Note that because of the imitation mechanism of PI, the configurations [x.sub.i] = 1 [for all]i and [x.sub.i] = 0 [for all]i are absorbing states: the system cannot escape from them and not even mistakes can reintroduce strategies, as they always involve imitation.
Compared to the situation with PI, in which we only found the absorbing states as equilibria, this points to the fact that more rational players would eventually converge to equilibria with higher payoffs.
where [p.sub.w] means the total probability of absorbing states where [??]VW[??] = w; E[[rcv.sub.w]] represents the expected number of all the packets sent before timeout; E[[T.sub.w]] is the expected time of this period, which includes the time of window evolution and timeout.
An element of B, [b.sub.ik], represents the probability of transiting from transient state i to absorbing state k.
These are an identity matrix [I.sub.4*4], a zero matrix [O.sub.4*7], a [R.sub.7*4] matrix which refers to the transitions from transient to absorbing states, and the [Q.sub.7*7] matrix which denotes transitions within the transient states.
Inactivity has become a much less absorbing state in Denmark, as the probability of staying inactive from one year to another has fallen from 0.8 to 0.69 between 1990 and 1997.
Looking at the transition probabilities from one labour market status to another, however, it appears that inactivity has been an increasingly absorbing state for the entire working-age population, despite a renewed effort to curb the number of social benefits recipients in the Netherlands.