Bisemivalues for bicooperative games

We introduce bisemivalues for bicooperative games and we also provide an interesting characterization of this kind of values by means of weighting coefficients in a similar way as it was given for semivalues in the context of cooperative games. Moreover, the notion of induced bisemivalues on lower cardinalities also makes sense and an adaptation of Dragan’s recurrence formula is obtained. For the particular case of (p, q)-bisemivalues, a computational procedure in terms of the multilinear extension of the game is given.Peer ReviewedPostprint (author's final draft

The selectope for bicooperative games

A bicooperative game is defined by a worth function on the set of ordered pairs of disjoint coalitions of players. The aim of this paper is to analyze the selectope for bicooperative games. This solution concept was introduced by Hammer et al. (1977) [20] and studied by Derks et al. (2000) [10] for cooperative games. We show the relations between the selectope, the core and the Weber set and obtain a characterization of almost positive bicooperative games as bicooperative games such that the core, the Weber set and the selectope coincide. Moreover, an axiomatic characterization of the elements of the selectope is obtained.Bicooperative game Core Weber set Selectope