Evolution of cooperation driven by self-recommendation

Hostility prevents the tragedy of the commons in metapopulation with asymmetric migration: A lesson from queenless ants

A colony of the queenless ant species, Pristomyrmex punctatus, can broadly be seen as consisting of small-body sized worker ants and relatively larger body-sized cheater ants. Hence, in the presence of intercolony migration, a set of constituent colonies act as a metapopulation exclusively composed of cooperators and defectors. Such a setup facilitates an evolutionary game-theoretic replication-selection model of population dynamics of the ants in a metapopulation. Using the model, we analytically probe the effects of territoriality induced hostility. Such hostility in the ant metapopulation proves to be crucial in preventing the tragedy of the commons, specifically, the workforce, a social good formed by cooperation. This mechanism applies to any metapopulation-not necessarily the ants-composed of cooperators and defectors where interpopulation migration occurs asymmetrically, i.e., cooperators and defectors migrate at different rates. Furthermore, our model validates that there is evolutionary benefit behind the queenless ants' behavior of showing more hostility towards the immigrants from nearby colonies than those from the far-off ones. In order to calibrate our model's parameters, we have extensively used the data available on the queenless ant species, P. punctatus.

Social relationship adjustments within the same sex promote marital bliss

Parental care is essential for biological systems. Marital bliss is one of the ideal paradigms for parental care, in which males contribute in raising offspring and females require a courtship time. Yet marital bliss state is neither Nash equilibrium nor Pareto optimum for the classic Battle of the Sexes. It thus leads to a gap between evolutionary theory and marital bliss. Previous works concentrate on the pairwise interactions between the two sexes to fill this gap, such as the courtship time and encounter rate. The social relationships within the same sex, however, receives much less attention. Here we investigate how social relationships within the same sex change marital bliss by introducing the coevolution of strategy and social network. Based on the time scale separation, it is found that a symmetric game is emergent via social adjustments within each sex, and the evolutionary outcome is determined by the interplay between the emergent symmetric game and the Battle of the Sexes. We find that marital bliss can be promoted when males are rational (strong selection limit) and females are irrational (weak selection limit); the stable Coy-Coy social relationships both stabilize and speed up marital bliss; the general criterion of stabilising marital bliss for arbitrary imitation function are found, which are verified by simulations. Furthermore, the emergent symmetric games are insightful for determining whether the stable marital bliss is global stable. Our work provides an alternative avenue to facilitate marital bliss, which can be applied for general asymmetric games on dynamical networks.

Multi-strategy evolutionary games: A Markov chain approach

Interacting strategies in evolutionary games is studied analytically in a well-mixed population using a Markov chain method. By establishing a correspondence between an evolutionary game and Markov chain dynamics, we show that results obtained from the fundamental matrix method in Markov chain dynamics are equivalent to corresponding ones in the evolutionary game. In the conventional fundamental matrix method, quantities like fixation probability and fixation time are calculable. Using a theorem in the fundamental matrix method, conditional fixation time in the absorbing Markov chain is calculable. Also, in the ergodic Markov chain, the stationary probability distribution that describes the Markov chain’s stationary state is calculable analytically. Finally, the Rock, scissor, paper evolutionary game are evaluated as an example, and the results of the analytical method and simulations are compared. Using this analytical method saves time and computational facility compared to prevalent simulation methods.

Impacts of preferences on the emergence of cooperation

Behavior decision making, where individuals can efficiently express their preferences for all options, has a great impact on cooperation. Hereby, we institute a minimal model in well-mixed populations where whether and how to sanction defectors are decided by cooperators via different decision-making mechanisms. The results illustrate that whether cooperation can outbreak depends on the cooperators' preferences for sanction and complying with the electoral outcome. We highlight the role of individuals' preferences in the emergence of cooperation and show that there exists an intermediate degree of the cooperators' preference for sanction at which the cooperators' preference for complying with the electoral outcome has a negligible impact on cooperation. We point out whether conformity facilitates the emergence of cooperation depends on the cooperators' preference for sanction. We find, compared with individual decision making, whether collective decision making is more conducive to promoting cooperation crucially depends on cooperators' preferences as well as the consensus required for employing sanction.

Evolution of cooperation under punishment

Punishment has been considered as an effective mechanism for promoting and sustaining cooperation. In most existing models, punishment always comes as a third strategy alongside cooperation and defection, and it is commonly assumed to be executed based on individual decision rules rather than collective decision rules. Differently from previous works, we employ a democratic procedure by which cooperators cast votes independently and simultaneously for whether to impose punishment on defectors, and we establish a relationship between the cooperators' willingness to punish defectors (WTPD) and whether the punishment is inflicted on defectors. The results illustrate that the population can evolve to full cooperation under consensual punishment. It is noteworthy that, compared with autonomous punishment, whether consensual punishment is more in favor of cooperation crucially depends on the minimum number of votes required for punishment execution as well as the cooperators' WTPD. Our findings highlight the importance of collective decision making in the evolution of cooperation and may provide a mathematical framework for explaining the prevalence of democracy in modern societies.