Modeling Strategic Intercommunity Connections in Evolutionary Games

Traditional evolutionary game theory (EGT) typically assumes fixed, well-mixed populations, neglecting the fact that agents in many real-world systems can strategically form or eliminate connections based on individual incentives. This article introduces a novel framework that integrates EGT with strategic network formation to model the co-evolution of strategies and intercommunity links. We consider populations in which agents interact primarily within their own communities but may establish external connections when such interactions yield higher payoffs. To formalize this, we propose a strategic connections model (SCM) based on the concept of pairwise stability that determines which subsets of agents from different communities form links, and how these links influence evolutionary dynamics. The SCM operates as a two-stage optimization process that accounts for mutual incentives and payoff improvements. Applying our framework to classical evolutionary games, we show that intercommunity connections reshape population-level outcomes. In the prisoner's dilemma, cooperation-typically unstable in well-mixed settings-can emerge and persist under a simple benefit-to-cost condition. In the rock-paper-scissors ( $RPS$ ) game, intercommunity links can alter or suppress the characteristic cycles observed, for instance, under replicator dynamics, affecting the long-term coexistence of strategies. In congestion games, our framework improves infrastructure usage and resource allocation, outperforming intuitive but nonstrategic connection choices. These results highlight the critical role of strategic intercommunity links in shaping collective behavior, offering new insights into the interplay between intercommunity and intracommunity dynamics in biological, social, and engineered systems, where such links can represent interactions among species, individuals, and/or machines within cybernetic environments.