strategy) social dilemmas. In particular, we provide further insight into the solution concepts that they describe, illustrate some recent analytical results on the dynamics of their model, and discuss the robustness of such results to occasional mistakes made by players in choosing their actions (i.e. trembling hands). It is shown here that the dynamics of their model are strongly dependent on the speed at which players learn. With high learning rates the system quickly reaches its asymptotic behaviour; on the other hand, when learning rates are low, two distinctively different transient regimes can be clearly observed. It is shown that the inclusion of small quantities of randomness in players\' decisions can change the dynamics of the model dramatically.Reinforcement Learning; Replication; Game Theory; Social Dilemmas; Agent-Based; Slow Learning

Evolutionary Games in Complex Topologies: Interplay between Structure and Dynamics

En este estudio exploramos la interrelación entre la estructura subyacente de una cierta población de individuos y el resultado de la dinámica que está teniendo lugar en ella, específicamente, el Dilema del Prisionero. En la primera parte de este trabajo analizamos el caso de una topología estática, en la que la red de conexiones no cambia en el tiempo. En la segunda parte, desarrollamos dos modelos para crecer redes, donde dicho crecimiento esta íntimamente relacionado con la dinámica

The Evolution of Cooperation in Spatially Heterogeneous Populations

A challenging problem in sociobiology is to understand the emergence of cooperation in a nonsocial world. Recent models of the iterated Prisoner's Dilemma (IPD) game conclude that population mixing due to individual mobility limits cooperation; however, these models represent space only implicitly. Here we develop a dynamical IPD model where temporal and spatial variations in the population are explicitly considered. Our model accounts for the stochastic motion of individuals and the inherent nonrandomness of local interactions. By deriving a spatial version of Hamilton's rule, we find that a threshold level of mobility in selfish always-defect (AD) players is required to beget invasion by social 'tit for tat'(TFT) players. Furthermore, the level of mobility of successful TFT newcomers must be approximately equal to or somewhat higher than that of resident defectors. Significant mobility promotes the assortment of TFT pioneers on the front of invasion and of AD intruders in the core of a cooperative cluster. It also maximizes the likelihood of TFT retaliation. Once this first step whereby TFT takes over AD is completed, more generous and perhaps more suspicious strategies may outperform and displace TFT. We derive the conditions under which this continued evolution of more robust cooperative strategies occurs

Co-evolution of strategies and update rules in the prisoner's dilemma game on complex networks

In this paper, we study a weak prisoner’s dilemma (PD) game in which both strategies and update rules are subjected to evolutionary pressure. Interactions among agents are specified by complex topologies, and we consider both homogeneous and heterogeneous situations. We consider deterministic and stochastic update rules for the strategies, which in turn may consider single links or the full context when selecting agents to copy from. Our results indicate that the co-evolutionary process preserves heterogeneous networks as a suitable framework for the emergence of cooperation. Furthermore, on those networks the update rule leading to a larger fraction, which we call replicator dynamics, is selected during co-evolution. On homogeneous networks, we observe that even if the replicator dynamics again turns out to be the selected update rule, the cooperation level is greater than on a fixed update rule framework. We conclude that for a variety of topologies, the fact that the dynamics co-evolves with the strategies leads, in general, to more cooperation in the weak PD game.Publicad

Religion and Economic Growth: Was Weber Right?

Evidence of falling wages in Catholic cities and rising wages in Protestant cities between 1500 and 1750, during the spread of literacy in the vernacular, is inconsistent with most theoretical models of economic growth. In The Protestant Ethic, Weber suggested an alternative explanation based on culture. Here, a theoretical model confirms that a small change in the subjective cost of cooperating with strangers can generate a profound transformation in trading networks. In explaining urban growth in early-modern Europe, specifications compatible with human-capital versions of the neoclassical model and endogenous-growth theory are rejected in favor of a “small-world” formulation based on the Weber thesis.L’évidence que les salaires réels ont diminué dans les villes catholiques et non dans les villes protestantes entre 1500 et 1750, période d’extension de l’alphabétisation dans le vernaculaire, contredit la plupart des modèles théoriques de croissance économique. Dans L’éthique protestante, Weber a suggéré une théorie alternative basée sur la culture. Ici un modèle théorique confirme qu’un petit changement dans le coût subjectif de coopérer avec des étrangers peut générer une transformation profonde des réseaux d’échange. Lors d’une tentative d’expliquer la croissance urbaine en Europe pré-industrielle, des spécifications compatibles avec la théorie néoclassique et avec la théorie de la croissance endogène sont rejetées en faveur d’une formulation de la thèse de Weber qui incorpore des effets de réseau

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

Abstract and lifelike experimental games

The theory of games seems to me to provide the most promising alternative to the traditional theories of social behaviour. Gaming modelS are inherently social in character (an individual's strategy choice in a game cannot even be properly defined without reference to at least one other individual) and they represent a radical departure from the "social stimulus - individual response" approach. They sean, furthermore, to be the only models which can adequately conceptualize an important (and large) class of social behaviours which arise from deliberate free choice. (From preface

The Current State of Normative Agent-Based Systems

Recent years have seen an increase in the application of ideas from the social sciences to computational systems. Nowhere has this been more pronounced than in the domain of multiagent systems. Because multiagent systems are composed of multiple individual agents interacting with each other many parallels can be drawn to human and animal societies. One of the main challenges currently faced in multiagent systems research is that of social control. In particular, how can open multiagent systems be configured and organized given their constantly changing structure? One leading solution is to employ the use of social norms. In human societies, social norms are essential to regulation, coordination, and cooperation. The current trend of thinking is that these same principles can be applied to agent societies, of which multiagent systems are one type. In this article, we provide an introduction to and present a holistic viewpoint of the state of normative computing (computational solutions that employ ideas based on social norms.) To accomplish this, we (1) introduce social norms and their application to agent-based systems; (2) identify and describe a normative process abstracted from the existing research; and (3) discuss future directions for research in normative multiagent computing. The intent of this paper is to introduce new researchers to the ideas that underlie normative computing and survey the existing state of the art, as well as provide direction for future research.Norms, Normative Agents, Agents, Agent-Based System, Agent-Based Simulation, Agent-Based Modeling