The Harsanyi paradox and the “right to talk” in bargaining among coalitions

We describe a coalitional value from a non-cooperative point of view, assuming coalitions are formed for the purpose of bargaining. The idea is that all the players have the same chances to make proposals. This means that players maintain their own “right to talk” when joining a coalition. The resulting value coincides with the weighted Shapley value in the game between coalitions, with weights given by the size of the coalitions. Moreover, the Harsanyi paradox (forming a coalition may be disadvantageous) disappears for convex games.

► Definition of a coalitional value.
► This coalitional value is joint-monotonic.
► Definition of the non-cooperative game (mechanism).
► The coalitional value is the unique expected stationary subgame perfect equilibrium payoff in strictly convex games.