Rewarding evolutionary fitness with links between populations promotes cooperation (1404.1069v1)

Abstract: Evolution of cooperation in the prisoner's dilemma and the public goods game is studied, where initially players belong to two independent structured populations. Simultaneously with the strategy evolution, players whose current utility exceeds a threshold are rewarded by an external link to a player belonging to the other population. Yet as soon as the utility drops below the threshold, the external link is terminated. The rewarding of current evolutionary fitness thus introduces a time-varying interdependence between the two populations. We show that, regardless of the details of the evolutionary game and the interaction structure, the self-organization of fitness and reward gives rise to distinguished players that act as strong catalysts of cooperative behavior. However, there also exist critical utility thresholds beyond which distinguished players are no longer able to percolate. The interdependence between the two populations then vanishes, and cooperators are forced to rely on traditional network reciprocity alone. We thus demonstrate that a simple strategy-independent form of rewarding may significantly expand the scope of cooperation on structured populations. The formation of links outside the immediate community seems particularly applicable in human societies, where an individual is typically member in many different social networks.

Promoting Cooperation Through Evolutionary Fitness Rewards in Interdependent Networks

The paper titled "Rewarding evolutionary fitness with links between populations promotes cooperation" explores the intricate dynamics of cooperation in evolutionary games set on interdependent network structures. Essentially, this work examines how the introduction of a fitness-based reward system—wherein individuals from distinct and initially isolated populations gain the temporary opportunity to create external links—can facilitate and enhance cooperative behavior. This analysis is grounded within the frameworks of two canonical evolutionary game theory models: the Prisoner's Dilemma and the Public Goods Game.

The paper's central innovation stems from the reward mechanism that dynamically adjusts interdependence between the two networks based on an individual's performance, measured by its utility exceeding a predefined threshold. Players are thus granted an external link, augmenting their utility by incorporating a fraction of a peer's utility from the opposite network. The disentanglement ensues when a player's utility falls beneath this threshold, severing the link. This dynamic allows for a robust time-varying feedback loop between populations, presenting an emergent form of interdependence that can significantly bolster cooperation beyond traditional intra-network dynamics.

Key Findings and Numerical Results

The introduction of reward-driven interdependence was empirically shown to amplify cooperation across both types of evolutionary games tested, signaling deep interactions between strategy success and network topology. When examining the Prisoner's Dilemma on square lattices and random graphs, intermediate utility thresholds markedly improved cooperative outcomes while avoiding the issues faced at extremes—either reliance on network reciprocity without interdependence at high thresholds or uniform dependence at low thresholds which diluted the reward’s effect. As the temptation to defect ($b$) or the harshness of the public goods environment (multiplication factor $r$) increased, optimal thresholds adjusted accordingly, showcasing the model's sensitivity to the social dilemma's intensity.

Strong Numerical Evidence:

1. Percolation of Distinguished Players: Key to enhanced cooperation was the critical balance that allowed this distinguished class of players—that is, those meeting the utility threshold—to percolate and effectively reinforce cooperative strategies across entire networks.
2. Utility Thresholds and Criticality: Cooperation was shown to peak at specific thresholds just before the critical value where the population interdependence collapses (no player reaches the utility required for external links). This was robustly evidenced by the stark drops in cooperation past these thresholds on both regular and random graph structures, validating the proposed dynamic.
3. Utility Analysis: The effects of varied $E$ values were scrutinized, revealing a direct correlation between the number and connectivity of link-eligible players and overall cooperative behavior—a subtle yet pivotal mechanism driving the global properties of the networked systems toward enhanced cooperation.

Implications and Future Prospects

The research offers tangible insights into the benefits of conditional interdependence in networked systems, highlighting a strategic mechanism capable of leveraging heterogeneity to foster cooperation. The implications span both theoretical understandings of cooperative regimes and practical applications in designing systems where interdependent yet autonomous entities decide behavior based on performance metrics.

Future research should focus on integrating more complex interdependencies and considering real-world topologies with larger stratifications of network interconnectedness. Further work could also explore the impact of strategic diversity and the inclusion of more intricate social systems dynamics, including multi-layer networks and adaptive link formations based on network states.

In conclusion, this paper provides a nuanced understanding of cooperation in multi-population systems characterized by interdependent networks. It extends the well-established themes of network reciprocity to incorporate dynamic, fitness-dependent interconnections, paving the way for innovative applications in designing cooperative systems and networks.