Evolutionary Games and Computer Simulations (original) (raw)
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Simulation models of the Reiterated Prisoner's Dilemma have been popular for studying the evolution of cooperation since more than 30 years now. However, there have been practically no successful instances of empirical application of any of these models. At the same time this lack of empirical testing and confirmation has almost entirely been ignored by the modelers community. In this paper, I examine some of the typical narratives and standard arguments with which these models are justified by their authors despite the lack of empirical validation. I find that most of the narratives and arguments are not at all compelling. None the less they seem to serve an important function in keeping the simulation business running despite its empirical shortcomings. *please use the link(s) below for the most updated version of the paper*
Journal of Statistical Mechanics: Theory and Experiment, 2006
We propose an extension of the evolutionary Prisoner's Dilemma cellular automata, introduced by Nowak and May , in which the pressure of the environment is taken into account. This is implemented by requiring that individuals need to collect a minimum score U min , representing indispensable resources (nutrients, energy, money, etc.) to prosper in this environment. So the agents, instead of evolving just by adopting the behaviour of the most successful neighbour (who got U msn ), also take into account if U msn is above or below the threshold U min . If U msn < U min an individual has a probability of adopting the opposite behaviour from the one used by its most successful neighbour. This modification allows the evolution of cooperation for payoffs for which defection was the rule (as it happens, for example, when the sucker's payoff is much worse than the punishment for mutual defection). We also analyse a more sophisticated version of this model in which the selective rule is supplemented with a "win-stay, lose-shift" criterion. The cluster structure is analyzed and, for this more complex version we found power-law scaling for a restricted region in the parameter space.
Gradual learning and the evolution of cooperation in the spatial Continuous Prisoner’s Dilemma
The European Physical Journal B, 2009
The usual mechanism for modeling learning in spatially structured evolutionary games has to date been imitation of some successful neighbor. However, it seems natural that individuals hesitate to imitate their neighbor's acts, specially if they can imply high costs. Here we study the effect of incorporating resistance to imitation on these models. Our framework is the spatial Continuous Prisoner's Dilemma. For this evolutionary game, it has been reported that occasional errors in the imitation process can explain the emergence of cooperation from a non-cooperative initial state. In this work, we show that this only occurs for particular regimes of low costs of cooperation. Furthermore, we display how resistance gets greater the range of scenarios where cooperative individuals can invade selfish populations. In this context, where resistance to imitation can be interpreted as a general rule of gradual learning, our results show that the less that is learnt in a single step from a successful neighbors, the larger the degree of global cooperation finally attained. In general, the effect of step-by-step learning can be more efficient for the evolution of cooperation than a full blast one. PACS. PACS-02.50Le Decision theory and game theory -PACS-89.75Fb Structures and organization in complex systems Send offprint requests to: Raúl Jiménez a e-mail: raul.jimenez@uc3m.es Jiménez et al.: Gradual learning and cooperation theory, researchers from many fields have attempted to shed light on the underlying mechanisms that outperform the vulnerability of cooperation of being cheated [6]. Models with spatial structures have been considered by these researches to mimic real population where individuals do not interact with everybody else. In these models, individuals are located on the nodes of a network, play repeatedly with their neighbors, and update their strategies by imitating (with occasional errors) the strategy of some more successful neighbor. Different update rules respond to the same evolutionary principle of reproduction of successful strategies [7] and are usually implemented through two basic operators: Selection, in which individuals identify whom to imitate, and mutation, occasional errors in the imitation process.
EVOLUTION OF COOPERATION IN A SPATIAL PRISONER'S DILEMMA
Advances in Complex Systems, 2002
We investigate the spatial distribution and the global frequency of agents who can either cooperate or defect. The agent interaction is described by a deterministic, non-iterated prisoner's dilemma game, further each agent only locally interacts with his neighbors. Based on a detailed analysis of the local payoff structures we derive critical conditions for the invasion or the spatial coexistence of cooperators and defectors. These results are concluded in a phase diagram that allows to identify five regimes, each characterized by a distinct spatiotemporal dynamics and a corresponding final spatial structure. In addition to the complete invasion of defectors, we find coexistence regimes with either a majority of cooperators in large spatial domains, or a minority of cooperators organized in small non-stationary domains or in small clusters. The analysis further allowed a verification of computer simulation results by . Eventually, we present simulation results of a true 5-person game on a lattice. This modification leads to non-uniform spatial interactions that may even enhance the effect of cooperation.
Physica A: Statistical Mechanics and its Applications, 2006
The Prisoner's Dilemma (PD) deals with the cooperation/defection conflict between two agents. The agents are represented by a cell of L × L square lattice. The agents are initially randomly distributed according to a certain proportion ρc(0) of cooperators. Each agent does not have memory of previous behaviors and plays the PD with eight nearest neighbors and then copies the behavior of who had the greatest payoff for next generation. This system shows that, when the conflict is established, cooperation among agents may emerge even for reasonably high defection temptation values. Contrary to previous studies, which treat mean inter-group interaction, here a model where the agents are not allowed to self-interact, representing intra-group interaction, is proposed. This leads to short time and asymptotic behaviors similar to the one found when self-interaction is considered. Nevertheless, the intermediate behavior is different, with no possible data collapse since oscillations are present. Also, the fluctuations are much smaller in the intra-group model. The geometrical configurations of cooperative clusters are distinct and explain the ρc(t) differences between inter and intra-group models. The boundary conditions do not affect the results.
Evolving learning rules and emergence of cooperation in spatial prisoner's dilemma
Journal of Theoretical Biology, 2009
In the evolutionary Prisoner's Dilemma (PD) game, agents play with each other and update their strategies in every generation according to some microscopic dynamical rule. In its spatial version, agents do not play with every other but, instead, interact only with their neighbors, thus mimicking the existing of a social or contact network 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 the entire 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 outcome is always full defection. We subsequently focus on two-strategy competition with nearest-neighbor interactions on the contact network and synchronized update of strategies. Our results show that, for an important range of the parameters of the game, the final state of the system is largely different from that arising 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, we have studied representative update rules, finding that some of them may become extinct while others prevail. We describe the new and rich variety of final outcomes that arise from this co-evolutionary dynamics. We include examples of other neighborhoods and asynchronous updating that confirm the robustness of our conclusions. Our results pave the way to an evolutionary rationale for modelling social interactions through game theory with a preferred set of update rules.
Simulation Models of the Evolution of Cooperation as Proofs of Logical Possibilities. How Useful Are They?, 2013
This paper discusses critically what simulation models of the evolution of cooperation can possibly prove by examining Axelrod’s “Evolution of Cooperation” (1984) and the modeling tradition it has inspired. Hardly any of the many simulation models of the evolution of cooperation in this tradition have been applicable empirically. Axelrod’s role model suggested a research design that seemingly allowed to draw general conclusions from simulation models even if the mechanisms that drive the simulation could not be identified empirically. But this research design was fundamentally flawed, because it is not possible to draw general empirical conclusions from theoretical simulations. At best such simulations can claim to prove logical possibilities, i.e. they prove that certain phenomena are possible as the consequence of the modeling assumptions built into the simulation, but not that they are possible or can be expected to occur in reality I suggest several requirements under which proofs of logical possibilities can nevertheless be considered useful. Sadly, most Axelrod-style simulations do not meet these requirements. I contrast this with Schelling’s neighborhood segregation model, the core mechanism of which can be retraced empirically.
The Evolution of Cooperation in Spatially Heterogeneous Populations
The American Naturalist, 1996
One of the most difficult problems of sociobiology is to understand the emergence of cooperation in a nonsocial world. For this purpose, the iterated Prisoner's Dilemma (IPD) game has proved to be a hitfbl tool of investigation. The outcome of this game is basically determined by the probability w of repeated interactions between players.
No Strategy Can Win in the Repeated Prisoner's Dilemma: Linking Game Theory and Computer Simulations
Frontiers in Robotics and AI, 2018
Computer simulations are regularly used for studying the evolution of strategies in repeated games. These simulations rarely pay attention to game theoretical results that can illuminate the data analysis or the questions being asked. Results from evolutionary game theory imply that for every Nash equilibrium, there are sequences of mutants that would destabilize them. If strategies are not limited to a finite set, populations move between a variety of Nash equilibria with different levels of cooperation. This instability is inescapable, regardless of how strategies are represented. We present algorithms that show that simulations do agree with the theory. This implies that cognition itself may only have limited impact on the cycling dynamics. We argue that the role of mutations or exploration is more important in determining levels of cooperation.