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- Biblioteca Digitais de Teses e Dissertações da USP
- The National Academy of Sciences
- Public Library of Science
- Springer
- Elsevier
- The Royal Society
- Journal of Artificial Societies and Social Simulation
- Escola de Pós-Graduação Naval
- Center for Applied Economics and Policy Research
- Instituto Universitário Europeu
- Elsevier Science BV
- Université de Montréal
- Evolutionary Ecology
- Sociedade Brasileira de Física
- Wiley-Blackwell
- Nature Publishing Group
- Universidade Cornell
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## ‣ Dilema do prisioneiro contínuo com agentes racionais e classificadores de cooperação; Continuous prisoners dilemma with rational agents and cooperation classifiers.

Fonte: Biblioteca Digitais de Teses e Dissertações da USP
Publicador: Biblioteca Digitais de Teses e Dissertações da USP

Tipo: Tese de Doutorado
Formato: application/pdf

Publicado em 23/11/2012
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#aversão ao risco#cluster entropy#coeficiente de Gini#continuous prisoners dilemma#cooperação#cooperation#darwinian strategy#dilema do prisioneiro#dilema do prisioneiro contínuo#econofísica.#econophysics.

O dilema do prisioneiro (DP) é um dos principais jogos da teoria dos jogos. No dilema do prisioneiro discreto (DPD), dois prisioneiros têm as opções de cooperar ou desertar. Um jogador cooperador não delata seu comparsa, já um desertor delata. Se um cooperar e o outro desertar, o cooperador fica preso por cinco anos e o desertor fica livre. Se ambos cooperarem, ficam presos por um ano e, se ambos desertarem, ficam presos por três anos. Quando o DP é repetido, a cooperação pode emergir entre agentes egoístas. Realizamos um estudo analítico para o DPD, que produziu uma formulação da evolução do nível médio de cooperação e da tentação crítica (valor de tentação que causa mudança abrupta do nível de cooperação). No dilema do prisioneiro contínuo (DPC), cada jogador apresenta um nível de cooperação que define o grau de cooperação. Utilizamos o DPC para estudar o efeito da personalidade dos jogadores sobre a emergência da cooperação. Para isso, propusemos novas estratégias: uma baseada na personalidade dos jogadores e outras duas baseadas na comparação entre o ganho obtido e a aspiração do jogador. Todas as estratégias apresentavam algum mecanismo de cópia do estado do vizinho com maior ganho na vizinhança...

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## ‣ Working memory constrains human cooperation in the Prisoner’s Dilemma

Fonte: The National Academy of Sciences
Publicador: The National Academy of Sciences

Tipo: Artigo de Revista Científica

Publicado em 10/11/1998
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Many problems in human society reflect the inability of selfish parties to cooperate. The “Iterated Prisoner’s Dilemma” has been used widely as a model for the evolution of cooperation in societies. Axelrod’s computer tournaments and the extensive simulations of evolution by Nowak and Sigmund and others have shown that natural selection can favor cooperative strategies in the Prisoner’s Dilemma. Rigorous empirical tests, however, lag behind the progress made by theorists. Clear predictions differ depending on the players’ capacity to remember previous rounds of the game. To test whether humans use the kind of cooperative strategies predicted, we asked students to play the iterated Prisoner’s Dilemma game either continuously or interrupted after each round by a secondary memory task (i.e., playing the game “Memory”) that constrained the students’ working-memory capacity. When playing without interruption, most students used “Pavlovian” strategies, as predicted, for greater memory capacity, and the rest used “generous tit-for-tat” strategies. The proportion of generous tit-for-tat strategies increased when games of Memory interfered with the subjects’ working memory, as predicted. Students who continued to use complex Pavlovian strategies were less successful in the Memory game...

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## ‣ Emergence of Super Cooperation of Prisoner’s Dilemma Games on Scale-Free Networks

Fonte: Public Library of Science
Publicador: Public Library of Science

Tipo: Artigo de Revista Científica

Publicado em 02/02/2015
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Recently, the authors proposed a quantum prisoner’s dilemma game based on the spatial game of Nowak and May, and showed that the game can be played classically. By using this idea, we proposed three generalized prisoner’s dilemma (GPD, for short) games based on the weak Prisoner’s dilemma game, the full prisoner’s dilemma game and the normalized Prisoner’s dilemma game, written by GPDW, GPDF and GPDN respectively. Our games consist of two players, each of which has three strategies: cooperator (C), defector (D) and super cooperator (denoted by Q), and have a parameter γ to measure the entangled relationship between the two players. We found that our generalised prisoner’s dilemma games have new Nash equilibrium principles, that entanglement is the principle of emergence and convergence (i.e., guaranteed emergence) of super cooperation in evolutions of our generalised prisoner’s dilemma games on scale-free networks, that entanglement provides a threshold for a phase transition of super cooperation in evolutions of our generalised prisoner’s dilemma games on scale-free networks, that the role of heterogeneity of the scale-free networks in cooperations and super cooperations is very limited, and that well-defined structures of scale-free networks allow coexistence of cooperators and super cooperators in the evolutions of the weak version of our generalised prisoner’s dilemma games.

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## ‣ The shared reward dilemma on structured populations

Fonte: Springer
Publicador: Springer

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em /11/2009
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#Emergence of cooperation#Prisoner’s dilemma#Shared reward dilemma#Structured population#Evolutionary games#Matemáticas

In this paper we study the recently introduced “shared reward dilemma” (Cuesta et al. in J Theor Biol 251:253–263, 2008, http://e-archivo.uc3m.es/handle/10016/7199) in the presence of a structure governing the interactions among the population. The shared reward dilemma arises when the prisoner’s dilemma is supplemented with a second stage in which a fixed reward is equally distributed among all cooperators. We first extend our previous results on the equilibrium structure of this game to the case of a one-shot game taking place on a regular network. Subsequently, we consider an evolutionary version of the game on both lattices and random networks. We show that the evolutionary game on graphs exhibits important differences with the case of well-mixed populations. In particular, there exists an important parameter range in which the cooperation is boosted and a single cooperator can invade a population of defectors. We study the dependence of the cooperation levels on the neighborhood size, finding that on random networks the level of cooperation reached decreases as the neighborhood size increases. Moreover, square lattices favor cooperation more than random networks, and on them cooperation may be almost full for certain parameter regions even for large neighborhood sizes. Further...

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## ‣ Evolving leraning rules and emergence of cooperation in spatial prisioner´s dilemma

Fonte: Elsevier
Publicador: Elsevier

Tipo: info:eu-repo/semantics/acceptedVersion; info:eu-repo/semantics/article
Formato: application/pdf

Publicado em 07/07/2009
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In the evolutionary Prisoner’s dilemma (PD) game, agent splay with each other and update their strategies in every generation according to some microscopic dynamical rule. Inits spatial version,
agents do not play with every other but, instead, interactonly with their neighbours, thus mimicking the existing of a social orcontactnetwork that defines who interacts with whom. In this work, we
explore evolutionary, spatial PD systems consisting of two types of agents, each with a certain update (reproduction, learning) rule. We investigate two different scenarios: in the first case, update rules
remain fixed for theen tire evolution of the system; in the second case, agents update both strategy and
update rule in every generation. We show that in a well mixed population the evolutionary out come is
always full defection. We subsequently focus on two strategy competition with nearest neighbour interactions on the contact network and synchronised update of strategies. Our results show that, for an
important range of the parameter sof the game, the final state of the system is largely different from that a rising from the usual setup of a single, fixed dynamical rule. Furthermore, the results are also very
different if update rules are fixed or evolve with the strategies. In these respect...

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## ‣ On the coexistence of cooperators, defectors and conditional cooperators in the multiplayer iterated Prisoner's dilemma

Fonte: Elsevier
Publicador: Elsevier

Tipo: info:eu-repo/semantics/submittedVersion; info:eu-repo/semantics/article

Publicado em 07/05/2012
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Recent experimental evidence [Grujić Fosco, Araujo, Cuesta, Sánchez, 2010. Social experiments in the mesoscale: humans playing a spatial Prisoner's dilemma. PLoS ONE 5, e13749] on the spatial Prisoner's Dilemma suggests that players choosing to cooperate or not on the basis of their previous action and the actions of their neighbors coexist with steady defectors and cooperators. We here study the coexistence of these three strategies in the multiplayer iterated Prisoner's Dilemma by means of the replicator dynamics. We consider groups with n=2, 3, 4 and 5 players and compute the payoffs to every type of player as the limit of a Markov chain where the transition probabilities between actions are found from the corresponding strategies. We show that for group sizes up to n=4 there exists an interior point in which the three strategies coexist, the corresponding basin of attraction decreasing with increasing number of players, whereas we have not been able to locate such a point for n =5. We analytically show that in the limit n→∞n→∞ no interior points can arise. We conclude by discussing the implications of this theoretical approach on the behavior observed in experiments.; This work was supported in part by MICINN (Spain) through grants PRODIEVO and MOSAICO...

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## ‣ Learning dynamics explains human behavior in Prisoner's Dilemma on networks

Fonte: The Royal Society
Publicador: The Royal Society

Tipo: info:eu-repo/semantics/acceptedVersion; info:eu-repo/semantics/article; info:eu-repo/semantics/conferenceObject

Publicado em 31/03/2014
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#Evolutionary game theory#Prisoner's dilemma#Social networks#Moody conditional cooperation#Reinforcement learning#Física#Matemáticas

Cooperative behavior lies at the very basis of human societies, yet its evolutionary origin remains a key unsolved puzzle. Whereas reciprocity or conditional cooperation is one of the most prominent mechanisms proposed to explain the emergence of cooperation in social dilemmas, recent experimental findings on networked Prisoner's Dilemma games suggest that conditional cooperation also depends on the previous action of the player—namely on the 'mood' in which the player currently is. Roughly, a majority of people behave as conditional cooperators if they cooperated in the past, while they ignore the context and free-ride with high probability if they did not. However, the ultimate origin of this behavior represents a conundrum itself. Here we aim specifically at providing an evolutionary explanation of moody conditional cooperation. To this end, we perform an extensive analysis of different evolutionary dynamics for players' behavioral traits—ranging from standard processes used in game theory based on payoff comparison to others that include non-economic or social factors. Our results show that only a dynamic built upon reinforcement learning is able to give rise to evolutionarily stable moody conditional cooperation, and at the end to reproduce the human behaviors observed in the experiments.; This work was supported by the Swiss Natural Science Fundation through grant PBFRP2_145872...

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## ‣ How Evolutionary Dynamics Affects Network Reciprocity in Prisoner's Dilemma

Fonte: Journal of Artificial Societies and Social Simulation
Publicador: Journal of Artificial Societies and Social Simulation

Tipo: info:eu-repo/semantics/publishedVersion; info:eu-repo/semantics/article

Publicado em 31/03/2015
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Cooperation lies at the foundations of human societies, yet why people cooperate remains a conundrum. The issue, known as network reciprocity, of whether population structure can foster cooperative behavior in social dilemmas has been addressed by many, but theoretical studies have yielded contradictory results so far—as the problem is very sensitive to how players adapt their strategy. However, recent experiments with the prisoner's dilemma game played on different networks and in a specific range of payoffs suggest that humans, at least for those experimental setups, do not consider neighbors' payoffs when making their decisions, and that the network structure does not influence the final outcome. In this work we carry out an extensive analysis of different evolutionary dynamics, taking into account most of the alternatives that have been proposed so far to implement players' strategy updating process. In this manner we show that the absence of network reciprocity is a general feature of the dynamics (among those we consider) that do not take neighbors' payoffs into account. Our results, together with experimental evidence, hint at how to properly model real people's behavior; This work was supported by the Swiss Natural Science Foundation through grant PBFRP2_145872 and by Ministerio de Economía y Competitividad (Spain) through grant PRODIEVO.

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## ‣ The shared reward dilemma

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artigo de Revista Científica
Formato: application/pdf

Publicado em 21/03/2008
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#Reward#Social dilemma#Prisoner's dilemma#n-Player game#Cooperation#Evolutionary dynamics#Nash equilibria#Matemáticas

One of the most direct human mechanisms of promoting cooperation is rewarding it. We study the effect of sharing a reward among cooperators in the most stringent form of social dilemma, namely the prisoner's dilemma (PD). Specifically, for a group of players that collect payoffs by playing a pairwise PD game with their partners, we consider an external entity that distributes a fixed reward equally among all cooperators. Thus, individuals confront a new dilemma: on the one hand, they may be inclined to choose the shared reward despite the possibility of being exploited by defectors; on the other hand, if too many players do that, cooperators will obtain a poor reward and defectors will outperform them. By appropriately tuning the amount to be shared a vast variety of scenarios arises, including the traditional ones in the study of cooperation as well as more complex situations where unexpected behavior can occur. We provide a complete classification of the equilibria of the n-player game as well as of its evolutionary dynamics.; This work is partially supported by Ministerio de Educación y Ciencia (Spain) under Grants Ingenio-MATHEMATICA, MOSAICO, and NAN2004-9087-C03-03 and by Comunidad de Madrid (Spain) under Grants SIMUMAT-CM and MOSSNOHO-CM.; 11 pages...

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## ‣ Prisoner's Dilemma

Fonte: Escola de Pós-Graduação Naval
Publicador: Escola de Pós-Graduação Naval

Tipo: game

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This simple game illustrates the principles of the Prisoner's dilemma. The student's goal is to accumulate the highest payoff possible.; OA3304; Decision Theory

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## ‣ Asymmetric Payoffs in Simultaneous and Sequential Prisoner's Dilemma Games

Fonte: Center for Applied Economics and Policy Research
Publicador: Center for Applied Economics and Policy Research

Tipo: Trabalho em Andamento
Formato: 274572 bytes; application/pdf

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#CAEPR#Center for Applied Economics and Policy Research#cooperation#prisoner’s dilemma#heterogeneity#exit option

We investigate the role of payoff asymmetry in laboratory prisoner’s dilemma games. Symmetric and Asymmetric games are examined in simultaneous and sequential settings. In the
asymmetric/sequential games, we study the impact of having payoff advantaged players moving
either first or second. Asymmetry reduces the rates of cooperation in simultaneous games. In
sequential games, asymmetry interacts with order of play such that the rate of cooperation is highest when payoff disadvantaged players move first. The presence of an exit option increases cooperation by the players who choose to play the game when payoffs are symmetric, or when payoffs are asymmetric and the payoff disadvantaged player moves first.

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## ‣ Habit, prisoner’s dilemma and Americans' welfare cost of working much more than Europeans

Fonte: Instituto Universitário Europeu
Publicador: Instituto Universitário Europeu

Tipo: Trabalho em Andamento
Formato: application/pdf

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Europeans work much less than Americans. Some studies claim this is due to high taxes in Europe, which would benefit by adopting US tax rates and work time; others find that taxes have little or no impact on work time. I examine the hypothesis that Americans would benefit by reducing work time to Europe’s level. Empirical and experimental studies show utility falls as other people’s income rises. Due to its historical experience, Europe is able to internalize this and other negative externalities by restricting work time – through minimum vacation time and maximum weekly work hours – while the US is not, resulting in a Prisoner’s Dilemma “overworking trap” equilibrium. A simple model and work time data are used to derive the US welfare gain from reducing work time to Europe’s level. Findings are: i) parameter values are consistent with experimental results on the relative impact of own and other people’s income; ii) the welfare gain’s present value is about 120 percent of annual welfare; and iii) even if Europe's policy reduces work time excessively, it does remain beneficial as long as the reduction is less than twice the optimal one.

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## ‣ Non-factorizable joint probabilities and evolutionarily stable strategies in the quantum prisoner's dilemma game

Fonte: Elsevier Science BV
Publicador: Elsevier Science BV

Tipo: Artigo de Revista Científica

Publicado em //2009
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#Quantum games#Prisoner's dilemma#Nash equilibrium#EPR–Bohm experiments#Joint probability#Quantum probability

The well-known refinement of the Nash Equilibrium (NE) called an Evolutionarily Stable Strategy (ESS) is investigated in the quantum Prisoner's Dilemma (PD) game that is played using an Einstein–Podolsky–Rosen type setting. Earlier results report that in this scheme the classical NE remains intact as the unique solution of the quantum PD game. In contrast, we show here that interestingly in this scheme a non-classical solution for the ESS emerges for the quantum PD.; http://www.elsevier.com/wps/find/journaldescription.cws_home/505705/description#description; Azhar Iqbal and Derek Abbott

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## ‣ Psychopathie chez les individus non incarcérés et coopération dans un dilemme du prisonnier itératif

Fonte: Université de Montréal
Publicador: Université de Montréal

Tipo: Thèse ou Mémoire numérique / Electronic Thesis or Dissertation

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#psychopathie#coopération#dilemme du prisonnier#théorie des jeux#stratégie donnant-donnant#Échelle Auto-rapportée de Psychopathie de Levenson#analyse multi-niveaux#psychopathy#cooperation#prisoner's dilemma#game theory

Au niveau interpersonnel, la psychopathie implique un manque de considération d’autrui pouvant se manifester par la tromperie, la manipulation et l’exploitation. La présente thèse a investigué la relation entre les caractéristiques psychopathiques d'individus non incarcérés et la tendance à coopérer dans un jeu du dilemme du prisonnier itératif. Un total de 85 hommes ont été recrutés via une annonce qui ciblait des traits de personnalité correspondant à des caractéristiques psychopathiques exprimées de façon non péjorative. Plusieurs méthodes ont été employées pour rejoindre les participants : 46 ont participés en personne après avoir répondu à une invitation affichée dans un journal local ainsi que sur des babillards à proximité d'une université; 39 ont complété l'étude sur Internet après avoir été recrutés via un site web de petites annonces. Chaque participant a répondu à un questionnaire incluant l’Échelle Auto-rapportée de Psychopathie (Levenson, Kiehl, & Fitzpatrick, 1995) et l’Échelle Auto-rapportée des Indicateurs de Psychopathie de l’Enfance et de l’Adolescence (Seto, Khattar, Lalumière, & Quinsey, 1997). Ils ont également complété une simulation informatique du dilemme du prisonnier itératif comprenant 90 essais. La simulation informatique utilisée pour évaluer les participants en personne ainsi que la version accessible par Internet ont été conçues et programmées spécifiquement pour la présente thèse. La simulation informatique incluait trois stratégies souvent associées au dilemme du prisonnier itératif : donnant-donnant...

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## ‣ The tragedy of the commons, the public goods dilemma, and the meaning of rivalry and excludability in evolutionary biology

Fonte: Evolutionary Ecology
Publicador: Evolutionary Ecology

Tipo: Artigo de Revista Científica

Publicado em //2006
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#collective action#excludability#prisoner's dilemma#public goods dilemma#rivalry#tragedy of the commons#Pathogenic Bacteria#Cooperation#Kin Selection Model#Prisoner’s dilemma#Public goods dilemma

Problem: In the study of conflicts, both economists and evolutionary biologists use the
concepts ‘tragedy of the commons’ and ‘public goods dilemma’. What is the relationship
between the economist and evolutionist views of these concepts?
Model features: The economics literature defines the tragedy of the commons and the public
goods dilemma in terms of rivalry and excludability of the good. In contrast, evolutionists
define these conflicts based on fitness functions with two components: individual and group
components of fitness.
Mathematical method: Evolutionary game theory and the calculation of evolutionarily stable
strategy trait values by standard optimization techniques and by replacing slopes of group
phenotype on individual genotype by coefficients of relatedness.
Conclusion: There is a direct relationship between rivalry and the individual component of
fitness and between excludability and the group component of fitness. Moreover, although the
prisoner’s dilemma constitutes a suitable metaphor to analyse both the public goods dilemma
and the tragedy of the commons, it gives the false idea that the two conflicts are symmetric since
they refer to situations in which individuals consume a common resource – tragedy of the
commons – or contribute to a collective action or common good – public goods dilemma.
However...

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## ‣ Exhaustive exploration of Prisoner's Dilemma Parameter space in one-dimensional cellular automata

Fonte: Sociedade Brasileira de Física
Publicador: Sociedade Brasileira de Física

Tipo: Artigo de Revista Científica

Português

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#Prisoner Dilemma#Emergence of Cooperation#Game Theory#One-dimensional cellular automata#Nonequilibrium phase transition

The Prisoner's Dilemma (PD) is one of the most popular games of the Game Theory due to the emergence of cooperation among competitive rational players. In this paper, we present the PD played in cells of one-dimension cellular automata, where the number of possible neighbors that each cell interacts, z, can vary. This makes possible to retrieve results obtained previously in regular lattices. Exhaustive exploration of the parameters space is presented. We show that the final state of the system is governed mainly by the number of neighbors z and there is a drastic difference if it is even or odd.; Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES); CNPq; FAPESP; CNPq - MCT

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## ‣ Transforming the Dilemma

Fonte: Wiley-Blackwell
Publicador: Wiley-Blackwell

Tipo: Artigo de Revista Científica

Português

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#Prisoner's Dilemma#network reciprocity (graph selection)#kin selection#group selection#evolution of cooperation#direct and indirect reciprocity

How does natural selection lead to cooperation between competing individuals? The Prisoner's Dilemma captures the essence of this problem. Two players can either cooperate or defect. The payoff for mutual cooperation, R, is greater than the payoff for mutual defection, P. But a defector versus a cooperator receives the highest payoff, T, where as the cooperator obtains the lowest payoff, S. Hence, the Prisoner's Dilemma is defined by the payoff ranking T > R > P > S . In a well-mixed population, defectors always have a higher expected payoff than cooperators, and therefore natural selection favors defectors. The evolution of cooperation requires specific mechanisms. Here we discuss five mechanisms for the evolution of cooperation: direct reciprocity, indirect reciprocity, kin selection, group selection, and network reciprocity (or graph selection). Each mechanism leads to a transformation of the Prisoner's Dilemma payoff matrix. From the transformed matrices, we derive the fundamental conditions for the evolution of cooperation. The transformed matrices can be used in standard frameworks of evolutionary dynamics such as the replicator equation or stochastic processes of game dynamics in finite populations.; Mathematics; Organismic and Evolutionary Biology

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## ‣ Entanglement Guarantees Emergence of Cooperation in Quantum Prisoner's Dilemma Games on Networks

Fonte: Nature Publishing Group
Publicador: Nature Publishing Group

Tipo: Artigo de Revista Científica

Publicado em 05/09/2014
Português

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It was known that cooperation of evolutionary prisoner's dilemma games fails to emerge in homogenous networks such as random graphs. Here we proposed a quantum prisoner's dilemma game. The game consists of two players, in which each player has three choices of strategy: cooperator (C), defector (D) and super cooperator (denoted by Q). We found that quantum entanglement guarantees emergence of a new cooperation, the super cooperation of the quantum prisoner's dilemma games, and that entanglement is the mechanism of guaranteed emergence of cooperation of evolutionary prisoner's dilemma games on networks. We showed that for a game with temptation b, there exists a threshold for a measurement of entanglement, beyond which, (super) cooperation of evolutionary quantum prisoner's dilemma games is guaranteed to quickly emerge, giving rise to stochastic convergence of the cooperations, that if the entanglement degree γ is less than the threshold , then the equilibrium frequency of cooperations of the games is positively correlated to the entanglement degree γ, and that if γ is less than and b is beyond some boundary, then the equilibrium frequency of cooperations of the games on random graphs decreases as the average degree of the graphs increases.

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## ‣ Exhaustive exploration of Prisoner's Dilemma Parameter space in one-dimensional cellular automata

Fonte: Sociedade Brasileira de Física
Publicador: Sociedade Brasileira de Física

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/03/2008
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#Prisoner Dilemma#Emergence of Cooperation#Game Theory#One-dimensional cellular automata#Nonequilibrium phase transition

The Prisoner's Dilemma (PD) is one of the most popular games of the Game Theory due to the emergence of cooperation among competitive rational players. In this paper, we present the PD played in cells of one-dimension cellular automata, where the number of possible neighbors that each cell interacts, z, can vary. This makes possible to retrieve results obtained previously in regular lattices. Exhaustive exploration of the parameters space is presented. We show that the final state of the system is governed mainly by the number of neighbors z and there is a drastic difference if it is even or odd.

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## ‣ Universalized Prisoner's Dilemma With Risk

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/09/2015
Português

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In this paper I present a mathematically novel approach to the Prisoner's
Dilemma. I do so by first defining recursively a distinct action type, what I
call 'universalizing', that I add to the original prisoner's dilemma. Such a
modified version of the Prisoner's Dilemma provides a very food productive
model of the choices that would be made in a prisoner's dilemma by agents who
trust each other. As I show, players playing a universalized prisoner's dilemma
get as far out of the dilemma as is mathematically possible. I then add the
concept of risk to the universalized version of prisoner's dilemma. Doing so
provide a model that is sensitive to the trustworthiness of the agents in any
prisoner's dilemma. As I show, with no risk, agents get out of the prisoners
dilemma; and with maximal risk, the succumb to it. succumb to it.; Comment: Includes four pages of Mathematica worksheets that verify the
mathematical claims made in the paper

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