| Article ID: | iaor20126352 |
| Volume: | 20 |
| Issue: | 4 |
| Start Page Number: | 743 |
| End Page Number: | 753 |
| Publication Date: | Dec 2012 |
| Journal: | Central European Journal of Operations Research |
| Authors: | Liao Yu-Hsien |
| Keywords: | multiple choice programming |
We extend the reduced games introduced by Moulin (1985) to multi‐choice games, and define related properties of consistency and its converse. Since the unit‐level‐core proposed by Hwang and Liao (2009) violates (weak) converse consistency, we propose to minimally enlarge the unit‐level‐core so as to recover (weak) converse consistency.