where $\delta_w$ and $\delta_l$ denotes the learning rate when win or lose separately, $\pi_i^j$ is agent $i$’s strategy and $\bar \pi_i^j$ is the average strategy, and $p_i^j(m)$ is the probability agent $i$ maintains for interacting with agent $j$.

Experimental Evaluations
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In this section, we evaluate the performance of our optimal rewiring strategy with two benchmark strategies against various interaction environments. Following that, we analyze the performance of different learning strategies under our social learning framework.

Parameter Settings
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We consider a population of hundreds of agents and three representative network topologies: regular network, small-world network and scale-free network. In our experiments, there is no apparent discrimination in results of these three initial topologies,[^4] and we use regular networks as default choice for following illustration. Besides, we consider a wide range of interaction environments $(x,y,z)$ from three major aspects: the number of agents $x$, the size of each agent’s initialized neighborhood $y$ and the size of each agent’s reachable agents $z$. For example, interaction environment $(100,4,12)$ denotes a scenario consisting of 100 agents which each agent has 4 neighbors ($O$) and 12 reachable agents initially($O\cup \bar O$). In following experiments the value of neighborhood $y$ are initialized to be different 