Evolution Of Cooperation Research Articles

Effects of value-driven social learning on cooperation in the prisoner's dilemma games.

Despite the growing attention and research on the impact of Q-learning-based strategy updating on the evolution of cooperation, the joint role of individual learners and social learners in evolutionary games has seldom been considered. Here, we propose a value-driven social learning model that incorporates a shape parameter, β, to characterize the degree of radicalism or conservatism in social learning. Using the prisoner's dilemma game on a square lattice as a paradigm, our simulation results show that the cooperation level has a non-trivial dependence of β, density ρ, and dilemma strength b. We find that both β and ρ have nonmonotonic effects on cooperation; specifically, moderate levels of radicalism in social learning can facilitate cooperation remarkably, and when slightly conservative, can form a favorable cooperation region with the appropriate ρ. Moreover, we have demonstrated that social learners play a key role in the formation of network reciprocity, whereas individual learners play a dual role of support and exploitation. Our results reveal a critical balance between individual learning and social learning that can maximize cooperation and provide insights into understanding the collective behavior in multi-agent systems.

Cooperative metaheuristic algorithm for global optimization and engineering problems inspired by heterosis theory

Swarm Intelligence-based metaheuristic algorithms are widely applied to global optimization and engineering design problems. However, these algorithms often suffer from two main drawbacks: susceptibility to the local optima in large search space and slow convergence rate. To address these issues, this paper develops a novel cooperative metaheuristic algorithm (CMA), which is inspired by heterosis theory. Firstly, simulating hybrid rice optimization algorithm (HRO) constucted based on heterosis theory, the population is sorted by fitness and divided into three subpopulations, corresponding to the maintainer, restorer, and sterile line in HRO, respectively, which engage in cooperative evolution. Subsequently, in each subpopulation, a novel three-phase local optima avoidance technique-Search-Escape-Synchronize (SES) is introduced. In the search phase, the well-established Particle Swarm Optimization algorithm (PSO) is used for global exploration. During the escape phase, escape energy is dynamically calculated for each agent. If it exceeds a threshold, a large-scale Lévy flight jump is performed; otherwise, PSO continues to conduct the local search. In the synchronize phase, the best solutions from subpopulations are shared through an elite-based strategy, while the classical Ant Colony Optimization algorithm is employed to perform fine-tuned local optimization near the shared optimal solutions. This process accelerates convergence, maintains population diversity, and ensures a balanced transition between global exploration and local exploitation. To validate the effectiveness of CMA, this study evaluates the algorithm using 26 well-known benchmark functions and 5 real-world engineering problems. Experimental results demonstrate that CMA outperforms the 10 state-of-the-art algorithms evaluated in the study, which is a very promising for engineering optimization problem solving.

Evolutionary dynamics in stochastic nonlinear public goods games

Understanding the evolution of cooperation in multi-player games is of vital significance for natural and social systems. An important challenge is that group interactions often lead to nonlinear synergistic effects. However, previous models mainly focus on deterministic nonlinearity, where synergy or discounting effects occur under specific conditions, not accounting for uncertainty and stochasticity in real-world systems. Here, we develop a probabilistic framework to study the cooperative behavior in stochastic nonlinear public goods games. Through both analytical treatment and Monte Carlo simulations, we provide a comprehensive understanding of social dilemmas with stochastic nonlinearity in both well-mixed and structured populations. We find that increasing the degree of nonlinearity makes synergy more advantageous when competing with discounting, thereby promoting cooperation. Furthermore, we show that network reciprocity loses effectiveness when the probability of synergy is small. Moreover, group size exhibits nonlinear effects on group cooperation regardless of the underlying structure. Our findings thus provide insights into how stochastic nonlinearity influences the emergence of prosocial behavior.

IPDToolkit: An R package for simulation and Bayesian analysis of iterated prisoner’s dilemma game-play under third-party arbitration

Recently, researchers have begun studying the role that third-party arbitration may play in the evolution of cooperation. Using the iterated prisoner’s dilemma (IPD), they show that arbitration can mitigate the negative effects of perception errors on the stability of cooperative strategies. Open questions, both theoretical and empirical, however, remain. To promote research on the role of third-party arbitration, we introduce an R package, IPDToolkit, which facilitates both simulation of synthetic data and Bayesian analysis of empirical data. To address theoretical questions, IPDToolkit provides a Monte Carlo simulation engine that can be used to generate play between arbitrary strategies in the IPD with arbitration and assess expected pay-offs. To address empirical questions, IPDToolkit provides customizable, Bayesian finite-mixture models that can be used to identify the strategies responsible for generating empirical game-play data. We present a complete workflow using IPDToolkit to teach end-users its functionality.

Multi-population coevolutionary algorithm for a green multi-objective flexible job shop scheduling problem with automated guided vehicles and variable processing speed constraints

This study focuses on addressing a multi-objective Flexible Job Shop Scheduling Problem with Automated Guided Vehicles (FJSP-AGVs) and variable processing speed constraints. First, a position-based mixed integer linear programming model (MILP) is proposed to optimize simultaneously the maximum completion time and the total energy consumption. Then, we decompose FJSP-AGVs into four interrelated subproblems and design a Multi-Population Coevolutionary Algorithm (MCEA) to solve them. In MCEA, (1) The effective encoding and decoding methods are used to accurately reflect the characteristics of the problem, and generate feasible scheduling solutions. (2) A multi-rule-based heuristic is proposed to enrich the diversity of four populations. (3) A disjunctive graph is constructed to depict and obtain the critical path(s). On this basis, (4) two cooperative evolution strategies based on critical paths are proposed to facilitate collaborative evolution between different populations and improve the global search capability of the algorithm. Furthermore, (5) a consumption reduction strategy is proposed by reducing the processing speed of operations on non-critical paths while ensuring that it does not affect the makespan. Finally, we validate the effectiveness of MCEA by GD, and IGD, and set coverage metrics on the four typical benchmark datasets. Based on the average GD (IGD) metric across 65 instances, MCEA shows reductions of 77.63% (93.60%), 95.30% (97.27%), and 96.17%(97.89%) relative to EHA, EMOEA, and mop-BRKGA, respectively. The set coverage metric, MCEA outperforms EHA, EMOEA, and mop-BRKGA in 59, 64, and 64 instances, respectively. These results clearly indicate that MCEA can solve the FJSP-AGVs with variable processing speed constraints.

The Limits of Our Explanation: A Case Study in Myxococcus xanthus Cooperation

AbstractIn this article, I demonstrate two ways in which our major theories of the evolution of cooperation may fail to capture particular social phenomena. The first shortcoming of our current major theories stems from the possibility of mischaracterizing the cooperative problem in game theory. The second shortcoming of our current major theories is the insensitivity of these explanatory models to ecological and genomic context. As a case study to illustrate these points, I will use the cooperative interaction of a species of myxobacteria called Myxococcus xanthus. M. xanthus cooperate in many areas of their life cycle—in quorum sensing, social motility, fruiting body formation, and predation. I focus in particular on predation as we have not yet discovered an adequate explanation of how they sustain cooperative predation in the face of developmental cheats. In explaining why we have not, I draw generalizable conclusions that shed light on our use of simplified models to explain real-world behaviors in a variety of organisms.

Research on Multi-Objective Evolutionary Algorithms Based on Large-Scale Decision Variable Analysis

Large-scale high-dimensional many-objective optimization problems (LaMaOPs) are prevalent in fields such as autonomous driving, cloud resource scheduling, and smart grids. LaMaOPs involve a large number of decision variables and multiple conflicting objectives that need to be optimized simultaneously. The challenges posed by the curse of dimensionality due to the vast number of decision variables, and the conflict between convergence and diversity caused by the numerous objective variables, make traditional optimization methods inadequate. To address these issues, this paper proposes a two-population cooperative evolutionary algorithm based on large-scale decision variable analysis (DVA-TPCEA). This algorithm integrates quantitative analysis methods for decision variables to deeply examine their impact on each objective and introduces a contribution-based objective detection method. Additionally, a dual-population cooperative evolution mechanism is employed, with targeted optimization strategies designed for convergence and diversity populations, achieving synergistic and complementary optimization between the two populations. To validate the algorithm’s effectiveness in practical applications, a large-scale container resource scheduling strategy based on the DVA-TPCEA algorithm is also proposed. The experimental results indicate that the proposed algorithm demonstrates significant advantages in both general datasets DTLZ, WFG, and LSMOP, and practical models.

On the implementation of zero-determinant strategies in repeated games

Zero-determinant strategies are a class of strategies in repeated games which unilaterally control payoffs. Zero-determinant strategies have attracted much attention in studies of social dilemma, particularly in the context of evolution of cooperation. So far, not only general properties of zero-determinant strategies have been investigated, but zero-determinant strategies have been applied to control in the fields of information and communications technology and analysis of imitation. Here, we further deepen our understanding on general mathematical properties of zero-determinant strategies. We first prove that zero-determinant strategies, if exist, can be implemented by some one-dimensional transition probability. Next, we prove that, if a two-player game has a non-trivial potential function, a zero-determinant strategy exists in its repeated version. These results assist us to implement zero-determinant strategies in broader situations.

Steering cooperation: Adversarial attacks on prisoner’s dilemma in complex networks

This study examines the application of adversarial attack concepts to control the evolution of cooperation in the prisoner’s dilemma game in complex networks. Specifically, it proposes a simple adversarial attack method that drives players’ strategies towards a target state by adding small perturbations to social networks. The proposed method is evaluated on both model and real-world networks. Numerical simulations demonstrate that the proposed method can effectively promote cooperation with significantly smaller perturbations compared to other techniques. Additionally, this study shows that adversarial attacks can also be useful in inhibiting cooperation (promoting defection). The findings reveal that adversarial attacks on social networks can be potent tools for both promoting and inhibiting cooperation, opening new possibilities for controlling cooperative behavior in social systems while also highlighting potential risks.

Adjustment of link weights based on tolerance promotes cooperation in spatial prisoner's dilemma game

Understanding and explaining cooperative behavior in human society has become an open question. In this paper, we propose a dynamic adjustment of pair relationships in a spatial prisoner's dilemma game. Unlike previous studies that individuals dynamically adjust the intensity of interaction with their opponents at each step, this work consider tolerance, in which the intensity of interaction is adjusted when the time of successive defections by an individual exceeds a tolerance threshold T. We find that although the proposed mechanism can significantly improve cooperation compared to traditional versions, a higher tolerance for continuous defection behavior is not conducive to the evolution of cooperation. Furthermore, an environmental adaptor that dynamically adjusts the paired relationship with the opponent at all times is beneficial for the evolution of cooperation. And the higher the degree of adjustment in the paired relationship, the lower the probability of continuous exploitation by defector. We hope that our work can provide some insights into explaining the existence and maintenance of cooperation.

Evolution of cooperation in heterogeneous populations with asymmetric payoff distribution.

The emergence and maintenance of cooperation is a complex and intriguing issue, especially in the context of widespread asymmetries in interactions that arise from individual differences in real-world scenarios. This study investigates how asymmetric payoff distribution affects cooperation in public goods games by considering a population composed of two types of individuals: strong and weak. The asymmetry is reflected in the fact that strong players receive a larger share of the public pool compared to weak players. Our results demonstrate that asymmetric payoff distribution can promote cooperation in well-mixed populations and trigger the co-evolution of cooperation between sub-populations of strong and weak players. In structured populations, however, the effect of asymmetric payoff distribution on cooperation is contingent on the proportion of strong players and the extent of their payoff share, which can either foster or inhibit cooperation. By adjusting the interaction probability between strong and weak players based on their spatial arrangement on lattice networks, we find that moderate interaction probabilities most effectively maintain cooperation. This study provides valuable insights into the dynamics of cooperation under asymmetric conditions, highlighting the complex role of asymmetrical interactions in the evolution of cooperation.

Reciprocal-reward–based environmental feedback promotes cooperation in spatial prisoner's dilemma game

Reciprocal rewards for cooperative behavior are seen as a way of solving social dilemmas. In fact, reward values should not be fixed, but rather linked to the level of social development. Thus, this work proposes a mechanism by which reciprocal reward values in the spatial prisoner's dilemma game depend on region environmental feedback. Therefore, the reciprocal reward values are non-linear and inversely correlated with the environmental state. Numerical simulations show that the non-linear and dynamic reciprocal reward can significantly improve cooperation compared to the traditional version, which can also reduce social costs to some extent. In addition, a higher level of sensitivity to changes in the environment is beneficial for cooperative evolution. Specifically, while setting reciprocal rewards based on greater local environmental feedback can increase the threshold of temptation b at which cooperators become extinct, its contribution to encouraging cooperation is limited. Furthermore, different interval ranges of b-values will have a corresponding range of local environment to encourage cooperation to achieve the optimum. Finally, the results show that the system has good robustness.

Cooperative behavior in multi-agent systems with intrinsic learners and extrinsic imitators

Under the framework of evolutionary games, how to update strategies when individuals interact with multiple neighbors at the same time is a key problem to understand the evolution of cooperation. At present, a widely known method is imitation updating. However, it is undeniable that when resources or capabilities are limited, it is difficult for individuals to obtain more comprehensive information about their counterparts, resulting in imitation method no longer applicable. Reinforcement learning algorithms attract attention because players do not need to know information such as the opponent's payoff, and only adjust strategies based on their own experience and expectations. In view of this, we consider both imitation and reinforcement learning as two behavioral adjustment models, and explore the evolution of cooperative behavior in mixed populations of extrinsic imitators and intrinsic learners. Numerous simulations have shown that when the value of temptation to defect is small, there exists an optimal proportion of intrinsic learners bring group cooperation to its peak. However, in interactive environments with larger social dilemmas, intrinsic learners are effective in resisting betrayal and maintaining group behavior compared to traditional extrinsic imitators. The proposed model reflects the characteristics of seeking advantages, avoiding disadvantages, and imitation in biological groups, and provides new ideas for the design of new game models.

Multi-agent cooperative evolution simulation analysis of PPP project operation supervision in mine wasteland management

Multi-agent cooperative evolution simulation analysis of PPP project operation supervision in mine wasteland management

Clarifying social norms which have robustness against reputation costs and defector invasion in indirect reciprocity

The evolution of cooperation through indirect reciprocity is a pivotal mechanism for sustaining large-scale societies. Because third parties return cooperative behaviour in indirect reciprocity, reputations that assess and share these third parties’ behaviour play an essential role. Studies on indirect reciprocity have predominantly focused on the costs associated with cooperative behaviour, overlooking the costs tied to the mechanisms underpinning reputation sharing. Here, we explore the robustness of social norms necessary to secure the stability of indirect reciprocity, considering both the costs of reputation and the resilience against perfect defectors. Firstly, our results replicate that only eight social norms, known as the ‘leading eight,’ can establish a cooperative regime. Secondly, we reveal the robustness of these norms against reputation costs and perfect defectors. Our analysis identifies four norms that exhibit resilience in the presence of defectors due to their neutral stance on justified defection and another four that demonstrate robustness against reputation costs through their negative evaluation of unjustified cooperation. The study underscores the need to further research how reputational information is shared within societies to promote cooperation in diverse and complex environments.

Particle swarm optimization with historical return decay enhances cooperation in public goods games with investment risks

In the realm of spatial public goods games, heterogeneous investment has emerged as a potent mechanism to enhance cooperative behavior. Savvy investors dynamically adjust their investment levels to optimize returns based on environmental conditions and personal circumstances. This study delves into the evolution of cooperation within a spatial public goods game framework, characterized by heterogeneous investment and associated risks, conducted on a square lattice. We introduce the investors (I) with heterogeneous investment, who updates his investment amount according to the current environment of the game and his own historical experience. We introduce a particle swarm optimization algorithm with decaying historical returns to fine-tune the investment levels of investors. Furthermore, a risk mechanism inspired by the ultimatum game is integrated into the model. This paper investigates the impact of the risk threshold θ on cooperative behavior and examines the influence of the risk decay factor α on cooperation. Additionally, it analyzes the investment behavior of investors in scenarios where two types of investors coexist. Finally, this study explores the effects of the historical best payoff decay factor β and the self-learning rate c1 on cooperative behavior. This research contributes to a nuanced understanding of heterogeneous investment behaviors in public goods games under specified risk mechanisms, providing novel insights into the intricate dynamics of cooperation in complex systems.

Stability of Certain Non-Autonomous Cooperative Systems of Difference Equations with the Application to Evolutionary Dynamics

This paper investigates the dynamics of non-autonomous cooperative systems of difference equations with asymptotically constant coefficients. We are mainly interested in global attractivity results for such systems and the application of such results to evolutionary population cooperation models. We use two methods to extend the global attractivity results for autonomous cooperative systems to related non-autonomous cooperative systems which appear in recent problems in evolutionary dynamics.

Evolution of cooperation in networks with well-connected cooperators

Evolution of cooperation in networks with well-connected cooperators

A bi-population cooperative scatter search algorithm for distributed hybrid flow shop scheduling with machine breakdown

The occurrence of machine breakdowns is a frequent and dynamic phenomenon in the production process. The implementation of effective preventive measures can mitigate such events and result in reduced production costs. This paper investigates the distributed hybrid flow shop scheduling problem with machine breakdown (DHFSSPB) considering short maintenance time. The bi-population cooperative scatter search (BCSS) algorithm is proposed to address the DHFSSPB, wherein the search for the optimal scheduling sequence is transformed into genetic evolution aiming to obtain a gene chain with both minimum lower bound and minimum cost attributes. Firstly, the DHFSSPB problem is modeled through a combination of predictive maintenance strategy and right-shift rescheduling rule. Subsequently, a diversification approach is developed to facilitate attribute inheritance, enhance the efficiency of job allocation, and establish a reference set. The reference set is partitioned into two subpopulations based on lower bound attributes and cost attributes, respectively. The corresponding hybrid search strategies are designed to enhance the efficiency of job sorting and machine selection for subpopulations with distinct attributes. The cooperative evolution between subpopulations occurs through the competitive interaction and fusion of individuals. An enhanced reinforcement learning approach is proposed to expedite the acceleration of individual attribute evolution by leveraging evolutionary knowledge acquired from populations, thereby effectively guiding the evolutionary trajectories of individuals. Additionally, a method for evaluating the population during the learning process is developed based on problem characteristics to enhance learning efficiency. Experimental results demonstrate that BCSS outperforms the comparative algorithm in solving the DHFSSPB.

The effects of herding and dispersal behaviour on the evolution of cooperation on complete networks

Evolutionary graph theory has considerably advanced the process of modelling the evolution of structured populations, which models the interactions between individuals as pairwise contests. In recent years, these classical evolution models have been extended to incorporate more realistic features, e.g. multiplayer games. A recent series of papers have developed a new evolutionary framework including structure, multiplayer interactions, evolutionary dynamics, and movement. However, so far, the developed models have mainly considered independent movement without coordinated behaviour. Although the theory underlying the framework has been developed and explored in various directions, several movement mechanisms have been produced which characterise coordinated movement, for example, herding. By embedding these newly constructed movement distributions, within the evolutionary setting of the framework, we demonstrate that certain levels of aggregation and dispersal benefit specific types of individuals. Moreover, by extending existing parameters within the framework, we are not only able to develop a general process of embedding any of the considered movement distributions into the evolutionary setting on complete graphs but also analytically produce the probability of fixation of a mutant on a complete N-sized network, for the multiplayer Public Goods and Hawk–Dove games. Also, by applying weak selection methods, we extended existing previous analyses on the pairwise Hawk–Dove Game to encompass the multiplayer version considered in this paper. By producing neutrality and equilibrium conditions, we show that hawks generally do worse in our models due to the multiplayer nature of the interactions.