  In this article we compute analytically the number of Nash Equilibria (NE)
for a two-choice game played on a (circular) ladder graph with $2n$ players. We
consider a set of games with generic payoff parameters, with the only
requirement that a NE occurs if the players choose opposite strategies
(anti-coordination game). The results show that for both, the ladder and
circular ladder, the number of NE grows exponentially with (half) the number of
players $n$, as $N_{NE}(2n)\sim C(\varphi)^n$, where $\varphi=1.618..$ is the
golden ratio and $C_{circ}>C_{ladder}$. In addition, the value of the scaling
factor $C_{ladder}$ depends on the value of the payoff parameters. However,
that is no longer true for the circular ladder (3-degree graph), that is
$C_{circ}$ is constant, which might suggest that the topology of the graph
indeed plays an important role for setting the number of NE.
