On non-cooperative foundation and implementation of the Nash solution in subgame perfect equilibrium via Rubinstein's game

In this paper we provide an exact non-cooperative foundation of the Nash solution via a unique (weakly) subgame perfect equilibrium payoff vector in a two-person bargaining game, which is a modification of the well-known alternate offer game by Rubinstein (1982). We also discuss the extent to which our exact and approximate supports of the Nash solution allow an implementation of the Nash solution in (weakly) subgame perfect equilibrium. We show that a sound interpretation as an implementation can only be found in very rare cases where the domains of players’ preferences are extremely restricted