Numerical analysis of a reinforcement learning model with the dynamic aspiration level in the iterated Prisoner's Dilemma

Humans and other animals can adapt their social behavior in response to environmental cues including the feedback obtained through experience. Nevertheless, the effects of the experience-based learning of players in evolution and maintenance of cooperation in social dilemma games remain relatively unclear. Some previous literature showed that mutual cooperation of learning players is difficult or requires a sophisticated learning model. In the context of the iterated Prisoner's Dilemma, we numerically examine the performance of a reinforcement learning model. Our model modifies those of Karandikar et al. (1998), Posch et al. (1999), and Macy and Flache (2002) in which players satisfice if the obtained payoff is larger than a dynamic threshold. We show that players obeying the modified learning mutually cooperate with high probability if the dynamics of threshold is not too fast and the association between the reinforcement signal and the action in the next round is sufficiently strong. The learning players also perform efficiently against the reactive strategy. In evolutionary dynamics, they can invade a population of players adopting simpler but competitive strategies. Our version of the reinforcement learning model does not complicate the previous model and is sufficiently simple yet flexible. It may serve to explore the relationships between learning and evolution in social dilemma situations.Comment: 7 figure

Partner Selection for the Emergence of Cooperation in Multi-Agent Systems Using Reinforcement Learning

Social dilemmas have been widely studied to explain how humans are able to cooperate in society. Considerable effort has been invested in designing artificial agents for social dilemmas that incorporate explicit agent motivations that are chosen to favor coordinated or cooperative responses. The prevalence of this general approach points towards the importance of achieving an understanding of both an agent's internal design and external environment dynamics that facilitate cooperative behavior. In this paper, we investigate how partner selection can promote cooperative behavior between agents who are trained to maximize a purely selfish objective function. Our experiments reveal that agents trained with this dynamic learn a strategy that retaliates against defectors while promoting cooperation with other agents resulting in a prosocial society.Comment:

Emergence of social networks via direct and indirect reciprocity

Many models of social network formation implicitly assume that network properties are static in steady-state. In contrast, actual social networks are highly dynamic: allegiances and collaborations expire and may or may not be renewed at a later date. Moreover, empirical studies show that human social networks are dynamic at the individual level but static at the global level: individuals' degree rankings change considerably over time, whereas network-level metrics such as network diameter and clustering coefficient are relatively stable. There have been some attempts to explain these properties of empirical social networks using agent-based models in which agents play social dilemma games with their immediate neighbours, but can also manipulate their network connections to strategic advantage. However, such models cannot straightforwardly account for reciprocal behaviour based on reputation scores ("indirect reciprocity"), which is known to play an important role in many economic interactions. In order to account for indirect reciprocity, we model the network in a bottom-up fashion: the network emerges from the low-level interactions between agents. By so doing we are able to simultaneously account for the effect of both direct reciprocity (e.g. "tit-for-tat") as well as indirect reciprocity (helping strangers in order to increase one's reputation). This leads to a strategic equilibrium in the frequencies with which strategies are adopted in the population as a whole, but intermittent cycling over different strategies at the level of individual agents, which in turn gives rise to social networks which are dynamic at the individual level but stable at the network level

Evolutionary Game Theory

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Cooperation in the iterated prisoner's dilemma is learned by operant conditioning mechanisms

The prisoner's dilemma (PD) is the leading metaphor for the evolution of cooperative behavior in populations of selfish agents. Although cooperation in the iterated prisoner's dilemma (IPD) has been studied for over twenty years, most of this research has been focused on strategies that involve nonlearned behavior. Another approach is to suppose that players' selection of the preferred reply might he enforced in the same way as feeding animals track the best way to feed in changing nonstationary environments. Learning mechanisms such as operant conditioning enable animals to acquire relevant characteristics of their environment in order to get reinforcements and to avoid punishments. In this study, the role of operant conditioning in the learning of cooperation was evaluated in the PD. We found that operant mechanisms allow the learning of IPD play against other strategies. When random moves are allowed in the game, the operant learning model showed low sensitivity. On the basis of this evidence, it is suggested that operant learning might be involved in reciprocal altruism.Fil: Gutnisky, D. A.. Universidad de Buenos Aires. Facultad de Ingenieria. Instituto de Ingeniería Biomédica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Zanutto, Bonifacio Silvano. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; Argentina. Universidad de Buenos Aires. Facultad de Ingenieria. Instituto de Ingeniería Biomédica; Argentin

Predicting Human Cooperation

The Prisoner's Dilemma has been a subject of extensive research due to its importance in understanding the ever-present tension between individual self-interest and social benefit. A strictly dominant strategy in a Prisoner's Dilemma (defection), when played by both players, is mutually harmful. Repetition of the Prisoner's Dilemma can give rise to cooperation as an equilibrium, but defection is as well, and this ambiguity is difficult to resolve. The numerous behavioral experiments investigating the Prisoner's Dilemma highlight that players often cooperate, but the level of cooperation varies significantly with the specifics of the experimental predicament. We present the first computational model of human behavior in repeated Prisoner's Dilemma games that unifies the diversity of experimental observations in a systematic and quantitatively reliable manner. Our model relies on data we integrated from many experiments, comprising 168,386 individual decisions. The computational model is composed of two pieces: the first predicts the first-period action using solely the structural game parameters, while the second predicts dynamic actions using both game parameters and history of play. Our model is extremely successful not merely at fitting the data, but in predicting behavior at multiple scales in experimental designs not used for calibration, using only information about the game structure. We demonstrate the power of our approach through a simulation analysis revealing how to best promote human cooperation.Comment: Added references. New inline citation style. Added small portions of text. Re-compiled Rmarkdown file with updated ggplot2 so small aesthetic changes to plot

A Spatial Agent-Based Model of N-Person Prisoner's Dilemma Cooperation in a Socio-Geographic Community

The purpose of this paper is to present a spatial agent-based model of N-person prisoner's dilemma that is designed to simulate the collective communication and cooperation within a socio-geographic community. Based on a tight coupling of REPAST and a vector Geographic Information System, the model simulates the emergence of cooperation from the mobility behaviors and interaction strategies of citizen agents. To approximate human behavior, the agents are set as stochastic learning automata with Pavlovian personalities and attitudes. A review of the theory of the standard prisoner's dilemma, the iterated prisoner's dilemma, and the N-person prisoner's dilemma is given as well as an overview of the generic architecture of the agent-based model. The capabilities of the spatial N-person prisoner's dilemma component are demonstrated with several scenario simulation runs for varied initial cooperation percentages and mobility dynamics. Experimental results revealed that agent mobility and context preservation bring qualitatively different effects to the evolution of cooperative behavior in an analyzed spatial environment.Agent Based Modeling, Cooperation, Prisoners Dilemma, Spatial Interaction Model, Spatially Structured Social Dilemma, Geographic Information Systems