denote agent $i$’s reachable peers, consisting of $O_i$ for agent $i$’s neighborhood and $\bar O_i$ for all non-neighbor agents that agent $i$ can potentially interact with through rewiring.

Moreover, unlimited increase of communication in real-world networks is usually impractical and the number of connections should have a upper bound due to finite connection resources [@zhang2013coordinating]. Each agent should break an old connection each time it decides to establish a new connection through rewiring.[^1] The interest of any rational agent is to maximize its accumulative payoff during the course of interactions. Therefore, a rational agent needs to balance the tradeoff between rewiring to explore more beneficial partners to interact with and exploiting the current connected neighbors to avoid rewiring cost.

Social Learning Framework
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Under the social learning framework, there is a population $N$ of agents and each agent learns its policy through repeated pair-wise interactions with its neighbors. The initial neighborhood of each agent is determined by the underlying topology and three representative topologies are considered here: Regular Network, Small-world Network, Scale-Free Network [@watts1998collective; @albert2002statistical]. The overall interaction flow under the social learning framework is shown in Algorithm 1.

Perform rewiring action. Play game $G_i^j$ with randomly chosen player $j 