This research states the stylised n players’ splitting problem as a mathematical programme, relying on definitions of the values of the game and problem stationarity to generate tractable reduced forms, and derives the known solutions after pertaining first-order conditions. Boundary constraints are introduced. Distinction between FOC’s of optimising behavior and equilibrium fitness is provided. Finally, the formal proof of the internal insufficiency of the usual approach to determine the equilibrium is advanced, and the imposing additional conditions – affecting cross multipliers – required for model solving forwarded. Two types of protocols were staged: alternate offers – Rubinstein’s like – and synchronised ones.