A Domination Notion in Biform Games

Brandenburger and Stuart [3] introduce the concept of biform game that is used to model the games that have a non-cooperative stage and another cooperative stage. In this mixed model, the choice of each strategy profile determines a cooperative game to be played. In order for the participants analyze and decide what strategy takes them to a game that guarantees the greatest benefit, we propose to generalize the concept of domination extending it to the case in which the imputations belong to two different games. Also, we generalize a theorem establishing necessary and/or sufficient conditions in order for an imputation not to be dominated, and we include examples to illustrate some situations.