Limit Property of a Multi-Choice Value: Comparison with the Fuzzy Value.

Multi-choice games and fuzzy games both deal with the situations where the players have more than two participants levels. Two values have been proposed for the multi-choice games: Hsiao-Raghavan (1993) and Nouweland et al. (1995). The former one depends on an arbitrarily given weight, and Hsia (1995) showed this value is not concerned with Aubin's (1981) fuzzy value for the fuzzy games. The latter one is derived from the permutation ides of the Shapley value. We will show the latter value is consistent with Aubin's value when the number of participation levels is sufficiently large.