A metric for positional games

✍ Scribed by J.Mark Ettinger

• Book ID: 104326777
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 105 KB
• Volume: 230
• Category: Article
• ISSN: 0304-3975
• DOI: 10.1016/s0304-3975(99)00107-3

✦ Synopsis

We deÿne an extended real-valued metric, , for positional games and prove that this class of games is a topological semigroup. We then show that two games are ÿnitely separated i they are path-connected and i two closely related Conway games are equivalent. If two games are at a ÿnite distance then this distance is bounded by the maximum di erence of any two atoms found in the games. We may improve on this estimate when two games have the same form, as given by a form match. Finally, we show that if (G; H ) = ∞ then for all X we have G + X ≡ H + X , a step towards proving cancellation for positional games.