+ U(\pi_i^*,<\bar O_i \backslash \{j\},y_i'>)$, where $y_i^\prime$ is the updated baseline value since agent $i$ breaks the connection with the worst-performance neighbor during rewiring.

The above way of formalizing the dynamics of an optimal strategy only considers the one-shot interaction benefits. However, in our social learning framework, each agent tries to maximize accumulated payoffs during multi-rounds interactions. To this end, we propose a new far-sight way of modeling our rewiring problem such that each agent considers the accumulated expected payoff through multiple interactions with any neighbor after rewiring. Formally, the $K$-step utility function $U_K(\pi_i^*,\epsilon)$ of an optimal strategy $\pi_i^*$ must satisfy the following recursive relation:

$$\begin{aligned}
\ U_K(\pi_i^*,\epsilon) = & \min \{
    K y_i, \max_{j \in \bar O_i} \{
        -c_i^j  +  \ U_K(\pi_i^*,<\bar O_i \backslash \{j\},x>) \cdot F_j^i(y_i) \\
        & +  \ \int_{x=y_i}^\infty U_K(\pi_i^*,<\bar O_i \backslash \{j\},y_i'>) \cdot \;\text{d}F_j^i(x)
  \}
\},
\end{aligned}$$

where the rewiring sight value of $K$ models an agent’s far-sight degree by taking the accumulated payoff from $K$ rounds of interactions into account during each rewiring. We can see that Eq.5 is essentially a Bellman equation, which could be solved by backward induction in principle. However, even for a moderate-size MAS, this approach quickly becomes intractable. To 