Convergence of the approximate cores to the aspiration core in partitioning games

The approximate core and the aspiration core are two non-empty solutions for cooperative games that have emerged in order to give an answer to cooperative games with an empty core. Although the approximate core and the aspiration core come from two different ideas, we show that both solutions are related in a very interesting way in partitioning games (or superadditive games). In fact, we prove that the approximate core converges to the aspiration core in partitioning games (or superadditive games).