Phase transitions in a coevolving snowdrift game with costly rewiring

The impact of dynamic linking on cooperation on complex networks

In complex social systems, individual relationships and the surrounding environment are constantly changing, allowing individuals to interact on dynamic networks. This study aims to investigate how individuals in a dynamic network engaged in a prisoner's dilemma game adapt their competitive environment through random edge breaks and reconnections when faced with incomplete information and adverse local conditions, thereby influencing the evolution of cooperative behavior. We find that random edge breaks and reconnections in dynamic networks can disrupt cooperative clusters, significantly hindering the development of cooperation. This negative impact becomes more pronounced over larger time scales. However, we also observe that nodes with higher degrees of connectivity exhibit greater resilience to this cooperation disruption. Our research reveals the profound impact of dynamic network structures on the evolution of cooperation and provides new insights into the mechanisms of cooperation in complex systems.

Mixing protocols in the public goods game

If interaction partners in social dilemma games are not selected randomly from the population but are instead determined by a network of contacts, it has far reaching consequences for the evolutionary dynamics. Selecting partners randomly leads to a well-mixed population, where pattern formation is essentially impossible. This rules out important mechanisms that can facilitate cooperation, most notably network reciprocity. In contrast, if interactions are determined by a lattice or a network, then the population is said to be structured, where cooperators can form compact clusters that protect them from invading defectors. Between these two extremes, however, there is ample middle ground that can be brought about by the consideration of temporal networks, mobility, or other coevolutionary processes. The question that we here seek to answer is, when does mixing on a lattice actually lead to well-mixed conditions? To that effect, we use the public goods game on a square lattice, and we consider nearest-neighbor and random mixing with different frequencies, as well as a mix of both mixing protocols. Not surprisingly, we find that nearest-neighbor mixing requires a higher frequency than random mixing to arrive at the well-mixed limit. The differences between the two mixing protocols are most expressed at intermediate mixing frequencies, whilst at very low and very high mixing frequencies the two almost converge. We also find a near universal exponential growth of the average size of cooperator clusters as their fraction increases from zero to one, regardless of whether this increase is due to increasing the multiplication factor of the public goods, decreasing the frequency of mixing, or gradually shifting the mixing from random to nearest neighbors.

Non-Markovian recovery makes complex networks more resilient against large-scale failures

Non-Markovian spontaneous recovery processes with a time delay (memory) are ubiquitous in the real world. How does the non-Markovian characteristic affect failure propagation in complex networks? We consider failures due to internal causes at the nodal level and external failures due to an adverse environment, and develop a pair approximation analysis taking into account the two-node correlation. In general, a high failure stationary state can arise, corresponding to large-scale failures that can significantly compromise the functioning of the network. We uncover a striking phenomenon: memory associated with nodal recovery can counter-intuitively make the network more resilient against large-scale failures. In natural systems, the intrinsic non-Markovian characteristic of nodal recovery may thus be one reason for their resilience. In engineering design, incorporating certain non-Markovian features into the network may be beneficial to equipping it with a strong resilient capability to resist catastrophic failures.

Aspiration-based coevolution of link weight promotes cooperation in the spatial prisoner's dilemma game

In this article, we propose an aspiration-based coevolution of link weight, and explore how this set-up affects the evolution of cooperation in the spatial prisoner's dilemma game. In particular, an individual will increase the weight of its link to its neighbours only if the payoff received via this interaction exceeds a pre-defined aspiration. Conversely, if the received payoff is below this aspiration, the link weight with the corresponding neighbour will decrease. Our results show that an appropriate aspiration level leads to a high-cooperation plateau, whereas too high or too low aspiration will impede the evolution of cooperation. We explain these findings with a comprehensive analysis of transition points and with a systematic analysis of typical configuration patterns. The presented results provide further theoretical insights with regards to the impact of different aspiration levels on cooperation in human societies.