If one player has Word of Command in his hand, and the other player controls Radagast, could player #1 pay for Word of Command, exhaust Radagast even though it's controlled by another player, and then look through his deck for a card? Or since it's the other player's Radagast, would player #2 look through his deck to find a card? Or can the across-the-table-exhaustion even work?

Thanks

That kind of cross-table work isn't allowed. Exhausting a character to pay for cards is considered a cost, and you have to pay for cost with your own resources.

Okay, thanks for that clarification.