Ideals in sequential bargaining structures

Purpose - The purpose of this paper is to suggest possible extensions of the baseline Rubinstein sequential bargaining structure – applied to the negotiation of stationary infinitely termed contracts – that incorporate a direct reference to the “ideal” utilities of the players. This is a feature of the Kalai‐Smorodinsky cooperative solution – even if not of the generalized Nash maximand; it is usually not encountered in non‐cooperative equilibria. Design/methodology/approach - First, it is argued that different bargaining protocols than conventionally staged are able to incorporate temporary all‐or (and)‐nothing splits of the pie. Scenarios are advanced where such episodes are interpreted either as – out of bargaining – war or unilateral appropriation events, or free experience contracts. Second, some modifications to the Rubinstein infinite horizon paradigm are experimented with, allowing for mixed strategies under alternate offers, and matching or synchronous decisions in a simultaneous (yet, discrete) bargaining environment. Solutions are derived where the reference to the winner‐takes‐it‐all outcome arises as a parallel – out‐of‐the‐protocol – outside option to the status quo point. In some cases, the limiting maximand for instantaneous bargaining was derived. Findings - Rubinstein's optimal periodic division in a closed contract remained robust to most of the settings. Originality/value - Presents possible extensions of the baseline Rubinstein sequential bargaining structure.