Fallback Bargaining

Abstract

Under fallback bargaining, bargainers begin by indicating their preference rankings over alternatives. They then fall back, in lockstep, to less and less preferred alternatives – starting with first choices, then adding second choices, and so on – until an alternative is found on which all bargainers agree. This common agreement, which becomes the outcome of the procedure, may be different if a decision rule other than unanimity is used. The outcome is always Pareto-optimal but need not be unique; if unanimity is used, it is at least middling in everybody's ranking. Fallback bargaining may not select a Condorcet alternative, or even the first choice of a majority of bargainers. However, it does maximize bargainers' minimum “satisfaction.” When bargainers are allowed to indicate “impasse” in their rankings – below which they would not descend because they prefer no agreement to any lower-level alternative – then impasse itself may become the outcome, foreclosing any agreement. The vulnerability of fallback bargaining to manipulation is analyzed in terms of both best responses and Nash equilibria. Although a bargainer can sometimes achieve a preferred outcome through an untruthful announcement, the risk of a mutually worst outcome in a Chicken-type game may well deter the bargainers from attempting to be exploitative, especially when information is incomplete. Fallback bargaining seems useful as a practicable procedure if a set of “reasonable” alternatives can be generated. It leapfrogs the give-and-take of conventional bargaining, which often bogs down in details, by finding a suitable settlement through the simultaneous consideration of all alternatives.