Balanced Silverman Games on General Discrete Sets

Games are studied in which within certain bounds the player with the larger number wins, but loses if it is too much larger than the other. The games model various bidding or spending situations governed by rules of this nature. Under quite general conditions the games reduce to finite matrix games.

Auteur
Univ. Prof. Dr. Ulrike Leopold-Wildburger, Universitätsprofessor für Wirtschaftsmathematik und Operations Research. Verfasserin zahlreicher Bücher und Artikel in Fachzeitschriften, mehrere best paper und research awards.

Contenu

1. Introduction.- 2. Games with saddle points.- 3. The 2 by 2 games.- 4. Some games which reduce to 2 by 2 when ? ? 1.- 5. Reduction by dominance.- 6. Balanced 3 by 3 games.- 7. Balanced 5 by 5 games.- 8. Reduction of balanced games to odd order.- 9. Reduction of balanced games to even order.- 10. Games with ±1 as central diagonal element.- 11. Further reduction to 2 by 2 when ? = 1.- 12. Explicit solutions for certain classes.- 13. Concluding remarks on irreducibility.- References.