Monotonic allocation schemes in clan games (Q1812293)

A game \((N, v)\) is a total clan game with clan \(C\in 2^N\setminus\{\emptyset, N\}\) if \(S(v)\) is a clan game with clan \(C\) for every \(S\in{\mathcal P}(C)= \{S\subseteq N: C\subseteq S\}\). The authors characterize this class of games by using monotonicity, veto power of the clan members and a concavity condition. They also show that each core element of a total clan game can be extended to both a population monotonic and a bi-monotonic allocation scheme. In the final section of the paper, they study the nucleolus of a big boss game, a special class of total clan games.