Groupe d’études et de recherche en analyse des décisions

# Bargaining with Intertemporal Maximin Payoffs

## Vincent Martinet, P Gajardo, Michel De Lara et H Ramírez Cabrera

We present a new class of dynamic bargaining problems, called "bargaining problems with intertemporal maximin payoffs," that may reflect sustainability problems having to encompass conflicting issues in the long-run. Each bargainer (or stake-holder) has a representative indicator, namely a function of the state and decisions, and aims at maximizing its minimal value over time. Bargaining on sustainability issues consists in defining the vector of stake-holder's payoffs. We are interested in defining the set of feasible outcomes of such problems. This set is interpreted as a support for a social choice of sustainability objectives. We introduce a MONDAI condition - Monotonicity of Dynamics And Indicators - consistent with many economic problems and, in particular, "environmental economic" sustainability issues. We characterize the set of feasible outcomes for problems satisfying these monotonicity properties, and the bargaining solutions under the axioms of Pareto efficiency and Independence of Irrelevant Alternatives. We also provide a "satisficing" common decision rule to achieve any given solution. We then examine the time-consistency of the solution under the axioms of Veto Power and Individual Rationality.

, 22 pages