Cardinal-ordinal invariant solutions
by
Emilio Calvo
Department of Economic Analysis. University of Valencia. Spain
Coauthors: Hans Peters (University of Maastricht. The Netherlands)

We consider Pure Bargaining problems in which there are two type of players: Cardinal and Ordinal players. Cardinal are players that can represent preferences over their payoffs by a unique utility function and all its positive affine transformations. Ordinal players have the freedom to represent their utility function by any differentiable order-preserving transformation.

We assume that the set of cardinal players is always nonempty and that suitable smoothness regularity conditions on the Pareto boundary of the problem are satisfied. In this setting we are able to build a bargaining solution through their disagreement point sets that is invariant under the allowed utility transformations for each corresponding type of player.

In our procedure we follow a path of intermediate agreements that end up in a final efficient agreement. The directions of the vector field used to build the paths follow a rule that is an extension of the weighted equalitarianism that satisfies the Nash Bargaining solution.

Date received: May 11, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafc-29.