Evolutionary stability of behavioural rules in bargaining

I study the evolutionary stability of behavioural rules in a bargaining game. Individuals draw random samples of strategies used in the past and respond to it by using a behavioural rule. Even though individuals actually respond to historical demands, a necessary condition for stability is the existence of a state such that it is as-if the individuals are hardwired to make the same demand. Furthermore, the state where all individuals demand half of the pie is the unique neutrally stable state; all other states are unstable in the face of an invasion by a mutant behavioural rule