**Strategy I:**

On day *t*, an agen<sup>t</sup> goes back to her last day's visited restaurant *k* with probability

$$p\_k^{(I)}(t) = [n\_k(t-1)]^{-a}, \; a > 0. \tag{4}$$

If *nk*(*<sup>t</sup>* − 1) > 1, each of the *nk*(*<sup>t</sup>* − 1) agents or players try to arrive at the same *k*-th restaurant next day *t* with the above probability and chooses a different one (*k* = *k*) among any of the neighboring restaurants *nr* on day *t*, with probability

$$p\_{k'}^{(I)}(t) = (1 - p\_k^{(I)}(t)) / n\_r. \tag{5}$$
