Journal of Mechanism and Institution Design ISSN: 2399-844X(Print), 2399-8458(Online) DOI:10.22574/jmid.2016.12.003 ON NON-COOPERATIVE FOUNDATION AND IMPLEMENTATION OF THE NASH SOLUTION IN SUBGAME PERFECT EQUILIBRIUM VIA RUBINSTEIN’S GAME Papatya Duman Istanbul Bilgi University, Turkey papatya.duman@bilgi.edu.tr Walter Trockel Istanbul Bilgi University, Turkey, and Bielefeld University, Germany walter.trockel@uni-bielefeld.de ABSTRACT 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. Keywords : Nash program, non-cooperative foundation, implementation. JEL Classification Numbers : C7, C71, C72. We are grateful to the editor for suggesting to us to relate our present results to the history of the underlying problem and to the broad literature on bargaining and on implementation. We also thank an associate editor and anonymous referees for valuable feedback. Copyright c Papatya Duman, Walter Trockel /(), 2016, 83–107. Licensed under the Creative Commons Attribution-NonCommercial License.0, http://creativecommons.org.