Minimality of a solution update in conflict resolution: An application of revision programming to the von Neumann-Morgenstern approach

• Published in: International journal of intelligent systems Vol. 20; no. 9; pp. 939 - 956
• Main Authors: Pivkina, Inna, Kreinovich, Vladik
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.09.2005; Wiley
• Subjects: Applied sciences; Artificial intelligence; Computer science; control theory; systems; Exact sciences and technology; Learning and adaptive systems; Logical, boolean and switching functions; Theoretical computing; Information system; Conflict resolution; Game theory; NP hard problem
• ISSN: 0884-8173; 1098-111X
• DOI: 10.1002/int.20100

In a 1944 book that started game theory (and the mathematical approach to conflict resolution), von Neumann and Morgenstern proposed the notion of a solution. When the situation changes, the old solution is often no longer a solution, so it needs to be updated. In practical applications, it is usually desirable to keep the solution change “minimal” in some reasonable sense. We show that for a seemingly straightforward formalization of this minimality, checking whether a change is minimal is NP‐hard. We also show that by representing the notion of a solution as a collection of revision rules, we can produce a reasonable notion of minimality for which there exists a feasible algorithm for checking the minimality of the update. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 939–956, 2005.