I study the evolutionary stability of behavioural rules in a bargaining game. Each individual bargains in a pairwise manner with all other individuals over the division of a pie of fixed size by claiming a share for himself; individuals in a pair receive their respective claims if and only if the sum of the claims does not exceed unity. Each individual is associated with a behavioural rule which determines the share he chooses to claim. A behavioural rule is a correspondence that maps from a set of demands that were claimed by individuals in the recent history of the game into a set of shares, and each share in the latter set is chosen by the individual with positive probability. The evolutionary fitness of a behavioural rule is determined by the shares obtained by individuals who follow that particular rule, and fitter behavioural rules are selected over rules that are less fit. A state, i.e. a profile of claims made by the individuals in the population, is defined to be stable (neutrally stable) if the population continues to be comprised only of the incumbent behavioural rules (all incumbent behavioural rules continue to exist) even in the face of an appearance of a mutant behavioural rule. I formalise this in terms of two conditions. Firstly, internal stability requires the incumbent behavioural rules in the population to be equally fit. Secondly, external stability (neutral external stability) requires incumbent behavioural rules to be fitter (to not be less fit) than any mutant behavioural rule. I show that: (i) a necessary condition for stability of a state is that the state must be such that each individual responds by claiming a time-invariant share of the pie, and (ii) the state where all individuals demand half of the pie is the only state that is both internally stable and neutrally externally stable. © 2021 Elsevier B.V.