Evolution of cooperation with respect to fixation probabilities in multi-player games with random payoffs

Social dilemma for 30 years: Progress, framework, and future based on CiteSpace analysis

Social dilemmas have been a popular research topic in the past 30 years, yet there is still a lack of interdisciplinary reviews. This study represents the first attempt to conduct a bibliometric analysis of social dilemma research over the past 30 years, aiming to identify the research status, research hotspots, and future trends in this domain. We conduct an interdisciplinary analysis of 3630 articles from 1993 to 2023 using CiteSpace software. We find that: (1) this research domain exhibits a fluctuating upward trend and possesses evident interdisciplinary characteristics. (2) Collaboration among authors, institutional and regional, is much more prevalent, especially in the evolutionary dynamics of human behavior, cooperation, and reinforcement learning. (3) The current hot trend in this field of research is to investigate the influencing factors and solutions for social dilemmas. Researchers have shown great interest in value orientation, social norms, fairness, punishment, and rewards in promoting cooperation. (4) In the future, this field will cover different disciplines, develop theoretical frameworks grounded in bounded rationality, explore the boundary conditions of effective strategies, and integrate emerging technologies. This study serves as a valuable reference for scholars seeking to navigate social dilemma research while also providing insights for managers aiming to devise practical solutions to social dilemmas.

Stochastic viability in an island model with partial dispersal: Approximation by a diffusion process in the limit of a large number of islands

In this paper, we investigate a finite population undergoing evolution through an island model with partial dispersal and without mutation, where generations are discrete and non-overlapping. The population is structured into D demes, each containing N individuals of two possible types, A and B, whose viability coefficients, sA and sB, respectively, vary randomly from one generation to the next. We assume that the means, variances and covariance of the viability coefficients are inversely proportional to the number of demes D, while higher-order moments are negligible in comparison to 1/D. We use a discrete-time Markov chain with two timescales to model the evolutionary process, and we demonstrate that as the number of demes D approaches infinity, the accelerated Markov chain converges to a diffusion process for any deme size N≥2. This diffusion process allows us to evaluate the fixation probability of type A following its introduction as a single mutant in a population that was fixed for type B. We explore the impact of increasing the variability in the viability coefficients on this fixation probability. At least when N is large enough, it is shown that increasing this variability for type B or decreasing it for type A leads to an increase in the fixation probability of a single A. The effect of the population-scaled variances, σA2 and σB2, can even cancel the effects of the population-scaled means, μA and μB. We also show that the fixation probability of a single A increases as the deme-scaled migration rate increases. Moreover, this probability is higher for type A than for type B if the population-scaled geometric mean viability coefficient is higher for type A than for type B, which means that μA-σA2/2>μB-σB2/2.

Game modelling and stability strategy research on distributed leadership pattern: A tripartite evolutionary game perspective

Distributed leadership pattern has been a topic of growing interest in recent years, recognizing that much remains to be known about this phenomenon. The research on distributed leadership acknowledges that responsibility and power are not exclusively limited to one formal leader, but are distributed between formal and informal leaders. The decision-making behavior of team members plays a vital role in optimizing cooperation and team performance. Nevertheless, little attention is paid to investigating the underlying mechanisms about how people in a team cooperate to initiate effective interactions and enhance team performance. Game theory offers a comprehensive analysis of rational behavior under the circumstances of strategic interdependence. By organizing the formal leader, the informal leader, and the ordinary employee in a team, this study constructs a tripartite evolutionary game model and analyzes the internal mechanism of distributed leadership patterns. The study finds that the equilibrium of the three parties is affected by multiple factors. The simulation results reveal that the empowerment of the formal leader to the informal leader is indispensable to promoting optimal cooperation and team performance in distributed leadership patterns. These findings have theoretical implications for the distributed leadership literature and managerial implications for practitioners.