Evolutionary stable strategies in networked games: the influence of topology

Evolutionary game theory is used to model the evolution of competing strategies in a population of players. Evolutionary stability of a strategy is a dynamic equilibrium, in which any competing mutated strategy would be wiped out from a population. If a strategy is weak evolutionarily stable, the competing strategy may manage to survive within the network. Understanding the network-related factors that affect the evolutionary stability of a strategy would be critical in making accurate predictions about the behaviour of a strategy in a real-world strategic decision making environment. In this work, we evaluate the effect of network topology on the evolutionary stability of a strategy. We focus on two well-known strategies known as the Zero-determinant strategy and the Pavlov strategy. Zero-determinant strategies have been shown to be evolutionarily unstable in a well-mixed population of players. We identify that the Zero-determinant strategy may survive, and may even dominate in a population of players connected through a non-homogeneous network. We introduce the concept of `topological stability' to denote this phenomenon. We argue that not only the network topology, but also the evolutionary process applied and the initial distribution of strategies are critical in determining the evolutionary stability of strategies. Further, we observe that topological stability could affect other well-known strategies as well, such as the general cooperator strategy and the cooperator strategy. Our observations suggest that the variation of evolutionary stability due to topological stability of strategies may be more prevalent in the social context of strategic evolution, in comparison to the biological context

Evolution of Human-like Social Grooming Strategies regarding Richness and Group Size

Human beings tend to cooperate with close friends, therefore they have to construct strong social relationships to recieve cooperation from others. Therefore they should have acquired their strategies of social relationship construction through an evolutionary process. The behavior of social relationship construction is know as "social grooming." In this paper, we show that there are four classes including a human-like strategy in evolutionary dynamics of social grooming strategies based on an evolutionary game simulation. Social relationship strengths (as measured by frequency of social grooming) often show a much skewed distribution (a power law distribution). It may be due to time costs constraints on social grooming, because the costs are too large to ignore for having many strong social relationships. Evolution of humans' strategies of construction of social relationships may explain the origin of human intelligence based on a social brain hypothesis. We constructed an individual-based model to explore the evolutionary dynamics of social grooming strategies. The model is based on behavior to win over others by strengthening social relationships with cooperators. The results of evolutionary simulations show the four classes of evolutionary dynamics. The results depend on total resources and the ratio of each cooperator's resource to the number of cooperators. One of the four classes is similar to a human strategy, i.e. the strategies based on the Yule--Simon process of power law.Comment: 21 pages, 10 figure

The Evolutionary Robustness of Forgiveness and Cooperation

We study the evolutionary robustness of strategies in infinitely repeated prisoners' dilemma games in which players make mistakes with a small probability and are patient. The evolutionary process we consider is given by the replicator dynamics. We show that there are strategies with a uniformly large basin of attraction independently of the size of the population. Moreover, we show that those strategies forgive defections and, assuming that they are symmetric, they cooperate

Survival of dominated strategies under evolutionary dynamics

We show that any evolutionary dynamic that satisfies three mild requirements— continuity, positive correlation, and innovation—does not eliminate strictly dominated strategies in all games. Likewise, we demonstrate that existing elimination results for evolutionary dynamics are not robust to small changes in the specifications of the dynamics

Evolutionary Stable Strategies Depending on Population Density

The concept of evolutionary stable strategies is extended to include density dependence. Dynamical stability is shown to follow for two-strategy games and for symmetric payoff matrices. It is conjectured that stability also results for general multi-strategy games

Survival of dominated strategies under evolutionary dynamics

We prove that any deterministic evolutionary dynamic satisfying four mild requirements fails to eliminate strictly dominated strategies in some games. We also show that existing elimination results for evolutionary dynamics are not robust to small changes in the specifications of the dynamics. Numerical analysis reveals that dominated strategies can persist at nontrivial frequencies even when the level of domination is not small.Evolutionary game theory, evolutionary game dynamics, nonconvergnece, dominated strategies