A Risk Aversion Value For N-Person Transferable Utility Games

While the Shapley value for n-person transferable utility games is based on the following principle: « in each according to their contribution », we propose a value in a cooperative game founded on the precautionary index (or the capacity of influence) of a player in a negotiation, as well as the order in which coalitions are formed. Let us note that the Shapley value (1953) and the Nowak and Radzik solidarity value (1994) are generalized by taking risk aversion into account. The main idea of this paper is that a player's marginal contribution will be distributed between this player and those already present in the constitution of the large coalition N . The sharing out of a player's marginal contribution rests on the idea that other players can question his/her taking over the whole marginal contribution and he/she knows it. He/she is therefore going to demand only what he/she is sure to appropriate. Since there are absolute not courageous players, the risk aversion value is efficient, additive, not necessarily individually rational, not necessarily symmetrical (not necessarily neutral) and not necessarily dummy.